Daily Papers

Human speech exhibits rich and flexible prosodic variations. To address the one-to-many mapping problem from text to prosody in a reasonable and flexible manner, we propose DiffStyleTTS, a multi-speaker acoustic model based on a conditional diffusion module and an improved classifier-free guidance, which hierarchically models speech prosodic features, and controls different prosodic styles to guide prosody prediction. Experiments show that our method outperforms all baselines in naturalness and achieves superior synthesis speed compared to three diffusion-based baselines. Additionally, by adjusting the guiding scale, DiffStyleTTS effectively controls the guidance intensity of the synthetic prosody.

Non-autoregressive text to speech (TTS) models such as FastSpeech can synthesize speech significantly faster than previous autoregressive models with comparable quality. The training of FastSpeech model relies on an autoregressive teacher model for duration prediction (to provide more information as input) and knowledge distillation (to simplify the data distribution in output), which can ease the one-to-many mapping problem (i.e., multiple speech variations correspond to the same text) in TTS. However, FastSpeech has several disadvantages: 1) the teacher-student distillation pipeline is complicated and time-consuming, 2) the duration extracted from the teacher model is not accurate enough, and the target mel-spectrograms distilled from teacher model suffer from information loss due to data simplification, both of which limit the voice quality. In this paper, we propose FastSpeech 2, which addresses the issues in FastSpeech and better solves the one-to-many mapping problem in TTS by 1) directly training the model with ground-truth target instead of the simplified output from teacher, and 2) introducing more variation information of speech (e.g., pitch, energy and more accurate duration) as conditional inputs. Specifically, we extract duration, pitch and energy from speech waveform and directly take them as conditional inputs in training and use predicted values in inference. We further design FastSpeech 2s, which is the first attempt to directly generate speech waveform from text in parallel, enjoying the benefit of fully end-to-end inference. Experimental results show that 1) FastSpeech 2 achieves a 3x training speed-up over FastSpeech, and FastSpeech 2s enjoys even faster inference speed; 2) FastSpeech 2 and 2s outperform FastSpeech in voice quality, and FastSpeech 2 can even surpass autoregressive models. Audio samples are available at https://speechresearch.github.io/fastspeech2/.

Pre-training models have been proved effective for a wide range of natural language processing tasks. Inspired by this, we propose a novel dialogue generation pre-training framework to support various kinds of conversations, including chit-chat, knowledge grounded dialogues, and conversational question answering. In this framework, we adopt flexible attention mechanisms to fully leverage the bi-directional context and the uni-directional characteristic of language generation. We also introduce discrete latent variables to tackle the inherent one-to-many mapping problem in response generation. Two reciprocal tasks of response generation and latent act recognition are designed and carried out simultaneously within a shared network. Comprehensive experiments on three publicly available datasets verify the effectiveness and superiority of the proposed framework.

Although neural end-to-end text-to-speech models can synthesize highly natural speech, there is still room for improvements to its efficiency and naturalness. This paper proposes a non-autoregressive neural text-to-speech model augmented with a variational autoencoder-based residual encoder. This model, called Parallel Tacotron, is highly parallelizable during both training and inference, allowing efficient synthesis on modern parallel hardware. The use of the variational autoencoder relaxes the one-to-many mapping nature of the text-to-speech problem and improves naturalness. To further improve the naturalness, we use lightweight convolutions, which can efficiently capture local contexts, and introduce an iterative spectrogram loss inspired by iterative refinement. Experimental results show that Parallel Tacotron matches a strong autoregressive baseline in subjective evaluations with significantly decreased inference time.

3D panoptic segmentation is a challenging perception task that requires both semantic segmentation and instance segmentation. In this task, we notice that images could provide rich texture, color, and discriminative information, which can complement LiDAR data for evident performance improvement, but their fusion remains a challenging problem. To this end, we propose LCPS, the first LiDAR-Camera Panoptic Segmentation network. In our approach, we conduct LiDAR-Camera fusion in three stages: 1) an Asynchronous Compensation Pixel Alignment (ACPA) module that calibrates the coordinate misalignment caused by asynchronous problems between sensors; 2) a Semantic-Aware Region Alignment (SARA) module that extends the one-to-one point-pixel mapping to one-to-many semantic relations; 3) a Point-to-Voxel feature Propagation (PVP) module that integrates both geometric and semantic fusion information for the entire point cloud. Our fusion strategy improves about 6.9% PQ performance over the LiDAR-only baseline on NuScenes dataset. Extensive quantitative and qualitative experiments further demonstrate the effectiveness of our novel framework. The code will be released at https://github.com/zhangzw12319/lcps.git.

Population-based search has recently emerged as a possible alternative to Reinforcement Learning (RL) for black-box neural architecture search (NAS). It performs well in practice even though it is not theoretically well understood. In particular, whereas traditional population-based search methods such as evolutionary algorithms (EAs) draw much power from crossover operations, it is difficult to take advantage of them in NAS. The main obstacle is believed to be the permutation problem: The mapping between genotype and phenotype in traditional graph representations is many-to-one, leading to a disruptive effect of standard crossover. This paper presents the first theoretical analysis of the behaviors of mutation, crossover and RL in black-box NAS, and proposes a new crossover operator based on the shortest edit path (SEP) in graph space. The SEP crossover is shown theoretically to overcome the permutation problem, and as a result, have a better expected improvement compared to mutation, standard crossover and RL. Further, it empirically outperform these other methods on state-of-the-art NAS benchmarks. The SEP crossover therefore allows taking full advantage of population-based search in NAS, and the underlying theory can serve as a foundation for deeper understanding of black-box NAS methods in general.

Model merging has emerged as an effective approach to combine multiple single-task models into a multitask model. This process typically involves computing a weighted average of the model parameters without any additional training. Existing model-merging methods focus on enhancing average task accuracy. However, interference and conflicts between the objectives of different tasks can lead to trade-offs during the merging process. In real-world applications, a set of solutions with various trade-offs can be more informative, helping practitioners make decisions based on diverse preferences. In this paper, we introduce a novel and low-compute algorithm, Model Merging with Amortized Pareto Front (MAP). MAP efficiently identifies a Pareto set of scaling coefficients for merging multiple models, reflecting the trade-offs involved. It amortizes the substantial computational cost of evaluations needed to estimate the Pareto front by using quadratic approximation surrogate models derived from a pre-selected set of scaling coefficients. Experimental results on vision and natural language processing tasks demonstrate that MAP can accurately identify the Pareto front, providing practitioners with flexible solutions to balance competing task objectives. We also introduce Bayesian MAP for scenarios with a relatively low number of tasks and Nested MAP for situations with a high number of tasks, further reducing the computational cost of evaluation.

The Travelling Salesman Problem (TSP) remains a fundamental challenge in combinatorial optimization, inspiring diverse algorithmic strategies. This paper revisits the "heatmap + Monte Carlo Tree Search (MCTS)" paradigm that has recently gained traction for learning-based TSP solutions. Within this framework, heatmaps encode the likelihood of edges forming part of the optimal tour, and MCTS refines this probabilistic guidance to discover optimal solutions. Contemporary approaches have predominantly emphasized the refinement of heatmap generation through sophisticated learning models, inadvertently sidelining the critical role of MCTS. Our extensive empirical analysis reveals two pivotal insights: 1) The configuration of MCTS strategies profoundly influences the solution quality, demanding meticulous tuning to leverage their full potential; 2) Our findings demonstrate that a rudimentary and parameter-free heatmap, derived from the intrinsic k-nearest nature of TSP, can rival or even surpass the performance of complicated heatmaps, with strong generalizability across various scales. Empirical evaluations across various TSP scales underscore the efficacy of our approach, achieving competitive results. These observations challenge the prevailing focus on heatmap sophistication, advocating a reevaluation of the paradigm to harness both components synergistically. Our code is available at: https://github.com/LOGO-CUHKSZ/rethink_mcts_tsp.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

Resource scheduling and allocation is a critical component of many high impact systems ranging from congestion control to cloud computing. Finding more optimal solutions to these problems often has significant impact on resource and time savings, reducing device wear-and-tear, and even potentially improving carbon emissions. In this paper, we focus on a specific instance of a scheduling problem, namely the memory mapping problem that occurs during compilation of machine learning programs: That is, mapping tensors to different memory layers to optimize execution time. We introduce an approach for solving the memory mapping problem using Reinforcement Learning. RL is a solution paradigm well-suited for sequential decision making problems that are amenable to planning, and combinatorial search spaces with high-dimensional data inputs. We formulate the problem as a single-player game, which we call the mallocGame, such that high-reward trajectories of the game correspond to efficient memory mappings on the target hardware. We also introduce a Reinforcement Learning agent, mallocMuZero, and show that it is capable of playing this game to discover new and improved memory mapping solutions that lead to faster execution times on real ML workloads on ML accelerators. We compare the performance of mallocMuZero to the default solver used by the Accelerated Linear Algebra (XLA) compiler on a benchmark of realistic ML workloads. In addition, we show that mallocMuZero is capable of improving the execution time of the recently published AlphaTensor matrix multiplication model.

We study the problem of designing models for machine learning tasks defined on sets. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics poczos13aistats, to anomaly detection in piezometer data of embankment dams Jung15Exploration, to cosmology Ntampaka16Dynamical,Ravanbakhsh16ICML1. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

Maps are fundamental medium to visualize and represent the real word in a simple and 16 philosophical way. The emergence of the 3rd wave information has made a proportion of maps are available to be generated ubiquitously, which would significantly enrich the dimensions and perspectives to understand the characteristics of the real world. However, a majority of map dataset have never been discovered, acquired and effectively used, and the map data used in many applications might not be completely fitted for the authentic demands of these applications. This challenge is emerged due to the lack of numerous well-labelled benchmark datasets for implementing the deep learning approaches into identifying complicated map content. Thus, we develop a large-scale benchmark dataset that includes well-labelled dataset for map text annotation recognition, map scene classification, map super-resolution reconstruction, and map style transferring. Furthermore, these well-labelled datasets would facilitate the state-of-the-art machine intelligence technologies to conduct map feature detection, map pattern recognition and map content retrieval. We hope our efforts would be useful for AI-enhanced cartographical applications.

In this article, we study the parameterized complexity of the Set Cover problem restricted to semi-ladder-free hypergraphs, a class defined by Fabianski et al. [Proceedings of STACS 2019]. We observe that two algorithms introduced by Langerman and Morin [Discrete & Computational Geometry 2005] in the context of geometric covering problems can be adapted to this setting, yielding simple FPT and kernelization algorithms for Set Cover in semi-ladder-free hypergraphs. We complement our algorithmic results with a compression lower bound for the problem, which proves the tightness of our kernelization under standard complexity-theoretic assumptions.

Large datasets have become commonplace in NLP research. However, the increased emphasis on data quantity has made it challenging to assess the quality of data. We introduce Data Maps---a model-based tool to characterize and diagnose datasets. We leverage a largely ignored source of information: the behavior of the model on individual instances during training (training dynamics) for building data maps. This yields two intuitive measures for each example---the model's confidence in the true class, and the variability of this confidence across epochs---obtained in a single run of training. Experiments across four datasets show that these model-dependent measures reveal three distinct regions in the data map, each with pronounced characteristics. First, our data maps show the presence of "ambiguous" regions with respect to the model, which contribute the most towards out-of-distribution generalization. Second, the most populous regions in the data are "easy to learn" for the model, and play an important role in model optimization. Finally, data maps uncover a region with instances that the model finds "hard to learn"; these often correspond to labeling errors. Our results indicate that a shift in focus from quantity to quality of data could lead to robust models and improved out-of-distribution generalization.

Maximizing a monotone submodular function under cardinality constraint k is a core problem in machine learning and database with many basic applications, including video and data summarization, recommendation systems, feature extraction, exemplar clustering, and coverage problems. We study this classic problem in the fully dynamic model where a stream of insertions and deletions of elements of an underlying ground set is given and the goal is to maintain an approximate solution using a fast update time. A recent paper at NeurIPS'20 by Lattanzi, Mitrovic, Norouzi{-}Fard, Tarnawski, Zadimoghaddam claims to obtain a dynamic algorithm for this problem with a 1{2} -epsilon approximation ratio and a query complexity bounded by poly(log(n),log(k),epsilon^{-1}). However, as we explain in this paper, the analysis has some important gaps. Having a dynamic algorithm for the problem with polylogarithmic update time is even more important in light of a recent result by Chen and Peng at STOC'22 who show a matching lower bound for the problem -- any randomized algorithm with a 1{2}+epsilon approximation ratio must have an amortized query complexity that is polynomial in n. In this paper, we develop a simpler algorithm for the problem that maintains a (1{2}-epsilon)-approximate solution for submodular maximization under cardinality constraint k using a polylogarithmic amortized update time.

Many fields use search algorithms, which automatically explore a search space to find high-performing solutions: chemists search through the space of molecules to discover new drugs; engineers search for stronger, cheaper, safer designs, scientists search for models that best explain data, etc. The goal of search algorithms has traditionally been to return the single highest-performing solution in a search space. Here we describe a new, fundamentally different type of algorithm that is more useful because it provides a holistic view of how high-performing solutions are distributed throughout a search space. It creates a map of high-performing solutions at each point in a space defined by dimensions of variation that a user gets to choose. This Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) algorithm illuminates search spaces, allowing researchers to understand how interesting attributes of solutions combine to affect performance, either positively or, equally of interest, negatively. For example, a drug company may wish to understand how performance changes as the size of molecules and their cost-to-produce vary. MAP-Elites produces a large diversity of high-performing, yet qualitatively different solutions, which can be more helpful than a single, high-performing solution. Interestingly, because MAP-Elites explores more of the search space, it also tends to find a better overall solution than state-of-the-art search algorithms. We demonstrate the benefits of this new algorithm in three different problem domains ranging from producing modular neural networks to designing simulated and real soft robots. Because MAP- Elites (1) illuminates the relationship between performance and dimensions of interest in solutions, (2) returns a set of high-performing, yet diverse solutions, and (3) improves finding a single, best solution, it will advance science and engineering.

We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., ell^1 or ell^2, such functionals provide more flexibility and allow using auxiliary information, such as class labels, to construct the required transport map. Existing methods for general costs are discrete and have limitations in practice, i.e. they do not provide an out-of-sample estimation. We address the challenge of designing a continuous OT approach for general costs that generalizes to new data points in high-dimensional spaces, such as images. Additionally, we provide the theoretical error analysis for our recovered transport plans. As an application, we construct a cost functional to map data distributions while preserving the class-wise structure.

Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose various structural conditions on the clustering schemes, under the general heading of functoriality. Functoriality refers to the idea that one should be able to compare the results of clustering algorithms as one varies the data set, for example by adding points or by applying functions to it. We show that within this framework, one can prove a theorems analogous to one of J. Kleinberg, in which for example one obtains an existence and uniqueness theorem instead of a non-existence result. We obtain a full classification of all clustering schemes satisfying a condition we refer to as excisiveness. The classification can be changed by varying the notion of maps of finite metric spaces. The conditions occur naturally when one considers clustering as the statistical version of the geometric notion of connected components. By varying the degree of functoriality that one requires from the schemes it is possible to construct richer families of clustering schemes that exhibit sensitivity to density.

This systematic review explores the application of Large Language Models (LLMs) in Combinatorial Optimization (CO). We report our findings using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. We conduct a literature search via Scopus and Google Scholar, examining over 2,000 publications. We assess publications against four inclusion and four exclusion criteria related to their language, research focus, publication year, and type. Eventually, we select 103 studies. We classify these studies into semantic categories and topics to provide a comprehensive overview of the field, including the tasks performed by LLMs, the architectures of LLMs, the existing datasets specifically designed for evaluating LLMs in CO, and the field of application. Finally, we identify future directions for leveraging LLMs in this field.

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.

A subgraph is constructed by using a subset of vertices and edges of a given graph. There exist many graph properties that are hereditary for subgraphs. Hence, researchers from different communities have paid a great deal of attention in studying numerous subgraph problems, on top of the ordinary graph problems. Many algorithms are proposed in studying subgraph problems, where one common approach is by extracting the patterns and structures of a given graph. Due to the complex structures of certain types of graphs and to improve overall performances of the existing frameworks, machine learning techniques have recently been employed in dealing with various subgraph problems. In this article, we present a comprehensive review on five well known subgraph problems that have been tackled by using machine learning methods. They are subgraph isomorphism (both counting and matching), maximum common subgraph, community detection and community search problems. We provide an outline of each proposed method, and examine its designs and performances. We also explore non-learning-based algorithms for each problem and a brief discussion is given. We then suggest some promising research directions in this area, hoping that relevant subgraph problems can be tackled by using a similar strategy. Since there is a huge growth in employing machine learning techniques in recent years, we believe that this survey will serve as a good reference point to relevant research communities.

A heuristic extending the Squarified Treemap technique for the representation of hierarchical information as treemaps is presented. The original technique gives high quality treemap views, since items are laid out with rectangles that approximate squares, allowing easy comparison and selection operations. New key steps, with a low computational impact, have been introduced to yield treemaps with even better aspect ratios and higher homogeneity among items.

The Airbnb search system grapples with many unique challenges as it continues to evolve. We oversee a marketplace that is nuanced by geography, diversity of homes, and guests with a variety of preferences. Crafting an efficient search system that can accommodate diverse guest needs, while showcasing relevant homes lies at the heart of Airbnb's success. Airbnb search has many challenges that parallel other recommendation and search systems but it has a unique information retrieval problem, upstream of ranking, called location retrieval. It requires defining a topological map area that is relevant to the searched query for homes listing retrieval. The purpose of this paper is to demonstrate the methodology, challenges, and impact of building a machine learning based location retrieval product from the ground up. Despite the lack of suitable, prevalent machine learning based approaches, we tackle cold start, generalization, differentiation and algorithmic bias. We detail the efficacy of heuristics, statistics, machine learning, and reinforcement learning approaches to solve these challenges, particularly for systems that are often unexplored by current literature.

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies can be achieved by reducing the input space if a minimal loss of information can be achieved. Clustering algorithms, in general, face two common problems: 1) these converge to different settings with different initial conditions and; 2) the number of clusters has to be arbitrarily decided beforehand. This problem has become critical in the realm of big data. Recently, clustering algorithms have emerged which can speedup computations using parallel processing over the grid but face the aforementioned problems. Goals: Our goals are to find methods to cluster data which: 1) guarantee convergence to the same settings irrespective of the initial conditions; 2) eliminate the need to establish the number of clusters beforehand, and 3) can be applied to cluster large datasets. Methods: We introduce a method that combines probabilistic and combinatorial clustering methods to produce repeatable and compact clusters that are not sensitive to initial conditions. This method harnesses the power of k-means (a combinatorial clustering method) to cluster/partition very large dimensional datasets and uses the Gaussian Mixture Model (a probabilistic clustering method) to validate the k-means partitions. Results: We show that this method produces very compact clusters that are not sensitive to initial conditions. This method can be used to identify the most 'separable' set in a dataset which increases the 'clusterability' of a dataset. This method also eliminates the need to specify the number of clusters in advance.

A vector database is used to store high-dimensional data that cannot be characterized by traditional DBMS. Although there are not many articles describing existing or introducing new vector database architectures, the approximate nearest neighbor search problem behind vector databases has been studied for a long time, and considerable related algorithmic articles can be found in the literature. This article attempts to comprehensively review relevant algorithms to provide a general understanding of this booming research area. The basis of our framework categorises these studies by the approach of solving ANNS problem, respectively hash-based, tree-based, graph-based and quantization-based approaches. Then we present an overview of existing challenges for vector databases. Lastly, we sketch how vector databases can be combined with large language models and provide new possibilities.

In this paper, we propose a new mixed-integer linear programming (MILP) model ontology and a novel constraint typology of MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life scheduling, routing, planning, resource allocation, and timetabling optimization problems providing optimized business solutions for industry sectors such as manufacturing, agriculture, defence, healthcare, medicine, energy, finance, and transportation. Despite the numerous real-life Combinatorial Optimization Problems found and solved and millions yet to be discovered and formulated, the number of types of constraints (the building blocks of a MILP) is relatively small. In the search for a suitable machine-readable knowledge representation structure for MILPs, we propose an optimization modelling tree built based upon an MILP model ontology that can be used as a guide for automated systems to elicit an MILP model from end-users on their combinatorial business optimization problems. Our ultimate aim is to develop a machine-readable knowledge representation for MILP that allows us to map an end-user's natural language description of the business optimization problem to an MILP formal specification as a first step towards automated mathematical modelling.

Data scientists today search large data lakes to discover and integrate datasets. In order to bring together disparate data sources, dataset discovery methods rely on some form of schema matching: the process of establishing correspondences between datasets. Traditionally, schema matching has been used to find matching pairs of columns between a source and a target schema. However, the use of schema matching in dataset discovery methods differs from its original use. Nowadays schema matching serves as a building block for indicating and ranking inter-dataset relationships. Surprisingly, although a discovery method's success relies highly on the quality of the underlying matching algorithms, the latest discovery methods employ existing schema matching algorithms in an ad-hoc fashion due to the lack of openly-available datasets with ground truth, reference method implementations, and evaluation metrics. In this paper, we aim to rectify the problem of evaluating the effectiveness and efficiency of schema matching methods for the specific needs of dataset discovery. To this end, we propose Valentine, an extensible open-source experiment suite to execute and organize large-scale automated matching experiments on tabular data. Valentine includes implementations of seminal schema matching methods that we either implemented from scratch (due to absence of open source code) or imported from open repositories. The contributions of Valentine are: i) the definition of four schema matching scenarios as encountered in dataset discovery methods, ii) a principled dataset fabrication process tailored to the scope of dataset discovery methods and iii) the most comprehensive evaluation of schema matching techniques to date, offering insight on the strengths and weaknesses of existing techniques, that can serve as a guide for employing schema matching in future dataset discovery methods.

Knowledge graph embedding refers to projecting entities and relations in knowledge graph into continuous vector spaces. State-of-the-art methods, such as TransE, TransH, and TransR build embeddings by treating relation as translation from head entity to tail entity. However, previous models can not deal with reflexive/one-to-many/many-to-one/many-to-many relations properly, or lack of scalability and efficiency. Thus, we propose a novel method, flexible translation, named TransF, to address the above issues. TransF regards relation as translation between head entity vector and tail entity vector with flexible magnitude. To evaluate the proposed model, we conduct link prediction and triple classification on benchmark datasets. Experimental results show that our method remarkably improve the performance compared with several state-of-the-art baselines.

Any optimization algorithm programming interface can be seen as a black-box function with additional free parameters. In this spirit, simulated annealing (SA) can be implemented in pseudo-code within the dimensions of a single slide with free parameters relating to the annealing schedule. Such an implementation, however, necessarily neglects much of the structure necessary to take advantage of advances in computing resources and algorithmic breakthroughs. Simulated annealing is often introduced in myriad disciplines, from discrete examples like the Traveling Salesman Problem (TSP) to molecular cluster potential energy exploration or even explorations of a protein's configurational space. Theoretical guarantees also demand a stricter structure in terms of statistical quantities, which cannot simply be left to the user. We will introduce several standard paradigms and demonstrate how these can be "lifted" into a unified framework using object-oriented programming in Python. We demonstrate how clean, interoperable, reproducible programming libraries can be used to access and rapidly iterate on variants of Simulated Annealing in a manner which can be extended to serve as a best practices blueprint or design pattern for a data-driven optimization library.

A fundamental problem in combinatorial optimization is identifying equivalent formulations, which can lead to more efficient solution strategies and deeper insights into a problem's computational complexity. The need to automatically identify equivalence between problem formulations has grown as optimization copilots--systems that generate problem formulations from natural language descriptions--have proliferated. However, existing approaches to checking formulation equivalence lack grounding, relying on simple heuristics which are insufficient for rigorous validation. Inspired by Karp reductions, in this work we introduce quasi-Karp equivalence, a formal criterion for determining when two optimization formulations are equivalent based on the existence of a mapping between their decision variables. We propose EquivaMap, a framework that leverages large language models to automatically discover such mappings, enabling scalable and reliable equivalence verification. To evaluate our approach, we construct the first open-source dataset of equivalent optimization formulations, generated by applying transformations such as adding slack variables or valid inequalities to existing formulations. Empirically, EquivaMap significantly outperforms existing methods, achieving substantial improvements in correctly identifying formulation equivalence.

In this paper, we explore the potential for quantum annealing to solve realistic routing problems. We focus on two NP-Hard problems, including the Traveling Salesman Problem with Time Windows and the Capacitated Vehicle Routing Problem with Time Windows. We utilize D-Wave's Quantum Annealer and Constrained Quadratic Model (CQM) solver within a hybrid framework to solve these problems. We demonstrate that while the CQM solver effectively minimizes route costs, it struggles to maintain time window feasibility as the problem size increases. To address this limitation, we implement a heuristic method that fixes infeasible solutions through a series of swapping operations. Testing on benchmark instances shows our method achieves promising results with an average optimality gap of 3.86%.

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such descriptors is {\em persistent homology}, which encodes the change in shape as a filtration parameter changes; a typical parameter is the feature scale. For many data sets, it is useful to simultaneously vary multiple filtration parameters, for example feature scale and density. While the theoretical properties of single parameter persistent homology are well understood, less is known about the multiparameter case. In particular, a central question is the problem of representing multiparameter persistent homology by elements of a vector space for integration with standard machine learning algorithms. Existing approaches to this problem either ignore most of the multiparameter information to reduce to the one-parameter case or are heuristic and potentially unstable in the face of noise. In this article, we introduce a new general representation framework that leverages recent results on {\em decompositions} of multiparameter persistent homology. This framework is rich in information, fast to compute, and encompasses previous approaches. Moreover, we establish theoretical stability guarantees under this framework as well as efficient algorithms for practical computation, making this framework an applicable and versatile tool for analyzing geometric and point cloud data. We validate our stability results and algorithms with numerical experiments that demonstrate statistical convergence, prediction accuracy, and fast running times on several real data sets.

Large Language Models (LLMs) struggle to directly generate correct plans for complex multi-constraint planning problems, even with self-verification and self-critique. For example, a U.S. domestic travel planning benchmark TravelPlanner was proposed in Xie et al. (2024), where the best LLM OpenAI o1-preview can only find viable travel plans with a 10% success rate given all needed information. In this work, we tackle this by proposing an LLM-based planning framework that formalizes and solves complex multi-constraint planning problems as constrained satisfiability problems, which are further consumed by sound and complete satisfiability solvers. We start with TravelPlanner as the primary use case and show that our framework achieves a success rate of 93.9% and is effective with diverse paraphrased prompts. More importantly, our framework has strong zero-shot generalizability, successfully handling unseen constraints in our newly created unseen international travel dataset and generalizing well to new fundamentally different domains. Moreover, when user input queries are infeasible, our framework can identify the unsatisfiable core, provide failure reasons, and offers personalized modification suggestions. We show that our framework can modify and solve for an average of 81.6% and 91.7% unsatisfiable queries from two datasets and prove with ablations that all key components of our framework are effective and necessary. Project page: https://sites.google.com/view/llm-rwplanning.

The exponential growth of scientific literature requires effective management and extraction of valuable insights. While existing scientific search engines excel at delivering search results based on relational databases, they often neglect the analysis of collaborations between scientific entities and the evolution of ideas, as well as the in-depth analysis of content within scientific publications. The representation of heterogeneous graphs and the effective measurement, analysis, and mining of such graphs pose significant challenges. To address these challenges, we present AceMap, an academic system designed for knowledge discovery through academic graph. We present advanced database construction techniques to build the comprehensive AceMap database with large-scale academic entities that contain rich visual, textual, and numerical information. AceMap also employs innovative visualization, quantification, and analysis methods to explore associations and logical relationships among academic entities. AceMap introduces large-scale academic network visualization techniques centered on nebular graphs, providing a comprehensive view of academic networks from multiple perspectives. In addition, AceMap proposes a unified metric based on structural entropy to quantitatively measure the knowledge content of different academic entities. Moreover, AceMap provides advanced analysis capabilities, including tracing the evolution of academic ideas through citation relationships and concept co-occurrence, and generating concise summaries informed by this evolutionary process. In addition, AceMap uses machine reading methods to generate potential new ideas at the intersection of different fields. Exploring the integration of large language models and knowledge graphs is a promising direction for future research in idea evolution. Please visit https://www.acemap.info for further exploration.

Enterprises often own large collections of structured data in the form of large databases or an enterprise data lake. Such data collections come with limited metadata and strict access policies that could limit access to the data contents and, therefore, limit the application of classic retrieval and analysis solutions. As a result, there is a need for solutions that can effectively utilize the available metadata. In this paper, we study the problem of matching table metadata to a business glossary containing data labels and descriptions. The resulting matching enables the use of an available or curated business glossary for retrieval and analysis without or before requesting access to the data contents. One solution to this problem is to use manually-defined rules or similarity measures on column names and glossary descriptions (or their vector embeddings) to find the closest match. However, such approaches need to be tuned through manual labeling and cannot handle many business glossaries that contain a combination of simple as well as complex and long descriptions. In this work, we leverage the power of large language models (LLMs) to design generic matching methods that do not require manual tuning and can identify complex relations between column names and glossaries. We propose methods that utilize LLMs in two ways: a) by generating additional context for column names that can aid with matching b) by using LLMs to directly infer if there is a relation between column names and glossary descriptions. Our preliminary experimental results show the effectiveness of our proposed methods.

We study the set of networks, which consist of sources, sinks and neutral points, bijective to the permutations. The set of directed edges, which characterizes a network, is constructed from a polyomino or a Rothe diagram of a permutation through a Dyck tiling on a ribbon. We introduce a new combinatorial object similar to a tree-like tableau, which we call a forest. A forest is shown to give a permutation, and be bijective to a network corresponding to the inverse of the permutation. We show that the poset of networks is a finite graded lattice and admits an EL-labeling. By use of this EL-labeling, we show the lattice is supersolvable and compute the M\"obius function of an interval of the poset.

Sparse roadmaps are important to compactly represent state spaces, to determine problems to be infeasible and to terminate in finite time. However, sparse roadmaps do not scale well to high-dimensional planning problems. In prior work, we showed improved planning performance on high-dimensional planning problems by using multilevel abstractions to simplify state spaces. In this work, we generalize sparse roadmaps to multilevel abstractions by developing a novel algorithm, the sparse multilevel roadmap planner (SMLR). To this end, we represent multilevel abstractions using the language of fiber bundles, and generalize sparse roadmap planners by using the concept of restriction sampling with visibility regions. We argue SMLR to be probabilistically complete and asymptotically near-optimal by inheritance from sparse roadmap planners. In evaluations, we outperform sparse roadmap planners on challenging planning problems, in particular problems which are high-dimensional, contain narrow passages or are infeasible. We thereby demonstrate sparse multilevel roadmaps as an efficient tool for feasible and infeasible high-dimensional planning problems.

With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics at the high-school, undergraduate, and graduate level, there are far fewer resources available that align with the level of difficulty and open endedness encountered by professional mathematicians working on open problems. To address this, we introduce a new collection of datasets, the Algebraic Combinatorics Dataset Repository (ACD Repo), representing either foundational results or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. Further differentiating our dataset collection is the fact that it aims at the conjecturing process. Each dataset includes an open-ended research-level question and a large collection of examples (up to 10M in some cases) from which conjectures should be generated. We describe all nine datasets, the different ways machine learning models can be applied to them (e.g., training with narrow models followed by interpretability analysis or program synthesis with LLMs), and discuss some of the challenges involved in designing datasets like these.

Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.

Optimal transport (OT) theory focuses, among all maps T:R^drightarrow R^d that can morph a probability measure onto another, on those that are the ``thriftiest'', i.e. such that the averaged cost c(x, T(x)) between x and its image T(x) be as small as possible. Many computational approaches have been proposed to estimate such Monge maps when c is the ell_2^2 distance, e.g., using entropic maps [Pooladian'22], or neural networks [Makkuva'20, Korotin'20]. We propose a new model for transport maps, built on a family of translation invariant costs c(x, y):=h(x-y), where h:=1{2}|cdot|_2^2+tau and tau is a regularizer. We propose a generalization of the entropic map suitable for h, and highlight a surprising link tying it with the Bregman centroids of the divergence D_h generated by h, and the proximal operator of tau. We show that choosing a sparsity-inducing norm for tau results in maps that apply Occam's razor to transport, in the sense that the displacement vectors Delta(x):= T(x)-x they induce are sparse, with a sparsity pattern that varies depending on x. We showcase the ability of our method to estimate meaningful OT maps for high-dimensional single-cell transcription data, in the 34000-d space of gene counts for cells, without using dimensionality reduction, thus retaining the ability to interpret all displacements at the gene level.

Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is accuracy and not the interpretability of the group assignments. This has spurred a recent line of work on explainable machine learning for clustering. In this paper we focus on the cluster description problem where, given a dataset and its partition into clusters, the task is to explain the clusters. We introduce a new approach to explain clusters by constructing polyhedra around each cluster while minimizing either the complexity of the resulting polyhedra or the number of features used in the description. We formulate the cluster description problem as an integer program and present a column generation approach to search over an exponential number of candidate half-spaces that can be used to build the polyhedra. To deal with large datasets, we introduce a novel grouping scheme that first forms smaller groups of data points and then builds the polyhedra around the grouped data, a strategy which out-performs simply sub-sampling data. Compared to state of the art cluster description algorithms, our approach is able to achieve competitive interpretability with improved description accuracy.

With the explosive influence caused by the success of large language models (LLM) like ChatGPT and GPT-4, there has been an extensive amount of recent work showing that foundation models can be used to solve a large variety of tasks. However, there is very limited work that shares insights on multi-agent planning. Multi-agent planning is different from other domains by combining the difficulty of multi-agent coordination and planning, and making it hard to leverage external tools to facilitate the reasoning needed. In this paper, we focus on the problem of multi-agent path finding (MAPF), which is also known as multi-robot route planning, and study the performance of solving MAPF with LLMs. We first show the motivating success on an empty room map without obstacles, then the failure to plan on the harder room map and maze map of the standard MAPF benchmark. We present our position on why directly solving MAPF with LLMs has not been successful yet, and we use various experiments to support our hypothesis. Based on our results, we discussed how researchers with different backgrounds could help with this problem from different perspectives.

Many organizations rely on data from government and third-party sources, and those sources rarely follow the same data formatting. This introduces challenges in integrating data from multiple sources or aligning external sources with internal databases. Commercial database systems do not offer adequate support for integrating data from heterogeneous sources, and manual integration is both time-consuming and inefficient. State-of-the-art data integration approaches that rely on similarity functions and textual transformations often fail to handle challenging cases where multiple mappings are required, or the mappings go beyond simple textual transformations. In this paper, we study the potentials of deep neural models for transforming tables for joinability. In particular, we cast the problem as a prediction task and develop a framework that leverages large deep-learning language models to transform tabular data from a source formatting to a desired target representation. Our framework can efficiently learn the patterns for mapping a source formatting into an expected target using just a few examples, which can then be used for tasks such as table joining, filling in missing values, and error detection. Compared to state-of-the-art mapping and joining approaches, our framework delivers noticeably more accurate and scalable performance on both real-world and synthetic datasets. Our experimental evaluation also shows that the performance of the proposed framework using our fine-tuned model is at par or better than large language models such as GPT-3, despite the significant difference in size, and that using large language models within our framework improves their performance.

In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

Twenty-seven years ago, E. Freuder highlighted that "Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it". Nowadays, CP users have great modeling tools available (like Minizinc and CPMpy), allowing them to formulate the problem and then let a solver do the rest of the job, getting closer to the stated goal. However, this still requires the CP user to know the formalism and respect it. Another significant challenge lies in the expertise required to effectively model combinatorial problems. All this limits the wider adoption of CP. In this position paper, we investigate a possible approach to leverage pre-trained Large Language Models to extract models from textual problem descriptions. More specifically, we take inspiration from the Natural Language Processing for Optimization (NL4OPT) challenge and present early results with a decomposition-based prompting approach to GPT Models.

Traditional similarity-based schema matching methods are incapable of resolving semantic ambiguities and conflicts in domain-specific complex mapping scenarios due to missing commonsense and domain-specific knowledge. The hallucination problem of large language models (LLMs) also makes it challenging for LLM-based schema matching to address the above issues. Therefore, we propose a Knowledge Graph-based Retrieval-Augmented Generation model for Schema Matching, referred to as the KG-RAG4SM. In particular, KG-RAG4SM introduces novel vector-based, graph traversal-based, and query-based graph retrievals, as well as a hybrid approach and ranking schemes that identify the most relevant subgraphs from external large knowledge graphs (KGs). We showcase that KG-based retrieval-augmented LLMs are capable of generating more accurate results for complex matching cases without any re-training. Our experimental results show that KG-RAG4SM outperforms the LLM-based state-of-the-art (SOTA) methods (e.g., Jellyfish-8B) by 35.89% and 30.50% in terms of precision and F1 score on the MIMIC dataset, respectively; KG-RAG4SM with GPT-4o-mini outperforms the pre-trained language model (PLM)-based SOTA methods (e.g., SMAT) by 69.20% and 21.97% in terms of precision and F1 score on the Synthea dataset, respectively. The results also demonstrate that our approach is more efficient in end-to-end schema matching, and scales to retrieve from large KGs. Our case studies on the dataset from the real-world schema matching scenario exhibit that the hallucination problem of LLMs for schema matching is well mitigated by our solution.

Foundation models, particularly those that incorporate Transformer architectures, have demonstrated exceptional performance in domains such as natural language processing and image processing. Adapting these models to structured data, like tables, however, introduces significant challenges. These difficulties are even more pronounced when addressing multi-table data linked via foreign key, which is prevalent in the enterprise realm and crucial for empowering business use cases. Despite its substantial impact, research focusing on such linked business tables within enterprise settings remains a significantly important yet underexplored domain. To address this, we introduce a curated dataset sourced from an Enterprise Resource Planning (ERP) system, featuring extensive linked tables. This dataset is specifically designed to support research endeavors in table representation learning. By providing access to authentic enterprise data, our goal is to potentially enhance the effectiveness and applicability of models for real-world business contexts.

We study the impact on mechanisms for facility location of moving from one dimension to two (or more) dimensions and Euclidean or Manhattan distances. We consider three fundamental axiomatic properties: anonymity which is a basic fairness property, Pareto optimality which is one of the most important efficiency properties, and strategy proofness which ensures agents do not have an incentive to mis-report. We also consider how well such mechanisms can approximate the optimal welfare. Our results are somewhat negative. Moving from one dimension to two (or more) dimensions often makes these axiomatic properties more difficult to achieve. For example, with two facilities in Euclidean space or with just a single facility in Manhattan space, no mechanism is anonymous, Pareto optimal and strategy proof. By contrast, mechanisms on the line exist with all three properties.We also show that approximation ratios may increase when moving to two (or more) dimensions. All our impossibility results are minimal. If we drop one of the three axioms (anonymity, Pareto optimality or strategy proofness) multiple mechanisms satisfy the other two axioms.

Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space. Although the multiparameter PH (MPH) of data that is filtered by several quantities of interest encodes much richer information than its one-parameter counterpart, the scarceness of stability results for MPH descriptors has so far limited the available options for the stable vectorization of MPH. In this paper, we aim to bring together the best of both worlds by showing how the interpretation of signed barcodes -- a recent family of MPH descriptors -- as signed measures leads to natural extensions of vectorization strategies from one parameter to multiple parameters. The resulting feature vectors are easy to define and to compute, and provably stable. While, as a proof of concept, we focus on simple choices of signed barcodes and vectorizations, we already see notable performance improvements when comparing our feature vectors to state-of-the-art topology-based methods on various types of data.

The goal of product mapping is to decide, whether two listings from two different e-shops describe the same products. Existing datasets of matching and non-matching pairs of products, however, often suffer from incomplete product information or contain only very distant non-matching products. Therefore, while predictive models trained on these datasets achieve good results on them, in practice, they are unusable as they cannot distinguish very similar but non-matching pairs of products. This paper introduces two new datasets for product mapping: ProMapCz consisting of 1,495 Czech product pairs and ProMapEn consisting of 1,555 English product pairs of matching and non-matching products manually scraped from two pairs of e-shops. The datasets contain both images and textual descriptions of the products, including their specifications, making them one of the most complete datasets for product mapping. Additionally, the non-matching products were selected in two phases, creating two types of non-matches -- close non-matches and medium non-matches. Even the medium non-matches are pairs of products that are much more similar than non-matches in other datasets -- for example, they still need to have the same brand and similar name and price. After simple data preprocessing, several machine learning algorithms were trained on these and two the other datasets to demonstrate the complexity and completeness of ProMap datasets. ProMap datasets are presented as a golden standard for further research of product mapping filling the gaps in existing ones.

The problem of designing NLP solvers for math word problems (MWP) has seen sustained research activity and steady gains in the test accuracy. Since existing solvers achieve high performance on the benchmark datasets for elementary level MWPs containing one-unknown arithmetic word problems, such problems are often considered "solved" with the bulk of research attention moving to more complex MWPs. In this paper, we restrict our attention to English MWPs taught in grades four and lower. We provide strong evidence that the existing MWP solvers rely on shallow heuristics to achieve high performance on the benchmark datasets. To this end, we show that MWP solvers that do not have access to the question asked in the MWP can still solve a large fraction of MWPs. Similarly, models that treat MWPs as bag-of-words can also achieve surprisingly high accuracy. Further, we introduce a challenge dataset, SVAMP, created by applying carefully chosen variations over examples sampled from existing datasets. The best accuracy achieved by state-of-the-art models is substantially lower on SVAMP, thus showing that much remains to be done even for the simplest of the MWPs.

In this note we establish a 1-to-1 correspondence between the class of generalized quadrangles with ovoids and the class of balanced incomplete block designs that posses a non-triangular local resolution system and have the appropriate parameters. We present a non-triangular local resolution system for a difference family BIBD construction of Sprott.

Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single real-valued function (the one-parameter setting), there is a canonical choice of descriptor for persistent homology: the barcode. The operation mapping a real-valued function to its barcode is differentiable almost everywhere, and the convergence of gradient descent for losses using barcodes is relatively well understood. When optimizing a vector-valued function (the multiparameter setting), there is no unique choice of descriptor for multiparameter persistent homology, and many distinct descriptors have been proposed. This calls for the development of a general framework for differentiability and optimization that applies to a wide range of multiparameter homological descriptors. In this article, we develop such a framework and show that it encompasses well-known descriptors of different flavors, such as signed barcodes and the multiparameter persistence landscape. We complement the theory with numerical experiments supporting the idea that optimizing multiparameter homological descriptors can lead to improved performances compared to optimizing one-parameter descriptors, even when using the simplest and most efficiently computable multiparameter descriptors.

The k-Coloring problem on hereditary graph classes has been a deeply researched problem over the last decade. A hereditary graph class is characterized by a (possibly infinite) list of minimal forbidden induced subgraphs. We say that a graph is (H_1,H_2,ldots)-free if it does not contain any of H_1,H_2,ldots as induced subgraphs. The complexity landscape of the problem remains unclear even when restricting to the case k=4 and classes defined by a few forbidden induced subgraphs. While the case of only one forbidden induced subgraph has been completely resolved lately, the complexity when considering two forbidden induced subgraphs still has a couple of unknown cases. In particular, 4-Coloring on (P_6,C_3)-free graphs is polynomial while it is NP-hard on (P_{22},C_3)-free graphs. We provide a reduction showing NP-completeness of 4-Coloring on (P_t,C_3)-free graphs for 19leq tleq 21, thus constricting the gap of cases whose complexity remains unknown. Our proof includes a computer search ensuring that the graph family obtained through the reduction is indeed P_{19}-free.

We consider the Similarity Sketching problem: Given a universe [u] = {0,ldots, u-1} we want a random function S mapping subsets Asubseteq [u] into vectors S(A) of size t, such that the Jaccard similarity J(A,B) = |Acap B|/|Acup B| between sets A and B is preserved. More precisely, define X_i = [S(A)[i] = S(B)[i]] and X = sum_{iin [t]} X_i. We want E[X_i]=J(A,B), and we want X to be strongly concentrated around E[X] = t cdot J(A,B) (i.e. Chernoff-style bounds). This is a fundamental problem which has found numerous applications in data mining, large-scale classification, computer vision, similarity search, etc. via the classic MinHash algorithm. The vectors S(A) are also called sketches. Strong concentration is critical, for often we want to sketch many sets B_1,ldots,B_n so that we later, for a query set A, can find (one of) the most similar B_i. It is then critical that no B_i looks much more similar to A due to errors in the sketch. The seminal ttimesMinHash algorithm uses t random hash functions h_1,ldots, h_t, and stores left ( min_{ain A} h_1(A),ldots, min_{ain A} h_t(A) right ) as the sketch of A. The main drawback of MinHash is, however, its O(tcdot |A|) running time, and finding a sketch with similar properties and faster running time has been the subject of several papers. (continued...)

Knowledge-grounded conversation (KGC) shows excellent potential to deliver an engaging and informative response. However, existing approaches emphasize selecting one golden knowledge given a particular dialogue context, overlooking the one-to-many phenomenon in dialogue. As a result, the existing paradigm limits the diversity of knowledge selection and generation. To this end, we establish a multi-reference KGC dataset and propose a series of metrics to systematically assess the one-to-many efficacy of existing KGC models. Furthermore, to extend the hypothesis space of knowledge selection to enhance the mapping relationship between multiple knowledge and multiple responses, we devise a span-based variational model and optimize the model in a wake-sleep style with an ameliorated evidence lower bound objective to learn the one-to-many generalization. Both automatic and human evaluations demonstrate the efficacy of our approach.

We investigate a general formulation for clustering and transductive few-shot learning, which integrates prototype-based objectives, Laplacian regularization and supervision constraints from a few labeled data points. We propose a concave-convex relaxation of the problem, and derive a computationally efficient block-coordinate bound optimizer, with convergence guarantee. At each iteration,our optimizer computes independent (parallel) updates for each point-to-cluster assignment. Therefore, it could be trivially distributed for large-scale clustering and few-shot tasks. Furthermore, we provides a thorough convergence analysis based on point-to-set maps. Were port comprehensive clustering and few-shot learning experiments over various data sets, showing that our method yields competitive performances, in term of accuracy and optimization quality, while scaling up to large problems. Using standard training on the base classes, without resorting to complex meta-learning and episodic-training strategies, our approach outperforms state-of-the-art few-shot methods by significant margins, across various models, settings and data sets. Surprisingly, we found that even standard clustering procedures (e.g., K-means), which correspond to particular, non-regularized cases of our general model, already achieve competitive performances in comparison to the state-of-the-art in few-shot learning. These surprising results point to the limitations of the current few-shot benchmarks, and question the viability of a large body of convoluted few-shot learning techniques in the recent literature.

Artificial intelligence (AI) has made remarkable progress across various domains, with large language models like ChatGPT gaining substantial attention for their human-like text-generation capabilities. Despite these achievements, spatial reasoning remains a significant challenge for these models. Benchmarks like StepGame evaluate AI spatial reasoning, where ChatGPT has shown unsatisfactory performance. However, the presence of template errors in the benchmark has an impact on the evaluation results. Thus there is potential for ChatGPT to perform better if these template errors are addressed, leading to more accurate assessments of its spatial reasoning capabilities. In this study, we refine the StepGame benchmark, providing a more accurate dataset for model evaluation. We analyze GPT's spatial reasoning performance on the rectified benchmark, identifying proficiency in mapping natural language text to spatial relations but limitations in multi-hop reasoning. We provide a flawless solution to the benchmark by combining template-to-relation mapping with logic-based reasoning. This combination demonstrates proficiency in performing qualitative reasoning on StepGame without encountering any errors. We then address the limitations of GPT models in spatial reasoning. We deploy Chain-of-thought and Tree-of-thoughts prompting strategies, offering insights into GPT's ``cognitive process", and achieving remarkable improvements in accuracy. Our investigation not only sheds light on model deficiencies but also proposes enhancements, contributing to the advancement of AI with more robust spatial reasoning capabilities.

Current LLM alignment techniques use pairwise human preferences at a sample level, and as such, they do not imply an alignment on the distributional level. We propose in this paper Alignment via Optimal Transport (AOT), a novel method for distributional preference alignment of LLMs. AOT aligns LLMs on unpaired preference data by making the reward distribution of the positive samples stochastically dominant in the first order on the distribution of negative samples. We introduce a convex relaxation of this first-order stochastic dominance and cast it as an optimal transport problem with a smooth and convex cost. Thanks to the one-dimensional nature of the resulting optimal transport problem and the convexity of the cost, it has a closed-form solution via sorting on empirical measures. We fine-tune LLMs with this AOT objective, which enables alignment by penalizing the violation of the stochastic dominance of the reward distribution of the positive samples on the reward distribution of the negative samples. We analyze the sample complexity of AOT by considering the dual of the OT problem and show that it converges at the parametric rate. Empirically, we show on a diverse set of alignment datasets and LLMs that AOT leads to state-of-the-art models in the 7B family of models when evaluated with Open LLM Benchmarks and AlpacaEval.

We propose and evaluate a number of solutions to the problem of calculating the cost to serve each location in a single-vehicle transport setting. Such cost to serve analysis has application both strategically and operationally in transportation. The problem is formally given by the traveling salesperson game (TSG), a cooperative total utility game in which agents correspond to locations in a traveling salesperson problem (TSP). The cost to serve a location is an allocated portion of the cost of an optimal tour. The Shapley value is one of the most important normative division schemes in cooperative games, giving a principled and fair allocation both for the TSG and more generally. We consider a number of direct and sampling-based procedures for calculating the Shapley value, and present the first proof that approximating the Shapley value of the TSG within a constant factor is NP-hard. Treating the Shapley value as an ideal baseline allocation, we then develop six proxies for that value which are relatively easy to compute. We perform an experimental evaluation using Synthetic Euclidean games as well as games derived from real-world tours calculated for fast-moving consumer goods scenarios. Our experiments show that several computationally tractable allocation techniques correspond to good proxies for the Shapley value.

Treemaps are a popular technique to visualize hierarchical data. The input is a weighted tree tree where the weight of each node is the sum of the weights of its children. A treemap for tree is a hierarchical partition of a rectangle into simply connected regions, usually rectangles. Each region represents a node of tree and its area is proportional to the weight of the corresponding node. An important quality criterion for treemaps is the aspect ratio of its regions. One cannot bound the aspect ratio if the regions are restricted to be rectangles. In contrast, polygonal partitions, that use convex polygons, have bounded aspect ratio. We are the first to obtain convex partitions with optimal aspect ratio O(depth(tree)). However, depth(tree) still depends on the input tree. Hence we introduce a new type of treemaps, namely orthoconvex treemaps, where regions representing leaves are rectangles, L-, and S-shapes, and regions representing internal nodes are orthoconvex polygons. We prove that any input tree, irrespective of the weights of the nodes and the depth of the tree, admits an orthoconvex treemap of constant aspect ratio. We also obtain several specialized results for single-level treemaps, that is, treemaps where the input tree has depth~1.

We consider the problem of estimating the optimal transport map between two probability distributions, P and Q in mathbb R^d, on the basis of i.i.d. samples. All existing statistical analyses of this problem require the assumption that the transport map is Lipschitz, a strong requirement that, in particular, excludes any examples where the transport map is discontinuous. As a first step towards developing estimation procedures for discontinuous maps, we consider the important special case where the data distribution Q is a discrete measure supported on a finite number of points in mathbb R^d. We study a computationally efficient estimator initially proposed by Pooladian and Niles-Weed (2021), based on entropic optimal transport, and show in the semi-discrete setting that it converges at the minimax-optimal rate n^{-1/2}, independent of dimension. Other standard map estimation techniques both lack finite-sample guarantees in this setting and provably suffer from the curse of dimensionality. We confirm these results in numerical experiments, and provide experiments for other settings, not covered by our theory, which indicate that the entropic estimator is a promising methodology for other discontinuous transport map estimation problems.

Despite the growing interest in replicating the scaled success of large language models (LLMs) in industrial search and recommender systems, most existing industrial efforts remain limited to transplanting Transformer architectures, which bring only incremental improvements over strong Deep Learning Recommendation Models (DLRMs). From a first principle perspective, the breakthroughs of LLMs stem not only from their architectures but also from two complementary mechanisms: context engineering, which enriches raw input queries with contextual cues to better elicit model capabilities, and multi-step reasoning, which iteratively refines model outputs through intermediate reasoning paths. However, these two mechanisms and their potential to unlock substantial improvements remain largely underexplored in industrial ranking systems. In this paper, we propose OnePiece, a unified framework that seamlessly integrates LLM-style context engineering and reasoning into both retrieval and ranking models of industrial cascaded pipelines. OnePiece is built on a pure Transformer backbone and further introduces three key innovations: (1) structured context engineering, which augments interaction history with preference and scenario signals and unifies them into a structured tokenized input sequence for both retrieval and ranking; (2) block-wise latent reasoning, which equips the model with multi-step refinement of representations and scales reasoning bandwidth via block size; (3) progressive multi-task training, which leverages user feedback chains to effectively supervise reasoning steps during training. OnePiece has been deployed in the main personalized search scenario of Shopee and achieves consistent online gains across different key business metrics, including over +2% GMV/UU and a +2.90% increase in advertising revenue.

Although LLM-based agents have attracted significant attention in domains such as software engineering and machine learning research, their role in advancing combinatorial optimization (CO) remains relatively underexplored. This gap underscores the need for a deeper understanding of their potential in tackling structured, constraint-intensive problems-a pursuit currently limited by the absence of comprehensive benchmarks for systematic investigation. To address this, we introduce CO-Bench, a benchmark suite featuring 36 real-world CO problems drawn from a broad range of domains and complexity levels. CO-Bench includes structured problem formulations and curated data to support rigorous investigation of LLM agents. We evaluate multiple agent frameworks against established human-designed algorithms, revealing key strengths and limitations of current approaches and identifying promising directions for future research. CO-Bench is publicly available at https://github.com/sunnweiwei/CO-Bench.

VRP (Vehicle Routing Problem) is an NP hard problem, and it has attracted a lot of research interest. In contexts where vehicles have limited carrying capacity, such as volume and weight but needed to deliver items at various locations. Initially before creating a route, each vehicle needs a group of delivery points that are not exceeding their maximum capacity. Drivers tend to deliver only to certain areas. Cluster-based is one of the approaches to give a basis for generating tighter routes. In this paper we propose new algorithms for producing such clusters/groups that do not exceed vehicles maximum capacity. Our basic assumptions are each vehicle originates from a depot, delivers the items to the customers and returns to the depot, also the vehicles are homogeneous. This methods are able to compact sub-areas in each cluster. Computational results demonstrate the effectiveness of our new procedures, which are able to assist users to plan service territories and vehicle routes more efficiently.

We study the problem of optimally projecting the transition matrix of a finite ergodic multivariate Markov chain onto a lower-dimensional state space. Specifically, we seek to construct a projected Markov chain that optimizes various information-theoretic criteria under cardinality constraints. These criteria include entropy rate, information-theoretic distance to factorizability, independence, and stationarity. We formulate these tasks as best subset selection problems over multivariate Markov chains and leverage the submodular (or supermodular) structure of the objective functions to develop efficient greedy-based algorithms with theoretical guarantees. We extend our analysis to k-submodular settings and introduce a generalized version of the distorted greedy algorithm, which may be of independent interest. Finally, we illustrate the theory and algorithms through extensive numerical experiments with publicly available code on multivariate Markov chains associated with the Bernoulli-Laplace and Curie-Weiss model.

We study the Levine hat problem, a classic combinatorial puzzle introduced by Lionel Levine in 2010. This problem involves a game in which n geq 2 players, each seeing an infinite stack of hats on each of their teammates' heads but not on their own, must simultaneously guess the index of a black hat on their own stack. If one of the players fails to do so, the team loses collectively. The players must therefore come up with a good strategy before the game starts. While the optimal winning probability V_{n} remains unknown even for n=2, we make three key advances. First, we develop a novel geometric framework for representing strategies through measurable functions, providing a new expression of V_{n} and a unified treatment of the game for finite and for infinite stacks via integral formulations. Secondly, we construct a new strategy K_{5} that reaches the conjectured optimal probability of victory : 0.35. We also show that K_{5} is part of a larger class of strategies that allow us to improve current bounds and resolve conjectured inequalities. Finally, we introduce and entirely solve a continuous generalization of the problem, demonstrating that extending to uncountable hat stacks increases the optimal winning probability to exactly 1/2. This generalization naturally leads to a broader and smoother strategic framework, within which we also describe how to compute optimal responses to a range of strategies.

The availability of performant pre-trained models has led to a proliferation of fine-tuned expert models that are specialized to a particular domain or task. Model MoErging methods aim to recycle expert models to create an aggregate system with improved performance or generalization. A key component of MoErging methods is the creation of a router that decides which expert model(s) to use for a particular input or application. The promise, effectiveness, and large design space of MoErging has spurred the development of many new methods over the past few years. This rapid pace of development has made it challenging to compare different MoErging methods, which are rarely compared to one another and are often validated in different experimental setups. To remedy such gaps, we present a comprehensive survey of MoErging methods that includes a novel taxonomy for cataloging key design choices and clarifying suitable applications for each method. Apart from surveying MoErging research, we inventory software tools and applications that make use of MoErging. We additionally discuss related fields of study such as model merging, multitask learning, and mixture-of-experts models. Taken as a whole, our survey provides a unified overview of existing MoErging methods and creates a solid foundation for future work in this burgeoning field.

Regularized optimal transport (OT) is now increasingly used as a loss or as a matching layer in neural networks. Entropy-regularized OT can be computed using the Sinkhorn algorithm but it leads to fully-dense transportation plans, meaning that all sources are (fractionally) matched with all targets. To address this issue, several works have investigated quadratic regularization instead. This regularization preserves sparsity and leads to unconstrained and smooth (semi) dual objectives, that can be solved with off-the-shelf gradient methods. Unfortunately, quadratic regularization does not give direct control over the cardinality (number of nonzeros) of the transportation plan. We propose in this paper a new approach for OT with explicit cardinality constraints on the transportation plan. Our work is motivated by an application to sparse mixture of experts, where OT can be used to match input tokens such as image patches with expert models such as neural networks. Cardinality constraints ensure that at most k tokens are matched with an expert, which is crucial for computational performance reasons. Despite the nonconvexity of cardinality constraints, we show that the corresponding (semi) dual problems are tractable and can be solved with first-order gradient methods. Our method can be thought as a middle ground between unregularized OT (recovered in the limit case k=1) and quadratically-regularized OT (recovered when k is large enough). The smoothness of the objectives increases as k increases, giving rise to a trade-off between convergence speed and sparsity of the optimal plan.

Let F_{k,d}(n) be the maximal size of a set {A}subseteq [n] such that the equation \[a_1a_2\dots a_k=x^d, \; a_1<a_2<\ldots<a_k\] has no solution with a_1,a_2,ldots,a_kA and integer x. Erdos, S\'ark\"ozy and T. S\'os studied F_{k,2}, and gave bounds when k=2,3,4,6 and also in the general case. We study the problem for d=3, and provide bounds for k=2,3,4,6 and 9, furthermore, in the general case, as well. In particular, we refute an 18 years old conjecture of Verstra\"ete. We also introduce another function f_{k,d} closely related to F_{k,d}: While the original problem requires a_1, ldots , a_k to all be distinct, we can relax this and only require that the multiset of the a_i's cannot be partitioned into d-tuples where each d-tuple consists of d copies of the same number.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Geometry problem solving is a well-recognized testbed for evaluating the high-level multi-modal reasoning capability of deep models. In most existing works, two main geometry problems: calculation and proving, are usually treated as two specific tasks, hindering a deep model to unify its reasoning capability on multiple math tasks. However, in essence, these two tasks have similar problem representations and overlapped math knowledge which can improve the understanding and reasoning ability of a deep model on both two tasks. Therefore, we construct a large-scale Unified Geometry problem benchmark, UniGeo, which contains 4,998 calculation problems and 9,543 proving problems. Each proving problem is annotated with a multi-step proof with reasons and mathematical expressions. The proof can be easily reformulated as a proving sequence that shares the same formats with the annotated program sequence for calculation problems. Naturally, we also present a unified multi-task Geometric Transformer framework, Geoformer, to tackle calculation and proving problems simultaneously in the form of sequence generation, which finally shows the reasoning ability can be improved on both two tasks by unifying formulation. Furthermore, we propose a Mathematical Expression Pretraining (MEP) method that aims to predict the mathematical expressions in the problem solution, thus improving the Geoformer model. Experiments on the UniGeo demonstrate that our proposed Geoformer obtains state-of-the-art performance by outperforming task-specific model NGS with over 5.6% and 3.2% accuracies on calculation and proving problems, respectively.

The recent emergence of new algorithms for permuting models into functionally equivalent regions of the solution space has shed some light on the complexity of error surfaces, and some promising properties like mode connectivity. However, finding the right permutation is challenging, and current optimization techniques are not differentiable, which makes it difficult to integrate into a gradient-based optimization, and often leads to sub-optimal solutions. In this paper, we propose a Sinkhorn re-basin network with the ability to obtain the transportation plan that better suits a given objective. Unlike the current state-of-art, our method is differentiable and, therefore, easy to adapt to any task within the deep learning domain. Furthermore, we show the advantage of our re-basin method by proposing a new cost function that allows performing incremental learning by exploiting the linear mode connectivity property. The benefit of our method is compared against similar approaches from the literature, under several conditions for both optimal transport finding and linear mode connectivity. The effectiveness of our continual learning method based on re-basin is also shown for several common benchmark datasets, providing experimental results that are competitive with state-of-art results from the literature.

Combinatorial optimization (CO) is naturally discrete, making machine learning based on differentiable optimization inapplicable. Karalias & Loukas (2020) adapted the probabilistic method to incorporate CO into differentiable optimization. Their work ignited the research on unsupervised learning for CO, composed of two main components: probabilistic objectives and derandomization. However, each component confronts unique challenges. First, deriving objectives under various conditions (e.g., cardinality constraints and minimum) is nontrivial. Second, the derandomization process is underexplored, and the existing derandomization methods are either random sampling or naive rounding. In this work, we aim to tackle prevalent (i.e., commonly involved) conditions in unsupervised CO. First, we concretize the targets for objective construction and derandomization with theoretical justification. Then, for various conditions commonly involved in different CO problems, we derive nontrivial objectives and derandomization to meet the targets. Finally, we apply the derivations to various CO problems. Via extensive experiments on synthetic and real-world graphs, we validate the correctness of our derivations and show our empirical superiority w.r.t. both optimization quality and speed.

k-Clustering in R^d (e.g., k-median and k-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality n, it remains open to find sublinear-time quantum algorithms. We give quantum algorithms that find coresets for k-clustering in R^d with O(nkd^{3/2}) query complexity. Our coreset reduces the input size from n to poly(kepsilon^{-1}d), so that existing alpha-approximation algorithms for clustering can run on top of it and yield (1 + epsilon)alpha-approximation. This eventually yields a quadratic speedup for various k-clustering approximation algorithms. We complement our algorithm with a nearly matching lower bound, that any quantum algorithm must make Omega(nk) queries in order to achieve even O(1)-approximation for k-clustering.

Multi-Task Learning (MTL) is a powerful technique that has gained popularity due to its performance improvement over traditional Single-Task Learning (STL). However, MTL is often challenging because there is an exponential number of possible task groupings, which can make it difficult to choose the best one, and some groupings might produce performance degradation due to negative interference between tasks. Furthermore, existing solutions are severely suffering from scalability issues, limiting any practical application. In our paper, we propose a new data-driven method that addresses these challenges and provides a scalable and modular solution for classification task grouping based on hand-crafted features, specifically Data Maps, which capture the training behavior for each classification task during the MTL training. We experiment with the method demonstrating its effectiveness, even on an unprecedented number of tasks (up to 100).

Knowledge graph embedding (KGE) is an increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.

We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model's performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.

Tabular representation learning has recently gained a lot of attention. However, existing approaches only learn a representation from a single table, and thus ignore the potential to learn from the full structure of relational databases, including neighboring tables that can contain important information for a contextualized representation. Moreover, current models are significantly limited in scale, which prevents that they learn from large databases. In this paper, we thus introduce our vision of relational representation learning, that can not only learn from the full relational structure, but also can scale to larger database sizes that are commonly found in real-world. Moreover, we also discuss opportunities and challenges we see along the way to enable this vision and present initial very promising results. Overall, we argue that this direction can lead to foundation models for relational databases that are today only available for text and images.

The Machine Learning for Combinatorial Optimization (ML4CO) NeurIPS 2021 competition aims to improve state-of-the-art combinatorial optimization solvers by replacing key heuristic components with machine learning models. On the dual task, we design models to make branching decisions to promote the dual bound increase faster. We propose a knowledge inheritance method to generalize knowledge of different models from the dataset aggregation process, named KIDA. Our improvement overcomes some defects of the baseline graph-neural-networks-based methods. Further, we won the 1st Place on the dual task. We hope this report can provide useful experience for developers and researchers. The code is available at https://github.com/megvii-research/NeurIPS2021-ML4CO-KIDA.

Projection maintenance is one of the core data structure tasks. Efficient data structures for projection maintenance have led to recent breakthroughs in many convex programming algorithms. In this work, we further extend this framework to the Kronecker product structure. Given a constraint matrix {sf A} and a positive semi-definite matrix Win R^{ntimes n} with a sparse eigenbasis, we consider the task of maintaining the projection in the form of {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}, where {sf B}={sf A}(Wotimes I) or {sf B}={sf A}(W^{1/2}otimes W^{1/2}). At each iteration, the weight matrix W receives a low rank change and we receive a new vector h. The goal is to maintain the projection matrix and answer the query {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}h with good approximation guarantees. We design a fast dynamic data structure for this task and it is robust against an adaptive adversary. Following the beautiful and pioneering work of [Beimel, Kaplan, Mansour, Nissim, Saranurak and Stemmer, STOC'22], we use tools from differential privacy to reduce the randomness required by the data structure and further improve the running time.

We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is to cluster a set of objects based on multiway interactions of different categories or types. We present improved approximation guarantees based on linear programming, and show they are tight by proving a matching integrality gap. Our results also include new approximation hardness results, a combinatorial 2-approximation whose runtime is linear in the hypergraph size, and several new connections to well-studied objectives such as vertex cover and hypergraph multiway cut.

Combinatorial problems are present in a wide range of industries. Constraint Programming (CP) is a well-suited problem-solving paradigm, but its core process, namely constraint modelling, is a bottleneck for wider adoption. Aiming to alleviate this bottleneck, recent studies have explored using Large Language Models (LLMs) as modelling assistants, transforming combinatorial problem descriptions to executable constraint models, similar to coding assistants. However, the existing evaluation datasets for constraint modelling are often limited to small, homogeneous, or domain-specific instances, which do not capture the diversity of real-world scenarios. This work addresses this gap by introducing CP-Bench, a novel benchmark dataset that includes a diverse set of well-known combinatorial problem classes sourced from the CP community, structured explicitly for evaluating LLM-driven CP modelling. With this dataset, and given the variety of constraint modelling frameworks, we compare and evaluate the modelling capabilities of LLMs for three distinct constraint modelling systems, which vary in abstraction level and underlying syntax: the high-level MiniZinc language and Python-based CPMpy library, and the lower-level Python interface of the OR-Tools CP-SAT solver. In order to enhance the ability of LLMs to produce valid constraint models, we systematically evaluate the use of prompt-based and inference-time compute methods adapted from existing LLM-based code generation research. Our results underscore the modelling convenience provided by Python-based frameworks, as well as the effectiveness of documentation-rich system prompts, which, augmented with repeated sampling and self-verification, achieve further improvements, reaching up to 70\% accuracy on this new, highly challenging benchmark.

We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.

Electronic maps consist of diverse entities, such as points of interest (POIs), road networks, and land parcels, playing a vital role in applications like ITS and LBS. Map entity representation learning (MapRL) generates versatile and reusable data representations, providing essential tools for efficiently managing and utilizing map entity data. Despite the progress in MapRL, two key challenges constrain further development. First, existing research is fragmented, with models classified by the type of map entity, limiting the reusability of techniques across different tasks. Second, the lack of unified benchmarks makes systematic evaluation and comparison of models difficult. To address these challenges, we propose a novel taxonomy for MapRL that organizes models based on functional module-such as encoders, pre-training tasks, and downstream tasks-rather than by entity type. Building on this taxonomy, we present a taxonomy-driven library, VecCity, which offers easy-to-use interfaces for encoding, pre-training, fine-tuning, and evaluation. The library integrates datasets from nine cities and reproduces 21 mainstream MapRL models, establishing the first standardized benchmarks for the field. VecCity also allows users to modify and extend models through modular components, facilitating seamless experimentation. Our comprehensive experiments cover multiple types of map entities and evaluate 21 VecCity pre-built models across various downstream tasks. Experimental results demonstrate the effectiveness of VecCity in streamlining model development and provide insights into the impact of various components on performance. By promoting modular design and reusability, VecCity offers a unified framework to advance research and innovation in MapRL. The code is available at https://github.com/Bigscity-VecCity/VecCity.

Talking face generation aims at generating photo-realistic video portraits of a target person driven by input audio. Due to its nature of one-to-many mapping from the input audio to the output video (e.g., one speech content may have multiple feasible visual appearances), learning a deterministic mapping like previous works brings ambiguity during training, and thus causes inferior visual results. Although this one-to-many mapping could be alleviated in part by a two-stage framework (i.e., an audio-to-expression model followed by a neural-rendering model), it is still insufficient since the prediction is produced without enough information (e.g., emotions, wrinkles, etc.). In this paper, we propose MemFace to complement the missing information with an implicit memory and an explicit memory that follow the sense of the two stages respectively. More specifically, the implicit memory is employed in the audio-to-expression model to capture high-level semantics in the audio-expression shared space, while the explicit memory is employed in the neural-rendering model to help synthesize pixel-level details. Our experimental results show that our proposed MemFace surpasses all the state-of-the-art results across multiple scenarios consistently and significantly.

Zero-shot Image Captioning (ZIC) increasingly utilizes synthetic datasets generated by text-to-image (T2I) models to mitigate the need for costly manual annotation. However, these T2I models often produce images that exhibit semantic misalignments with their corresponding input captions (e.g., missing objects, incorrect attributes), resulting in noisy synthetic image-caption pairs that can hinder model training. Existing dataset pruning techniques are largely designed for removing noisy text in web-crawled data. However, these methods are ill-suited for the distinct challenges of synthetic data, where captions are typically well-formed, but images may be inaccurate representations. To address this gap, we introduce SynC, a novel framework specifically designed to refine synthetic image-caption datasets for ZIC. Instead of conventional filtering or regeneration, SynC focuses on reassigning captions to the most semantically aligned images already present within the synthetic image pool. Our approach employs a one-to-many mapping strategy by initially retrieving multiple relevant candidate images for each caption. We then apply a cycle-consistency-inspired alignment scorer that selects the best image by verifying its ability to retrieve the original caption via image-to-text retrieval. Extensive evaluations demonstrate that SynC consistently and significantly improves performance across various ZIC models on standard benchmarks (MS-COCO, Flickr30k, NoCaps), achieving state-of-the-art results in several scenarios. SynC offers an effective strategy for curating refined synthetic data to enhance ZIC.

Vehicle Routing Problems (VRPs) are a class of NP-hard problems ubiquitous in several real-world logistics scenarios that pose significant challenges for optimization. Neural Combinatorial Optimization (NCO) has emerged as a promising alternative to classical approaches, as it can learn fast heuristics to solve VRPs. However, most research works in NCO for VRPs focus on simplified settings, which do not account for asymmetric distances and travel durations that cannot be derived by simple Euclidean distances and unrealistic data distributions, hindering real-world deployment. This work introduces RRNCO (Real Routing NCO) to bridge the gap of NCO between synthetic and real-world VRPs in the critical aspects of both data and modeling. First, we introduce a new, openly available dataset with real-world data containing a diverse dataset of locations, distances, and duration matrices from 100 cities, considering realistic settings with actual routing distances and durations obtained from Open Source Routing Machine (OSRM). Second, we propose a novel approach that efficiently processes both node and edge features through contextual gating, enabling the construction of more informed node embedding, and we finally incorporate an Adaptation Attention Free Module (AAFM) with neural adaptive bias mechanisms that effectively integrates not only distance matrices but also angular relationships between nodes, allowing our model to capture rich structural information. RRNCO achieves state-of-the-art results in real-world VRPs among NCO methods. We make our dataset and code publicly available at https://github.com/ai4co/real-routing-nco.

We introduce OneKE, a dockerized schema-guided knowledge extraction system, which can extract knowledge from the Web and raw PDF Books, and support various domains (science, news, etc.). Specifically, we design OneKE with multiple agents and a configure knowledge base. Different agents perform their respective roles, enabling support for various extraction scenarios. The configure knowledge base facilitates schema configuration, error case debugging and correction, further improving the performance. Empirical evaluations on benchmark datasets demonstrate OneKE's efficacy, while case studies further elucidate its adaptability to diverse tasks across multiple domains, highlighting its potential for broad applications. We have open-sourced the Code at https://github.com/zjunlp/OneKE and released a Video at http://oneke.openkg.cn/demo.mp4.

We formulate and solve the H-SARA Problem, a Vehicle Routing and Appointment Scheduling Problem motivated by home services management. We assume that travel times, service durations, and customer cancellations are stochastic. We use a two-stage process that first generates teams and routes using a VRP Solver with optional extensions and then uses an MC Scheduler that determines expected arrival times by teams at customers. We further introduce two different models of cancellation and their associated impacts on routing and scheduling. Finally, we introduce the Route Fracture Metaheuristic that iteratively improves an H-SARA solution by replacing the worst-performing teams. We present insights into the problem and a series of numerical experiments that illustrate properties of the optimal routing, scheduling, and the impact of the Route Fracture Metaheuristic for both models of cancellation.

We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order. This class of functions includes monotone submodular functions as a sub-family. To understand the importance of this structure in optimization problems we consider the problem of maximizing function value under various types of constraints. To demonstrate the modeling power of submodular order functions we show applications in two different settings. First, we apply our results to the extensively studied problem of assortment optimization. While the objectives in assortment optimization are known to be non-submodular (and non-monotone) even for simple choice models, we show that they are compatible with the notion of submodular order. Consequently, we obtain new and in some cases the first constant factor guarantee for constrained assortment optimization in fundamental choice models. As a second application of submodular order functions, we show an intriguing connection to the maximization of monotone submodular functions in the streaming model. We recover some best known guarantees for this problem as a corollary of our results.

The Text-to-SQL task, aiming to translate the natural language of the questions into SQL queries, has drawn much attention recently. One of the most challenging problems of Text-to-SQL is how to generalize the trained model to the unseen database schemas, also known as the cross-domain Text-to-SQL task. The key lies in the generalizability of (i) the encoding method to model the question and the database schema and (ii) the question-schema linking method to learn the mapping between words in the question and tables/columns in the database schema. Focusing on the above two key issues, we propose a Structure-Aware Dual Graph Aggregation Network (SADGA) for cross-domain Text-to-SQL. In SADGA, we adopt the graph structure to provide a unified encoding model for both the natural language question and database schema. Based on the proposed unified modeling, we further devise a structure-aware aggregation method to learn the mapping between the question-graph and schema-graph. The structure-aware aggregation method is featured with Global Graph Linking, Local Graph Linking, and Dual-Graph Aggregation Mechanism. We not only study the performance of our proposal empirically but also achieved 3rd place on the challenging Text-to-SQL benchmark Spider at the time of writing.

Solving the inverse problem is the key step in evaluating the capacity of a physical model to describe real phenomena. In medical image computing, it aligns with the classical theme of image-based model personalization. Traditionally, a solution to the problem is obtained by performing either sampling or variational inference based methods. Both approaches aim to identify a set of free physical model parameters that results in a simulation best matching an empirical observation. When applied to brain tumor modeling, one of the instances of image-based model personalization in medical image computing, the overarching drawback of the methods is the time complexity for finding such a set. In a clinical setting with limited time between imaging and diagnosis or even intervention, this time complexity may prove critical. As the history of quantitative science is the history of compression, we align in this paper with the historical tendency and propose a method compressing complex traditional strategies for solving an inverse problem into a simple database query task. We evaluated different ways of performing the database query task assessing the trade-off between accuracy and execution time. On the exemplary task of brain tumor growth modeling, we prove that the proposed method achieves one order speed-up compared to existing approaches for solving the inverse problem. The resulting compute time offers critical means for relying on more complex and, hence, realistic models, for integrating image preprocessing and inverse modeling even deeper, or for implementing the current model into a clinical workflow.

This is the first work to look at the application of large language models (LLMs) for the purpose of model space edits in automated planning tasks. To set the stage for this union, we explore two different flavors of model space problems that have been studied in the AI planning literature and explore the effect of an LLM on those tasks. We empirically demonstrate how the performance of an LLM contrasts with combinatorial search (CS) -- an approach that has been traditionally used to solve model space tasks in planning, both with the LLM in the role of a standalone model space reasoner as well as in the role of a statistical signal in concert with the CS approach as part of a two-stage process. Our experiments show promising results suggesting further forays of LLMs into the exciting world of model space reasoning for planning tasks in the future.

Language models and specialized table embedding models have recently demonstrated strong performance on many tasks over tabular data. Researchers and practitioners are keen to leverage these models in many new application contexts; but limited understanding of the strengths and weaknesses of these models, and the table representations they generate, makes the process of finding a suitable model for a given task reliant on trial and error. There is an urgent need to gain a comprehensive understanding of these models to minimize inefficiency and failures in downstream usage. To address this need, we propose Observatory, a formal framework to systematically analyze embedding representations of relational tables. Motivated both by invariants of the relational data model and by statistical considerations regarding data distributions, we define eight primitive properties, and corresponding measures to quantitatively characterize table embeddings for these properties. Based on these properties, we define an extensible framework to evaluate language and table embedding models. We collect and synthesize a suite of datasets and use Observatory to analyze nine such models. Our analysis provides insights into the strengths and weaknesses of learned representations over tables. We find, for example, that some models are sensitive to table structure such as column order, that functional dependencies are rarely reflected in embeddings, and that specialized table embedding models have relatively lower sample fidelity. Such insights help researchers and practitioners better anticipate model behaviors and select appropriate models for their downstream tasks, while guiding researchers in the development of new models.

We consider the problem of fairly allocating a sequence of indivisible items that arrive online in an arbitrary order to a group of n agents with additive normalized valuation functions. We consider both the allocation of goods and chores and propose algorithms for approximating maximin share (MMS) allocations. When agents have identical valuation functions the problem coincides with the semi-online machine covering problem (when items are goods) and load balancing problem (when items are chores), for both of which optimal competitive ratios have been achieved. In this paper, we consider the case when agents have general additive valuation functions. For the allocation of goods, we show that no competitive algorithm exists even when there are only three agents and propose an optimal 0.5-competitive algorithm for the case of two agents. For the allocation of chores, we propose a (2-1/n)-competitive algorithm for n>=3 agents and a square root of 2 (approximately 1.414)-competitive algorithm for two agents. Additionally, we show that no algorithm can do better than 15/11 (approximately 1.364)-competitive for two agents.

Accurate and efficient record linkage is an open challenge of particular relevance to Australian Government Agencies, who recognise that so-called wicked social problems are best tackled by forming partnerships founded on large-scale data fusion. Names and addresses are the most common attributes on which data from different government agencies can be linked. In this paper, we focus on the problem of address linking. Linkage is particularly problematic when the data has significant quality issues. The most common approach for dealing with quality issues is to standardise raw data prior to linking. If a mistake is made in standardisation, however, it is usually impossible to recover from it to perform linkage correctly. This paper proposes a novel algorithm for address linking that is particularly practical for linking large disparate sets of addresses, being highly scalable, robust to data quality issues and simple to implement. It obviates the need for labour intensive and problematic address standardisation. We demonstrate the efficacy of the algorithm by matching two large address datasets from two government agencies with good accuracy and computational efficiency.

We consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this end, we propose an algorithm referred to as Pessimistic ASsortment opTimizAtion (PASTA for short) designed based on the principle of pessimism, that can correctly identify the optimal assortment by only requiring the offline data to cover the optimal assortment under general settings. In particular, we establish a regret bound for the offline assortment optimization problem under the celebrated multinomial logit model. We also propose an efficient computational procedure to solve our pessimistic assortment optimization problem. Numerical studies demonstrate the superiority of the proposed method over the existing baseline method.

Much of the world's most valued data is stored in relational databases and data warehouses, where the data is organized into many tables connected by primary-foreign key relations. However, building machine learning models using this data is both challenging and time consuming. The core problem is that no machine learning method is capable of learning on multiple tables interconnected by primary-foreign key relations. Current methods can only learn from a single table, so the data must first be manually joined and aggregated into a single training table, the process known as feature engineering. Feature engineering is slow, error prone and leads to suboptimal models. Here we introduce an end-to-end deep representation learning approach to directly learn on data laid out across multiple tables. We name our approach Relational Deep Learning (RDL). The core idea is to view relational databases as a temporal, heterogeneous graph, with a node for each row in each table, and edges specified by primary-foreign key links. Message Passing Graph Neural Networks can then automatically learn across the graph to extract representations that leverage all input data, without any manual feature engineering. Relational Deep Learning leads to more accurate models that can be built much faster. To facilitate research in this area, we develop RelBench, a set of benchmark datasets and an implementation of Relational Deep Learning. The data covers a wide spectrum, from discussions on Stack Exchange to book reviews on the Amazon Product Catalog. Overall, we define a new research area that generalizes graph machine learning and broadens its applicability to a wide set of AI use cases.

In this paper, we propose OpenSatMap, a fine-grained, high-resolution satellite dataset for large-scale map construction. Map construction is one of the foundations of the transportation industry, such as navigation and autonomous driving. Extracting road structures from satellite images is an efficient way to construct large-scale maps. However, existing satellite datasets provide only coarse semantic-level labels with a relatively low resolution (up to level 19), impeding the advancement of this field. In contrast, the proposed OpenSatMap (1) has fine-grained instance-level annotations; (2) consists of high-resolution images (level 20); (3) is currently the largest one of its kind; (4) collects data with high diversity. Moreover, OpenSatMap covers and aligns with the popular nuScenes dataset and Argoverse 2 dataset to potentially advance autonomous driving technologies. By publishing and maintaining the dataset, we provide a high-quality benchmark for satellite-based map construction and downstream tasks like autonomous driving.

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at https://github.com/BitSecret/FGPS.

Joint representation learning over multi-sourced knowledge graphs (KGs) yields transferable and expressive embeddings that improve downstream tasks. Entity alignment (EA) is a critical step in this process. Despite recent considerable research progress in embedding-based EA, how it works remains to be explored. In this paper, we provide a similarity flooding perspective to explain existing translation-based and aggregation-based EA models. We prove that the embedding learning process of these models actually seeks a fixpoint of pairwise similarities between entities. We also provide experimental evidence to support our theoretical analysis. We propose two simple but effective methods inspired by the fixpoint computation in similarity flooding, and demonstrate their effectiveness on benchmark datasets. Our work bridges the gap between recent embedding-based models and the conventional similarity flooding algorithm. It would improve our understanding of and increase our faith in embedding-based EA.

Compatible features enable the direct comparison of old and new learned features allowing to use them interchangeably over time. In visual search systems, this eliminates the need to extract new features from the gallery-set when the representation model is upgraded with novel data. This has a big value in real applications as re-indexing the gallery-set can be computationally expensive when the gallery-set is large, or even infeasible due to privacy or other concerns of the application. In this paper, we propose CoReS, a new training procedure to learn representations that are compatible with those previously learned, grounding on the stationarity of the features as provided by fixed classifiers based on polytopes. With this solution, classes are maximally separated in the representation space and maintain their spatial configuration stationary as new classes are added, so that there is no need to learn any mappings between representations nor to impose pairwise training with the previously learned model. We demonstrate that our training procedure largely outperforms the current state of the art and is particularly effective in the case of multiple upgrades of the training-set, which is the typical case in real applications.

Let T be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in T is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high. We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes. We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in R^d. We use these partitions with slack for embedding ultrametrics into d-dimensional Euclidean space: we give a rm polylog(Delta)-approximation algorithm for embedding n-point ultrametrics into R^d with minimum distortion, where Delta denotes the spread of the metric, i.e., the ratio between the largest and the smallest distance between two points. The previously best-known approximation ratio for this problem was polynomial in n. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.

Combinatorial optimization problems involving multiple agents are notoriously challenging due to their NP-hard nature and the necessity for effective agent coordination. Despite advancements in learning-based methods, existing approaches often face critical limitations, including suboptimal agent coordination, poor generalizability, and high computational latency. To address these issues, we propose Parallel AutoRegressive Combinatorial Optimization (PARCO), a reinforcement learning framework designed to construct high-quality solutions for multi-agent combinatorial tasks efficiently. To this end, PARCO integrates three key components: (1) transformer-based communication layers to enable effective agent collaboration during parallel solution construction, (2) a multiple pointer mechanism for low-latency, parallel agent decision-making, and (3) priority-based conflict handlers to resolve decision conflicts via learned priorities. We evaluate PARCO in multi-agent vehicle routing and scheduling problems where our approach outperforms state-of-the-art learning methods and demonstrates strong generalization ability and remarkable computational efficiency. Code available at: https://github.com/ai4co/parco.

Among the most important properties of algorithms investigated in computer science are soundness, completeness, and complexity. These properties, however, are rarely analyzed for the vast collection of recently proposed methods for planning with large language models. In this work, we alleviate this gap. We analyse these properties of using LLMs for planning and highlight that recent trends abandon both soundness and completeness for the sake of inefficiency. We propose a significantly more efficient approach that can, at the same time, maintain both soundness and completeness. We exemplify on four representative search problems, comparing to the LLM-based solutions from the literature that attempt to solve these problems. We show that by using LLMs to produce the code for the search components we can solve the entire datasets with 100\% accuracy with only a few calls to the LLM. We argue for a responsible use of compute resources; urging research community to investigate sound and complete LLM-based approaches that uphold efficiency.

The use of graph neural networks has produced significant advances in point cloud problems, such as those found in high energy physics. The question of how to produce a graph structure in these problems is usually treated as a matter of heuristics, employing fully connected graphs or K-nearest neighbors. In this work, we elevate this question to utmost importance as the Topology Problem. We propose an attention mechanism that allows a graph to be constructed in a learned space that handles geometrically the flow of relevance, providing one solution to the Topology Problem. We test this architecture, called GravNetNorm, on the task of top jet tagging, and show that it is competitive in tagging accuracy, and uses far fewer computational resources than all other comparable models.

While large language models (LLMs) have recently demonstrated strong potential in solving planning problems, there is a trade-off between flexibility and complexity. LLMs, as zero-shot planners themselves, are still not capable of directly generating valid plans for complex planning problems such as multi-constraint or long-horizon tasks. On the other hand, many frameworks aiming to solve complex planning problems often rely on task-specific preparatory efforts, such as task-specific in-context examples and pre-defined critics/verifiers, which limits their cross-task generalization capability. In this paper, we tackle these challenges by observing that the core of many planning problems lies in optimization problems: searching for the optimal solution (best plan) with goals subject to constraints (preconditions and effects of decisions). With LLMs' commonsense, reasoning, and programming capabilities, this opens up the possibilities of a universal LLM-based approach to planning problems. Inspired by this observation, we propose LLMFP, a general-purpose framework that leverages LLMs to capture key information from planning problems and formally formulate and solve them as optimization problems from scratch, with no task-specific examples needed. We apply LLMFP to 9 planning problems, ranging from multi-constraint decision making to multi-step planning problems, and demonstrate that LLMFP achieves on average 83.7% and 86.8% optimal rate across 9 tasks for GPT-4o and Claude 3.5 Sonnet, significantly outperforming the best baseline (direct planning with OpenAI o1-preview) with 37.6% and 40.7% improvements. We also validate components of LLMFP with ablation experiments and analyzed the underlying success and failure reasons.

We study the problem of online prediction, in which at each time step t, an individual x_t arrives, whose label we must predict. Each individual is associated with various groups, defined based on their features such as age, sex, race etc., which may intersect. Our goal is to make predictions that have regret guarantees not just overall but also simultaneously on each sub-sequence comprised of the members of any single group. Previous work such as [Blum & Lykouris] and [Lee et al] provide attractive regret guarantees for these problems; however, these are computationally intractable on large model classes. We show that a simple modification of the sleeping experts technique of [Blum & Lykouris] yields an efficient reduction to the well-understood problem of obtaining diminishing external regret absent group considerations. Our approach gives similar regret guarantees compared to [Blum & Lykouris]; however, we run in time linear in the number of groups, and are oracle-efficient in the hypothesis class. This in particular implies that our algorithm is efficient whenever the number of groups is polynomially bounded and the external-regret problem can be solved efficiently, an improvement on [Blum & Lykouris]'s stronger condition that the model class must be small. Our approach can handle online linear regression and online combinatorial optimization problems like online shortest paths. Beyond providing theoretical regret bounds, we evaluate this algorithm with an extensive set of experiments on synthetic data and on two real data sets -- Medical costs and the Adult income dataset, both instantiated with intersecting groups defined in terms of race, sex, and other demographic characteristics. We find that uniformly across groups, our algorithm gives substantial error improvements compared to running a standard online linear regression algorithm with no groupwise regret guarantees.

Instance-specific algorithm configuration and algorithm portfolios have been shown to offer significant improvements over single algorithm approaches in a variety of application domains. In the SAT and CSP domains algorithm portfolios have consistently dominated the main competitions in these fields for the past five years. For a portfolio approach to be effective there are two crucial conditions that must be met. First, there needs to be a collection of complementary solvers with which to make a portfolio. Second, there must be a collection of problem features that can accurately identify structural differences between instances. This paper focuses on the latter issue: feature representation, because, unlike SAT, not every problem has well-studied features. We employ the well-known SATzilla feature set, but compute alternative sets on different SAT encodings of CSPs. We show that regardless of what encoding is used to convert the instances, adequate structural information is maintained to differentiate between problem instances, and that this can be exploited to make an effective portfolio-based CSP solver.

Document clustering is a text mining technique used to provide better document search and browsing in digital libraries or online corpora. A lot of research has been done on biomedical document clustering that is based on using existing ontology. But, associations and co-occurrences of the medical concepts are not well represented by using ontology. In this research, a vector representation of concepts of diseases and similarity measurement between concepts are proposed. They identify the closest concepts of diseases in the context of a corpus. Each document is represented by using the vector space model. A weight scheme is proposed to consider both local content and associations between concepts. A Self-Organizing Map is used as document clustering algorithm. The vector projection and visualization features of SOM enable visualization and analysis of the clusters distributions and relationships on the two dimensional space. The experimental results show that the proposed document clustering framework generates meaningful clusters and facilitate visualization of the clusters based on the concepts of diseases.

We present FIMO, an innovative dataset comprising formal mathematical problem statements sourced from the International Mathematical Olympiad (IMO) Shortlisted Problems. Designed to facilitate advanced automated theorem proving at the IMO level, FIMO is currently tailored for the Lean formal language. It comprises 149 formal problem statements, accompanied by both informal problem descriptions and their corresponding LaTeX-based informal proofs. Through initial experiments involving GPT-4, our findings underscore the existing limitations in current methodologies, indicating a substantial journey ahead before achieving satisfactory IMO-level automated theorem proving outcomes.

Recent studies in using deep reinforcement learning (DRL) to solve Job-shop scheduling problems (JSSP) focus on construction heuristics. However, their performance is still far from optimality, mainly because the underlying graph representation scheme is unsuitable for modelling partial solutions at each construction step. This paper proposes a novel DRL-guided improvement heuristic for solving JSSP, where graph representation is employed to encode complete solutions. We design a Graph Neural-Network-based representation scheme, consisting of two modules to effectively capture the information of dynamic topology and different types of nodes in graphs encountered during the improvement process. To speed up solution evaluation during improvement, we present a novel message-passing mechanism that can evaluate multiple solutions simultaneously. We prove that the computational complexity of our method scales linearly with problem size. Experiments on classic benchmarks show that the improvement policy learned by our method outperforms state-of-the-art DRL-based methods by a large margin.

Recent breakthroughs in large language models (LLMs) exemplified by the impressive mathematical and scientific reasoning capabilities of the o1 model have spotlighted the critical importance of high-quality training data in advancing LLM performance across STEM disciplines. While the mathematics community has benefited from a growing body of curated datasets, the scientific domain at the higher education level has long suffered from a scarcity of comparable resources. To address this gap, we present SCP-116K, a new large-scale dataset of 116,756 high-quality problem-solution pairs, automatically extracted from heterogeneous sources using a streamlined and highly generalizable pipeline. Our approach involves stringent filtering to ensure the scientific rigor and educational level of the extracted materials, while maintaining adaptability for future expansions or domain transfers. By openly releasing both the dataset and the extraction pipeline, we seek to foster research on scientific reasoning, enable comprehensive performance evaluations of new LLMs, and lower the barrier to replicating the successes of advanced models like o1 in the broader science community. We believe SCP-116K will serve as a critical resource, catalyzing progress in high-level scientific reasoning tasks and promoting further innovations in LLM development. The dataset and code are publicly available at https://github.com/AQA6666/SCP-116K-open.

Despite the success of neural-based combinatorial optimization methods for end-to-end heuristic learning, out-of-distribution generalization remains a challenge. In this paper, we present a novel formulation of Combinatorial Optimization Problems (COPs) as Markov Decision Processes (MDPs) that effectively leverages common symmetries of COPs to improve out-of-distribution robustness. Starting from a direct MDP formulation of a constructive method, we introduce a generic way to reduce the state space, based on Bisimulation Quotienting (BQ) in MDPs. Then, for COPs with a recursive nature, we specialize the bisimulation and show how the reduced state exploits the symmetries of these problems and facilitates MDP solving. Our approach is principled and we prove that an optimal policy for the proposed BQ-MDP actually solves the associated COPs. We illustrate our approach on five classical problems: the Euclidean and Asymmetric Traveling Salesman, Capacitated Vehicle Routing, Orienteering and Knapsack Problems. Furthermore, for each problem, we introduce a simple attention-based policy network for the BQ-MDPs, which we train by imitation of (near) optimal solutions of small instances from a single distribution. We obtain new state-of-the-art results for the five COPs on both synthetic and realistic benchmarks. Notably, in contrast to most existing neural approaches, our learned policies show excellent generalization performance to much larger instances than seen during training, without any additional search procedure.

Large Language Models (LLMs) have exhibited impressive proficiency in various natural language processing (NLP) tasks, which involve increasingly complex reasoning. Knowledge reasoning, a primary type of reasoning, aims at deriving new knowledge from existing one.While it has been widely studied in the context of knowledge graphs (KGs), knowledge reasoning in LLMs remains underexplored. In this paper, we introduce Chain-of-Knowledge, a comprehensive framework for knowledge reasoning, including methodologies for both dataset construction and model learning. For dataset construction, we create KnowReason via rule mining on KGs. For model learning, we observe rule overfitting induced by naive training. Hence, we enhance CoK with a trial-and-error mechanism that simulates the human process of internal knowledge exploration. We conduct extensive experiments with KnowReason. Our results show the effectiveness of CoK in refining LLMs in not only knowledge reasoning, but also general reasoning benchmarkms.

Constraint Programming (CP) is a declarative programming paradigm that allows for modeling and solving combinatorial optimization problems, such as the Job-Shop Scheduling Problem (JSSP). While CP solvers manage to find optimal or near-optimal solutions for small instances, they do not scale well to large ones, i.e., they require long computation times or yield low-quality solutions. Therefore, real-world scheduling applications often resort to fast, handcrafted, priority-based dispatching heuristics to find a good initial solution and then refine it using optimization methods. This paper proposes a novel end-to-end approach to solving scheduling problems by means of CP and Reinforcement Learning (RL). In contrast to previous RL methods, tailored for a given problem by including procedural simulation algorithms, complex feature engineering, or handcrafted reward functions, our neural-network architecture and training algorithm merely require a generic CP encoding of some scheduling problem along with a set of small instances. Our approach leverages existing CP solvers to train an agent learning a Priority Dispatching Rule (PDR) that generalizes well to large instances, even from separate datasets. We evaluate our method on seven JSSP datasets from the literature, showing its ability to find higher-quality solutions for very large instances than obtained by static PDRs and by a CP solver within the same time limit.

Class-agnostic counting methods enumerate objects of an arbitrary class, providing tremendous utility in many fields. Prior works have limited usefulness as they require either a set of examples of the type to be counted or that the query image contains only a single type of object. A significant factor in these shortcomings is the lack of a dataset to properly address counting in settings with more than one kind of object present. To address these issues, we propose the first Multi-class, Class-Agnostic Counting dataset (MCAC) and A Blind Counter (ABC123), a method that can count multiple types of objects simultaneously without using examples of type during training or inference. ABC123 introduces a new paradigm where instead of requiring exemplars to guide the enumeration, examples are found after the counting stage to help a user understand the generated outputs. We show that ABC123 outperforms contemporary methods on MCAC without needing human in-the-loop annotations. We also show that this performance transfers to FSC-147, the standard class-agnostic counting dataset. MCAC is available at MCAC.active.vision and ABC123 is available at ABC123.active.vision.

Optimization problems are prevalent across various scenarios. Formulating and then solving optimization problems described by natural language often requires highly specialized human expertise, which could block the widespread application of optimization-based decision making. To automate problem formulation and solving, leveraging large language models (LLMs) has emerged as a potential way. However, this kind of approach suffers from the issue of optimization generalization. Namely, the accuracy of most current LLM-based methods and the generality of optimization problem types that they can model are still limited. In this paper, we propose a unified learning-based framework called LLMOPT to boost optimization generalization. Starting from the natural language descriptions of optimization problems and a pre-trained LLM, LLMOPT constructs the introduced five-element formulation as a universal model for learning to define diverse optimization problem types. Then, LLMOPT employs the multi-instruction tuning to enhance both problem formalization and solver code generation accuracy and generality. After that, to prevent hallucinations in LLMs, such as sacrificing solving accuracy to avoid execution errors, the model alignment and self-correction mechanism are adopted in LLMOPT. We evaluate the optimization generalization ability of LLMOPT and compared methods across six real-world datasets covering roughly 20 fields such as health, environment, energy and manufacturing, etc. Extensive experiment results show that LLMOPT is able to model various optimization problem types such as linear/nonlinear programming, mixed integer programming, and combinatorial optimization, and achieves a notable 11.08% average solving accuracy improvement compared with the state-of-the-art methods. The code is available at https://github.com/caigaojiang/LLMOPT.

Audio-driven talking head generation has drawn much attention in recent years, and many efforts have been made in lip-sync, expressive facial expressions, natural head pose generation, and high video quality. However, no model has yet led or tied on all these metrics due to the one-to-many mapping between audio and motion. In this paper, we propose VividTalk, a two-stage generic framework that supports generating high-visual quality talking head videos with all the above properties. Specifically, in the first stage, we map the audio to mesh by learning two motions, including non-rigid expression motion and rigid head motion. For expression motion, both blendshape and vertex are adopted as the intermediate representation to maximize the representation ability of the model. For natural head motion, a novel learnable head pose codebook with a two-phase training mechanism is proposed. In the second stage, we proposed a dual branch motion-vae and a generator to transform the meshes into dense motion and synthesize high-quality video frame-by-frame. Extensive experiments show that the proposed VividTalk can generate high-visual quality talking head videos with lip-sync and realistic enhanced by a large margin, and outperforms previous state-of-the-art works in objective and subjective comparisons.

Answering complex logical queries on incomplete knowledge graphs is a challenging task, and has been widely studied. Embedding-based methods require training on complex queries, and cannot generalize well to out-of-distribution query structures. Recent work frames this task as an end-to-end optimization problem, and it only requires a pretrained link predictor. However, due to the exponentially large combinatorial search space, the optimal solution can only be approximated, limiting the final accuracy. In this work, we propose QTO (Query Computation Tree Optimization) that can efficiently find the exact optimal solution. QTO finds the optimal solution by a forward-backward propagation on the tree-like computation graph, i.e., query computation tree. In particular, QTO utilizes the independence encoded in the query computation tree to reduce the search space, where only local computations are involved during the optimization procedure. Experiments on 3 datasets show that QTO obtains state-of-the-art performance on complex query answering, outperforming previous best results by an average of 22%. Moreover, QTO can interpret the intermediate solutions for each of the one-hop atoms in the query with over 90% accuracy. The code of our paper is at https://github.com/bys0318/QTO.

We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training data, only detectors for attributes and a description of how those attributes are correlated with the target classes, called the class-attribute matrix. We develop the first non-trivial lower bound on the worst-case error of the best map from attributes to classes for this setting, even with perfect attribute detectors. The lower bound characterizes the theoretical intrinsic difficulty of the zero-shot problem based on the available information -- the class-attribute matrix -- and the bound is practically computable from it. Our lower bound is tight, as we show that we can always find a randomized map from attributes to classes whose expected error is upper bounded by the value of the lower bound. We show that our analysis can be predictive of how standard zero-shot methods behave in practice, including which classes will likely be confused with others.

The Honeymoon Oberwolfach Problem HOP(2m_1,2m_2,ldots,2m_t) asks the following question. Given n=m_1+m_2+ldots +m_t newlywed couples at a conference and t round tables of sizes 2m_1,2m_2,ldots,2m_t, is it possible to arrange the 2n participants at these tables for 2n-2 meals so that each participant sits next to their spouse at every meal, and sits next to every other participant exactly once? A solution to HOP(2m_1,2m_2,ldots,2m_t) is a decomposition of K_{2n}+(2n-3)I, the complete graph K_{2n} with 2n-3 additional copies of a fixed 1-factor I, into 2-factors, each consisting of disjoint I-alternating cycles of lengths 2m_1,2m_2,ldots,2m_t. The Honeymoon Oberwolfach Problem was introduced in a 2019 paper by Lepine and Sajna. The authors conjectured that HOP(2m_1,2m_2,ldots, 2m_t) has a solution whenever the obvious necessary conditions are satisfied, and proved the conjecture for several large cases, including the uniform cycle length case m_1=ldots=m_t, and the small cases with n le 9. In the present paper, we extend the latter result to all cases with n le 20 using a computer search.

Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability is still lacking. In this work, we introduce a comprehensive benchmarking framework designed to systematically evaluate a range of quantum optimization techniques against well-established NP-hard combinatorial problems. Our framework focuses on key problem classes, including the Multi-Dimensional Knapsack Problem (MDKP), Maximum Independent Set (MIS), Quadratic Assignment Problem (QAP), and Market Share Problem (MSP). Our study evaluates gate-based quantum approaches, including the Variational Quantum Eigensolver (VQE) and its CVaR-enhanced variant, alongside advanced quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) and its extensions. To address resource constraints, we incorporate qubit compression techniques like Pauli Correlation Encoding (PCE) and Quantum Random Access Optimization (QRAO). Experimental results, obtained from simulated quantum environments and classical solvers, provide key insights into feasibility, optimality gaps, and scalability. Our findings highlight both the promise and current limitations of quantum optimization, offering a structured pathway for future research and practical applications in quantum-enhanced decision-making.

We present EMMa, an Extensible, Multimodal dataset of Amazon product listings that contains rich Material annotations. It contains more than 2.8 million objects, each with image(s), listing text, mass, price, product ratings, and position in Amazon's product-category taxonomy. We also design a comprehensive taxonomy of 182 physical materials (e.g., Plastic rightarrow Thermoplastic rightarrow Acrylic). Objects are annotated with one or more materials from this taxonomy. With the numerous attributes available for each object, we develop a Smart Labeling framework to quickly add new binary labels to all objects with very little manual labeling effort, making the dataset extensible. Each object attribute in our dataset can be included in either the model inputs or outputs, leading to combinatorial possibilities in task configurations. For example, we can train a model to predict the object category from the listing text, or the mass and price from the product listing image. EMMa offers a new benchmark for multi-task learning in computer vision and NLP, and allows practitioners to efficiently add new tasks and object attributes at scale.

We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the s-uniform variant of the problem is NP-complete when s geq 3, we identify two populations of input sequences, most of which can be solved in polynomial time using a recursive algorithm that we contribute. Combining with a sampler for the simplicial configuration model [J.-G. Young et al., Phys. Rev. E 96, 032312 (2017)], we facilitate the efficient sampling of simplicial ensembles from arbitrary degree and size distributions. We find that, contrary to expectations based on dyadic networks, increasing the nodes' degrees reduces the number of loops in simplicial complexes. Our work unveils a fundamental constraint on the degree-size sequences and sheds light on further analysis of higher-order phenomena based on local structures.

Numerous real-world decision-making problems can be formulated and solved using Mixed-Integer Linear Programming (MILP) models. However, the transformation of these problems into MILP models heavily relies on expertise in operations research and mathematical optimization, which restricts non-experts' accessibility to MILP. To address this challenge, we propose a framework for automatically formulating MILP models from unstructured natural language descriptions of decision problems, which integrates Large Language Models (LLMs) and mathematical modeling techniques. This framework consists of three phases: i) identification of decision variables, ii) classification of objective and constraints, and iii) finally, generation of MILP models. In this study, we present a constraint classification scheme and a set of constraint templates that can guide the LLMs in synthesizing a complete MILP model. After fine-tuning LLMs, our approach can identify and synthesize logic constraints in addition to classic demand and resource constraints. The logic constraints have not been studied in existing work. To evaluate the performance of the proposed framework, we extend the NL4Opt dataset with more problem descriptions and constraint types, and with the new dataset, we compare our framework with one-step model generation methods offered by LLMs. The experimental results reveal that with respect to the accuracies of generating the correct model, objective, and constraints, our method which integrates constraint classification and templates with LLMs significantly outperforms the others. The prototype system that we developed has a great potential to capture more constraints for more complex MILPs. It opens up opportunities for developing training tools for operations research practitioners and has the potential to be a powerful tool for automatic decision problem modeling and solving in practice.

In this paper, we investigate the challenge of integrating tables from data lakes, focusing on three core tasks: 1) pairwise integrability judgment, which determines whether a tuple pair in a table is integrable, accounting for any occurrences of semantic equivalence or typographical errors; 2) integrable set discovery, which aims to identify all integrable sets in a table based on pairwise integrability judgments established in the first task; 3) multi-tuple conflict resolution, which resolves conflicts among multiple tuples during integration. We train a binary classifier to address the task of pairwise integrability judgment. Given the scarcity of labeled data, we propose a self-supervised adversarial contrastive learning algorithm to perform classification, which incorporates data augmentation methods and adversarial examples to autonomously generate new training data. Upon the output of pairwise integrability judgment, each integrable set is considered as a community, a densely connected sub-graph where nodes and edges correspond to tuples in the table and their pairwise integrability, respectively. We proceed to investigate various community detection algorithms to address the integrable set discovery objective. Moving forward to tackle multi-tuple conflict resolution, we introduce an novel in-context learning methodology. This approach capitalizes on the knowledge embedded within pretrained large language models to effectively resolve conflicts that arise when integrating multiple tuples. Notably, our method minimizes the need for annotated data. Since no suitable test collections are available for our tasks, we develop our own benchmarks using two real-word dataset repositories: Real and Join. We conduct extensive experiments on these benchmarks to validate the robustness and applicability of our methodologies in the context of integrating tables within data lakes.

Co-speech gesture video generation aims to synthesize realistic, audio-aligned videos of speakers, complete with synchronized facial expressions and body gestures. This task presents challenges due to the significant one-to-many mapping between audio and visual content, further complicated by the scarcity of large-scale public datasets and high computational demands. We propose a lightweight framework that utilizes 2D full-body skeletons as an efficient auxiliary condition to bridge audio signals with visual outputs. Our approach introduces a diffusion model conditioned on fine-grained audio segments and a skeleton extracted from the speaker's reference image, predicting skeletal motions through skeleton-audio feature fusion to ensure strict audio coordination and body shape consistency. The generated skeletons are then fed into an off-the-shelf human video generation model with the speaker's reference image to synthesize high-fidelity videos. To democratize research, we present CSG-405-the first public dataset with 405 hours of high-resolution videos across 71 speech types, annotated with 2D skeletons and diverse speaker demographics. Experiments show that our method exceeds state-of-the-art approaches in visual quality and synchronization while generalizing across speakers and contexts. Code, models, and CSG-405 are publicly released at https://mpi-lab.github.io/Democratizing-CSG/

Floor labels of crowdsourced RF signals are crucial for many smart-city applications, such as multi-floor indoor localization, geofencing, and robot surveillance. To build a prediction model to identify the floor number of a new RF signal upon its measurement, conventional approaches using the crowdsourced RF signals assume that at least few labeled signal samples are available on each floor. In this work, we push the envelope further and demonstrate that it is technically feasible to enable such floor identification with only one floor-labeled signal sample on the bottom floor while having the rest of signal samples unlabeled. We propose FIS-ONE, a novel floor identification system with only one labeled sample. FIS-ONE consists of two steps, namely signal clustering and cluster indexing. We first build a bipartite graph to model the RF signal samples and obtain a latent representation of each node (each signal sample) using our attention-based graph neural network model so that the RF signal samples can be clustered more accurately. Then, we tackle the problem of indexing the clusters with proper floor labels, by leveraging the observation that signals from an access point can be detected on different floors, i.e., signal spillover. Specifically, we formulate a cluster indexing problem as a combinatorial optimization problem and show that it is equivalent to solving a traveling salesman problem, whose (near-)optimal solution can be found efficiently. We have implemented FIS-ONE and validated its effectiveness on the Microsoft dataset and in three large shopping malls. Our results show that FIS-ONE outperforms other baseline algorithms significantly, with up to 23% improvement in adjusted rand index and 25% improvement in normalized mutual information using only one floor-labeled signal sample.

Vision-specific concepts such as "region" have played a key role in extending general machine learning frameworks to tasks like object detection. Given the success of region-based detectors for supervised learning and the progress of intra-image methods for contrastive learning, we explore the use of regions for reconstructive pre-training. Starting from Masked Autoencoding (MAE) both as a baseline and an inspiration, we propose a parallel pre-text task tailored to address the one-to-many mapping between images and regions. Since such regions can be generated in an unsupervised way, our approach (R-MAE) inherits the wide applicability from MAE, while being more "region-aware". We conduct thorough analyses during the development of R-MAE, and converge on a variant that is both effective and efficient (1.3% overhead over MAE). Moreover, it shows consistent quantitative improvements when generalized to various pre-training data and downstream detection and segmentation benchmarks. Finally, we provide extensive qualitative visualizations to enhance the understanding of R-MAE's behaviour and potential. Code will be made available at https://github.com/facebookresearch/r-mae.

JSON Schema is an important, evolving standard schema language for families of JSON documents. It is based on a complex combination of structural and Boolean assertions, and features negation and recursion. The static analysis of JSON Schema documents comprises practically relevant problems, including schema satisfiability, inclusion, and equivalence. These three problems can be reduced to witness generation: given a schema, generate an element of the schema, if it exists, and report failure otherwise. Schema satisfiability, inclusion, and equivalence have been shown to be decidable, by reduction to reachability in alternating tree automata. However, no witness generation algorithm has yet been formally described. We contribute a first, direct algorithm for JSON Schema witness generation. We study its effectiveness and efficiency, in experiments over several schema collections, including thousands of real-world schemas. Our focus is on the completeness of the language, where we only exclude the uniqueItems operator, and on the ability of the algorithm to run in a reasonable time on a large set of real-world examples, despite the exponential complexity of the underlying problem.

Recent research in tabular data synthesis has focused on single tables, whereas real-world applications often involve complex data with tens or hundreds of interconnected tables. Previous approaches to synthesizing multi-relational (multi-table) data fall short in two key aspects: scalability for larger datasets and capturing long-range dependencies, such as correlations between attributes spread across different tables. Inspired by the success of diffusion models in tabular data modeling, we introduce Cluster Latent Variable guided Denoising Diffusion Probabilistic Models (ClavaDDPM). This novel approach leverages clustering labels as intermediaries to model relationships between tables, specifically focusing on foreign key constraints. ClavaDDPM leverages the robust generation capabilities of diffusion models while incorporating efficient algorithms to propagate the learned latent variables across tables. This enables ClavaDDPM to capture long-range dependencies effectively. Extensive evaluations on multi-table datasets of varying sizes show that ClavaDDPM significantly outperforms existing methods for these long-range dependencies while remaining competitive on utility metrics for single-table data.

Deep neural networks are often applied to medical images to automate the problem of medical diagnosis. However, a more clinically relevant question that practitioners usually face is how to predict the future trajectory of a disease. Current methods for prognosis or disease trajectory forecasting often require domain knowledge and are complicated to apply. In this paper, we formulate the prognosis prediction problem as a one-to-many prediction problem. Inspired by a clinical decision-making process with two agents -- a radiologist and a general practitioner -- we predict prognosis with two transformer-based components that share information with each other. The first transformer in this framework aims to analyze the imaging data, and the second one leverages its internal states as inputs, also fusing them with auxiliary clinical data. The temporal nature of the problem is modeled within the transformer states, allowing us to treat the forecasting problem as a multi-task classification, for which we propose a novel loss. We show the effectiveness of our approach in predicting the development of structural knee osteoarthritis changes and forecasting Alzheimer's disease clinical status directly from raw multi-modal data. The proposed method outperforms multiple state-of-the-art baselines with respect to performance and calibration, both of which are needed for real-world applications. An open-source implementation of our method is made publicly available at https://github.com/Oulu-IMEDS/CLIMATv2.

Large language models (LLM) have been attracting much attention from the community recently, due to their remarkable performance in all kinds of downstream tasks. According to the well-known scaling law, scaling up a dense LLM enhances its capabilities, but also significantly increases the computational complexity. Mixture-of-Experts (MoE) models address that by allowing the model size to grow without substantially raising training or inference costs. Yet MoE models face challenges regarding knowledge sharing among experts, making their performance somehow sensitive to routing accuracy. To tackle that, previous works introduced shared experts and combined their outputs with those of the top K routed experts in an ``addition'' manner. In this paper, inspired by collective matrix factorization to learn shared knowledge among data, we propose CartesianMoE, which implements more effective knowledge sharing among experts in more like a ``multiplication'' manner. Extensive experimental results indicate that CartesianMoE outperforms previous MoE models for building LLMs, in terms of both perplexity and downstream task performance. And we also find that CartesianMoE achieves better expert routing robustness.

In recent years, there has been remarkable progress in leveraging Language Models (LMs), encompassing Pre-trained Language Models (PLMs) and Large-scale Language Models (LLMs), within the domain of mathematics. This paper conducts a comprehensive survey of mathematical LMs, systematically categorizing pivotal research endeavors from two distinct perspectives: tasks and methodologies. The landscape reveals a large number of proposed mathematical LLMs, which are further delineated into instruction learning, tool-based methods, fundamental CoT techniques, and advanced CoT methodologies. In addition, our survey entails the compilation of over 60 mathematical datasets, including training datasets, benchmark datasets, and augmented datasets. Addressing the primary challenges and delineating future trajectories within the field of mathematical LMs, this survey is positioned as a valuable resource, poised to facilitate and inspire future innovation among researchers invested in advancing this domain.

Schema linking is a critical bottleneck in applying existing Text-to-SQL models to real-world, large-scale, multi-database environments. Through error analysis, we identify two major challenges in schema linking: (1) Database Retrieval: accurately selecting the target database from a large schema pool, while effectively filtering out irrelevant ones; and (2) Schema Item Grounding: precisely identifying the relevant tables and columns within complex and often redundant schemas for SQL generation. Based on these, we introduce LinkAlign, a novel framework tailored for large-scale databases with thousands of fields. LinkAlign comprises three key steps: multi-round semantic enhanced retrieval and irrelevant information isolation for Challenge 1, and schema extraction enhancement for Challenge 2. Each stage supports both Agent and Pipeline execution modes, enabling balancing efficiency and performance via modular design. To enable more realistic evaluation, we construct AmbiDB, a synthetic dataset designed to reflect the ambiguity of real-world schema linking. Experiments on widely-used Text-to-SQL benchmarks demonstrate that LinkAlign consistently outperforms existing baselines on all schema linking metrics. Notably, it improves the overall Text-to-SQL pipeline and achieves a new state-of-the-art score of 33.09% on the Spider 2.0-Lite benchmark using only open-source LLMs, ranking first on the leaderboard at the time of submission. The codes are available at https://github.com/Satissss/LinkAlign

Recently, Ainsworth et al. showed that using weight matching (WM) to minimize the L_2 distance in a permutation search of model parameters effectively identifies permutations that satisfy linear mode connectivity (LMC), in which the loss along a linear path between two independently trained models with different seeds remains nearly constant. This paper provides a theoretical analysis of LMC using WM, which is crucial for understanding stochastic gradient descent's effectiveness and its application in areas like model merging. We first experimentally and theoretically show that permutations found by WM do not significantly reduce the L_2 distance between two models and the occurrence of LMC is not merely due to distance reduction by WM in itself. We then provide theoretical insights showing that permutations can change the directions of the singular vectors, but not the singular values, of the weight matrices in each layer. This finding shows that permutations found by WM mainly align the directions of singular vectors associated with large singular values across models. This alignment brings the singular vectors with large singular values, which determine the model functionality, closer between pre-merged and post-merged models, so that the post-merged model retains functionality similar to the pre-merged models, making it easy to satisfy LMC. Finally, we analyze the difference between WM and straight-through estimator (STE), a dataset-dependent permutation search method, and show that WM outperforms STE, especially when merging three or more models.

Historical maps contain detailed geographic information difficult to find elsewhere covering long-periods of time (e.g., 125 years for the historical topographic maps in the US). However, these maps typically exist as scanned images without searchable metadata. Existing approaches making historical maps searchable rely on tedious manual work (including crowd-sourcing) to generate the metadata (e.g., geolocations and keywords). Optical character recognition (OCR) software could alleviate the required manual work, but the recognition results are individual words instead of location phrases (e.g., "Black" and "Mountain" vs. "Black Mountain"). This paper presents an end-to-end approach to address the real-world problem of finding and indexing historical map images. This approach automatically processes historical map images to extract their text content and generates a set of metadata that is linked to large external geospatial knowledge bases. The linked metadata in the RDF (Resource Description Framework) format support complex queries for finding and indexing historical maps, such as retrieving all historical maps covering mountain peaks higher than 1,000 meters in California. We have implemented the approach in a system called mapKurator. We have evaluated mapKurator using historical maps from several sources with various map styles, scales, and coverage. Our results show significant improvement over the state-of-the-art methods. The code has been made publicly available as modules of the Kartta Labs project at https://github.com/kartta-labs/Project.

Large crowd-sourced datasets are often noisy and relation classification (RC) datasets are no exception. Reannotating the entire dataset is one probable solution however it is not always viable due to time and budget constraints. This paper addresses the problem of efficient reannotation of a large noisy dataset for the RC. Our goal is to catch more annotation errors in the dataset while reannotating fewer instances. Existing work on RC dataset reannotation lacks the flexibility about how much data to reannotate. We introduce the concept of a reannotation budget to overcome this limitation. The immediate follow-up problem is: Given a specific reannotation budget, which subset of the data should we reannotate? To address this problem, we present two strategies to selectively reannotate RC datasets. Our strategies utilize the taxonomic hierarchy of relation labels. The intuition of our work is to rely on the graph distance between actual and predicted relation labels in the label hierarchy graph. We evaluate our reannotation strategies on the well-known TACRED dataset. We design our experiments to answer three specific research questions. First, does our strategy select novel candidates for reannotation? Second, for a given reannotation budget is our reannotation strategy more efficient at catching annotation errors? Third, what is the impact of data reannotation on RC model performance measurement? Experimental results show that our both reannotation strategies are novel and efficient. Our analysis indicates that the current reported performance of RC models on noisy TACRED data is inflated.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, yet their direct application to NP-hard combinatorial problems (CPs) remains underexplored. In this work, we systematically investigate the reasoning abilities of LLMs on a variety of NP-hard combinatorial optimization tasks and introduce ACCORD: Autoregressive Constraint-satisfying generation for COmbinatorial optimization with Routing and Dynamic attention. ACCORD features a novel dataset representation and model architecture that leverage the autoregressive nature of LLMs to dynamically enforce feasibility constraints, coupled with attention-based routing to activate problem-specific LoRA modules. We also present the ACCORD-90k supervised dataset, covering six NP-hard combinatorial problems: TSP, VRP, Knapsack, FlowShop, JSSP, and BinPacking. Extensive experiments demonstrate that our ACCORD model, built on an 8B-parameter Llama backbone, consistently outperforms standard prompting and input-output methods, even when compared to much larger LLMs, such as gpt-4. Ablation studies further show that our output structure enhances solution feasibility. To the best of our knowledge, this is the first large-scale, end-to-end framework for exploring the applications of LLMs to a broad spectrum of combinatorial optimization problems. The codes are publicly available at https://github.com/starjob42/ACCORD

Learning heuristics for vehicle routing problems (VRPs) has gained much attention due to the less reliance on hand-crafted rules. However, existing methods are typically trained and tested on the same task with a fixed size and distribution (of nodes), and hence suffer from limited generalization performance. This paper studies a challenging yet realistic setting, which considers generalization across both size and distribution in VRPs. We propose a generic meta-learning framework, which enables effective training of an initialized model with the capability of fast adaptation to new tasks during inference. We further develop a simple yet efficient approximation method to reduce the training overhead. Extensive experiments on both synthetic and benchmark instances of the traveling salesman problem (TSP) and capacitated vehicle routing problem (CVRP) demonstrate the effectiveness of our method. The code is available at: https://github.com/RoyalSkye/Omni-VRP.

This paper develops a hierarchical clustering algorithm for weighted projective spaces P_{q}, utilizing a Finsler metric d_F([z], [w]) and its rational analogue d_{F,Q}([z], [w]) to define distances that preserve the non-Euclidean geometry of these quotient manifolds. Defined via geodesic integrals of a scaling invariant Finsler norm weighted by the grades q = (q_0, q_1, dots, q_n), these metrics satisfy true metric properties including the triangle inequality, overcoming the limitations of the non-metric dissimilarity measure from prior work.

This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topological Representation Learning". The competition asked participants to provide creative contributions to the fields of computational geometry and topology through the open-source repositories Geomstats and Giotto-TDA. The challenge attracted 16 teams in its two month duration. This paper describes the design of the challenge and summarizes its main findings.

Generalized Tur\'an problems ask for the maximum number of copies of a graph H in an n-vertex, F-free graph, denoted by ex(n,H,F). We show how to extend the new, localized approach of Bradac, Malec, and Tompkins to generalized Tur\'{a}n problems. We weight the copies of H (typically taking H=K_t), instead of the edges, based on the size of the largest clique, path, or star containing the vertices of the copy of H, and in each case prove a tight upper bound on the sum of the weights. A consequence of our new localized theorems is an asymptotic determination of ex(n,H,K_{1,r}) for every H having at least one dominating vertex and mex(m,H,K_{1,r}) for every H having at least two dominating vertices.

Large-scale task planning is a major challenge. Recent work exploits large language models (LLMs) directly as a policy and shows surprisingly interesting results. This paper shows that LLMs provide a commonsense model of the world in addition to a policy that acts on it. The world model and the policy can be combined in a search algorithm, such as Monte Carlo Tree Search (MCTS), to scale up task planning. In our new LLM-MCTS algorithm, the LLM-induced world model provides a commonsense prior belief for MCTS to achieve effective reasoning; the LLM-induced policy acts as a heuristic to guide the search, vastly improving search efficiency. Experiments show that LLM-MCTS outperforms both MCTS alone and policies induced by LLMs (GPT2 and GPT3.5) by a wide margin, for complex, novel tasks. Further experiments and analyses on multiple tasks -- multiplication, multi-hop travel planning, object rearrangement -- suggest minimum description length (MDL) as a general guiding principle: if the description length of the world model is substantially smaller than that of the policy, using LLM as a world model for model-based planning is likely better than using LLM solely as a policy.

We introduce a novel dataset designed to benchmark the physical and spatial reasoning capabilities of Large Language Models (LLM) based on topology optimization, a method for computing optimal material distributions within a design space under prescribed loads and supports. In this dataset, LLMs are provided with conditions such as 2D boundary, applied forces and supports, and must reason about the resulting optimal material distribution. The dataset includes a variety of tasks, ranging from filling in masked regions within partial structures to predicting complete material distributions. Solving these tasks requires understanding the flow of forces and the required material distribution under given constraints, without access to simulation tools or explicit physical models, challenging models to reason about structural stability and spatial organization. Our dataset targets the evaluation of spatial and physical reasoning abilities in 2D settings, offering a complementary perspective to traditional language and logic benchmarks.

Entity resolution (record linkage, microclustering) systems are notoriously difficult to evaluate. Looking for a needle in a haystack, traditional evaluation methods use sophisticated, application-specific sampling schemes to find matching pairs of records among an immense number of non-matches. We propose an alternative that facilitates the creation of representative, reusable benchmark data sets without necessitating complex sampling schemes. These benchmark data sets can then be used for model training and a variety of evaluation tasks. Specifically, we propose an entity-centric data labeling methodology that integrates with a unified framework for monitoring summary statistics, estimating key performance metrics such as cluster and pairwise precision and recall, and analyzing root causes for errors. We validate the framework in an application to inventor name disambiguation and through simulation studies. Software: https://github.com/OlivierBinette/er-evaluation/

Learning neural subset selection tasks, such as compound selection in AI-aided drug discovery, have become increasingly pivotal across diverse applications. The existing methodologies in the field primarily concentrate on constructing models that capture the relationship between utility function values and subsets within their respective supersets. However, these approaches tend to overlook the valuable information contained within the superset when utilizing neural networks to model set functions. In this work, we address this oversight by adopting a probabilistic perspective. Our theoretical findings demonstrate that when the target value is conditioned on both the input set and subset, it is essential to incorporate an invariant sufficient statistic of the superset into the subset of interest for effective learning. This ensures that the output value remains invariant to permutations of the subset and its corresponding superset, enabling identification of the specific superset from which the subset originated. Motivated by these insights, we propose a simple yet effective information aggregation module designed to merge the representations of subsets and supersets from a permutation invariance perspective. Comprehensive empirical evaluations across diverse tasks and datasets validate the enhanced efficacy of our approach over conventional methods, underscoring the practicality and potency of our proposed strategies in real-world contexts.

Math word problem (MWP) solving requires generating a reasoning path based on a given problem description that often contains irrelevant conditions. Existing chain-of-thought (CoT) prompting methods elicited multi-step reasoning abilities of large language models (LLMs) to solve MWPs. However, they were seriously confused by the irrelevant conditions, resulting in low accuracy. In this paper, we propose a novel approach named I^3C that instructs LLMs to identify and ignore irrelevant conditions. It identifies a set of irrelevant condition candidates that have a weak semantic relevance with the question. Then it prompts LLMs to verify the irrelevant conditions. Lastly it instructs the LLMs with the verification on relevant and irrelevant conditions to avoid confusion and improve reasoning paths. Moreover, we propose to select (problem, reasoning paths) pairs as demonstrations to enhance I^3C with few-shot reasoning. We develop I^3C-Select that selects the most confusing problems based on the semantic relevance measurement. We conduct extensive experiments on eight MWP datasets. I^3C can be combined with any CoT prompting methods to improve the performance of solving MWPs. Notably, with GPT-3.5-Turbo and I^3C-Select, we achieve an accuracy of 96.0 and 94.1 on GSM-IC2-1K and GSM-ICM-1K, respectively, significantly outperforming the state-of-the-art few-shot prompting method Complex-CoT by +11.7 and +11.1. Our implementation is made publicly available at https://wzy6642.github.io/I3C.github.io/.

Combinatorial optimization (CO) problems are often NP-hard and thus out of reach for exact algorithms, making them a tempting domain to apply machine learning methods. The highly structured constraints in these problems can hinder either optimization or sampling directly in the solution space. On the other hand, GFlowNets have recently emerged as a powerful machinery to efficiently sample from composite unnormalized densities sequentially and have the potential to amortize such solution-searching processes in CO, as well as generate diverse solution candidates. In this paper, we design Markov decision processes (MDPs) for different combinatorial problems and propose to train conditional GFlowNets to sample from the solution space. Efficient training techniques are also developed to benefit long-range credit assignment. Through extensive experiments on a variety of different CO tasks with synthetic and realistic data, we demonstrate that GFlowNet policies can efficiently find high-quality solutions.

Given a matrix Min R^{mtimes n}, the low rank matrix completion problem asks us to find a rank-k approximation of M as UV^top for Uin R^{mtimes k} and Vin R^{ntimes k} by only observing a few entries specified by a set of entries Omegasubseteq [m]times [n]. In particular, we examine an approach that is widely used in practice -- the alternating minimization framework. Jain, Netrapalli and Sanghavi~jns13 showed that if M has incoherent rows and columns, then alternating minimization provably recovers the matrix M by observing a nearly linear in n number of entries. While the sample complexity has been subsequently improved~glz17, alternating minimization steps are required to be computed exactly. This hinders the development of more efficient algorithms and fails to depict the practical implementation of alternating minimization, where the updates are usually performed approximately in favor of efficiency. In this paper, we take a major step towards a more efficient and error-robust alternating minimization framework. To this end, we develop an analytical framework for alternating minimization that can tolerate moderate amount of errors caused by approximate updates. Moreover, our algorithm runs in time widetilde O(|Omega| k), which is nearly linear in the time to verify the solution while preserving the sample complexity. This improves upon all prior known alternating minimization approaches which require widetilde O(|Omega| k^2) time.

The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the complexity of the problem statement. Here, we focus on establishing partial optimality conditions for the special case of complete graphs and cubic objective functions. In addition, we define and implement algorithms for testing these conditions and examine their effect numerically, on two datasets.

Ontologies and taxonomies of research fields are critical for managing and organising scientific knowledge, as they facilitate efficient classification, dissemination and retrieval of information. However, the creation and maintenance of such ontologies are expensive and time-consuming tasks, usually requiring the coordinated effort of multiple domain experts. Consequently, ontologies in this space often exhibit uneven coverage across different disciplines, limited inter-domain connectivity, and infrequent updating cycles. In this study, we investigate the capability of several large language models to identify semantic relationships among research topics within three academic domains: biomedicine, physics, and engineering. The models were evaluated under three distinct conditions: zero-shot prompting, chain-of-thought prompting, and fine-tuning on existing ontologies. Additionally, we assessed the cross-domain transferability of fine-tuned models by measuring their performance when trained in one domain and subsequently applied to a different one. To support this analysis, we introduce PEM-Rel-8K, a novel dataset consisting of over 8,000 relationships extracted from the most widely adopted taxonomies in the three disciplines considered in this study: MeSH, PhySH, and IEEE. Our experiments demonstrate that fine-tuning LLMs on PEM-Rel-8K yields excellent performance across all disciplines.

Our study contributes to the scheduling and combinatorial optimization literature with new heuristics discovered by leveraging the power of Large Language Models (LLMs). We focus on the single-machine total tardiness (SMTT) problem, which aims to minimize total tardiness by sequencing n jobs on a single processor without preemption, given processing times and due dates. We develop and benchmark two novel LLM-discovered heuristics, the EDD Challenger (EDDC) and MDD Challenger (MDDC), inspired by the well-known Earliest Due Date (EDD) and Modified Due Date (MDD) rules. In contrast to prior studies that employed simpler rule-based heuristics, we evaluate our LLM-discovered algorithms using rigorous criteria, including optimality gaps and solution time derived from a mixed-integer programming (MIP) formulation of SMTT. We compare their performance against state-of-the-art heuristics and exact methods across various job sizes (20, 100, 200, and 500 jobs). For instances with more than 100 jobs, exact methods such as MIP and dynamic programming become computationally intractable. Up to 500 jobs, EDDC improves upon the classic EDD rule and another widely used algorithm in the literature. MDDC consistently outperforms traditional heuristics and remains competitive with exact approaches, particularly on larger and more complex instances. This study shows that human-LLM collaboration can produce scalable, high-performing heuristics for NP-hard constrained combinatorial optimization, even under limited resources when effectively configured.

In this paper, we propose a novel learning paradigm, termed Chain-of-Model (CoM), which incorporates the causal relationship into the hidden states of each layer as a chain style, thereby introducing great scaling efficiency in model training and inference flexibility in deployment. We introduce the concept of Chain-of-Representation (CoR), which formulates the hidden states at each layer as a combination of multiple sub-representations (i.e., chains) at the hidden dimension level. In each layer, each chain from the output representations can only view all of its preceding chains in the input representations. Consequently, the model built upon CoM framework can progressively scale up the model size by increasing the chains based on the previous models (i.e., chains), and offer multiple sub-models at varying sizes for elastic inference by using different chain numbers. Based on this principle, we devise Chain-of-Language-Model (CoLM), which incorporates the idea of CoM into each layer of Transformer architecture. Based on CoLM, we further introduce CoLM-Air by introducing a KV sharing mechanism, that computes all keys and values within the first chain and then shares across all chains. This design demonstrates additional extensibility, such as enabling seamless LM switching, prefilling acceleration and so on. Experimental results demonstrate our CoLM family can achieve comparable performance to the standard Transformer, while simultaneously enabling greater flexiblity, such as progressive scaling to improve training efficiency and offer multiple varying model sizes for elastic inference, paving a a new way toward building language models. Our code will be released in the future at: https://github.com/microsoft/CoLM.

Modern machine learning research relies on relatively few carefully curated datasets. Even in these datasets, and typically in `untidy' or raw data, practitioners are faced with significant issues of data quality and diversity which can be prohibitively labor intensive to address. Existing methods for dealing with these challenges tend to make strong assumptions about the particular issues at play, and often require a priori knowledge or metadata such as domain labels. Our work is orthogonal to these methods: we instead focus on providing a unified and efficient framework for Metadata Archaeology -- uncovering and inferring metadata of examples in a dataset. We curate different subsets of data that might exist in a dataset (e.g. mislabeled, atypical, or out-of-distribution examples) using simple transformations, and leverage differences in learning dynamics between these probe suites to infer metadata of interest. Our method is on par with far more sophisticated mitigation methods across different tasks: identifying and correcting mislabeled examples, classifying minority-group samples, prioritizing points relevant for training and enabling scalable human auditing of relevant examples.

Deep clustering, which learns representation and semantic clustering without labels information, poses a great challenge for deep learning-based approaches. Despite significant progress in recent years, most existing methods focus on uniformly distributed datasets, significantly limiting the practical applicability of their methods. In this paper, we propose a more practical problem setting named deep imbalanced clustering, where the underlying classes exhibit an imbalance distribution. To address this challenge, we introduce a novel optimal transport-based pseudo-label learning framework. Our framework formulates pseudo-label generation as a Semantic-regularized Progressive Partial Optimal Transport (SP^2OT) problem, which progressively transports each sample to imbalanced clusters under several prior distribution and semantic relation constraints, thus generating high-quality and imbalance-aware pseudo-labels. To solve SP^2OT, we develop a Majorization-Minimization-based optimization algorithm. To be more precise, we employ the strategy of majorization to reformulate the SP^2OT problem into a Progressive Partial Optimal Transport problem, which can be transformed into an unbalanced optimal transport problem with augmented constraints and can be solved efficiently by a fast matrix scaling algorithm. Experiments on various datasets, including a human-curated long-tailed CIFAR100, challenging ImageNet-R, and large-scale subsets of fine-grained iNaturalist2018 datasets, demonstrate the superiority of our method.

In Multi-Task Learning (MTL), tasks may compete and limit the performance achieved on each other, rather than guiding the optimization to a solution, superior to all its single-task trained counterparts. Since there is often not a unique solution optimal for all tasks, practitioners have to balance tradeoffs between tasks' performance, and resort to optimality in the Pareto sense. Most MTL methodologies either completely neglect this aspect, and instead of aiming at learning a Pareto Front, produce one solution predefined by their optimization schemes, or produce diverse but discrete solutions. Recent approaches parameterize the Pareto Front via neural networks, leading to complex mappings from tradeoff to objective space. In this paper, we conjecture that the Pareto Front admits a linear parameterization in parameter space, which leads us to propose Pareto Manifold Learning, an ensembling method in weight space. Our approach produces a continuous Pareto Front in a single training run, that allows to modulate the performance on each task during inference. Experiments on multi-task learning benchmarks, ranging from image classification to tabular datasets and scene understanding, show that Pareto Manifold Learning outperforms state-of-the-art single-point algorithms, while learning a better Pareto parameterization than multi-point baselines.

Sublinear time complexity is required by the massively parallel computation (MPC) model. Breaking dynamic programs into a set of sparse dynamic programs that can be divided, solved, and merged in sublinear time. The rectangle escape problem (REP) is defined as follows: For n axis-aligned rectangles inside an axis-aligned bounding box B, extend each rectangle in only one of the four directions: up, down, left, or right until it reaches B and the density k is minimized, where k is the maximum number of extensions of rectangles to the boundary that pass through a point inside bounding box B. REP is NP-hard for k>1. If the rectangles are points of a grid (or unit squares of a grid), the problem is called the square escape problem (SEP) and it is still NP-hard. We give a 2-approximation algorithm for SEP with kgeq2 with time complexity O(n^{3/2}k^2). This improves the time complexity of existing algorithms which are at least quadratic. Also, the approximation ratio of our algorithm for kgeq 3 is 3/2 which is tight. We also give a 8-approximation algorithm for REP with time complexity O(nlog n+nk) and give a MPC version of this algorithm for k=O(1) which is the first parallel algorithm for this problem.

Several approaches are proposed to deal with the problem of the Automatic Schema Matching (ASM). The challenges and difficulties caused by the complexity and uncertainty characterizing both the process and the outcome of Schema Matching motivated us to investigate how bio-inspired emerging paradigm can help with understanding, managing, and ultimately overcoming those challenges. In this paper, we explain how we approached Automatic Schema Matching as a systemic and Complex Adaptive System (CAS) and how we modeled it using the approach of Agent-Based Modeling and Simulation (ABMS). This effort gives birth to a tool (prototype) for schema matching called Reflex-SMAS. A set of experiments demonstrates the viability of our approach on two main aspects: (i) effectiveness (increasing the quality of the found matchings) and (ii) efficiency (reducing the effort required for this efficiency). Our approach represents a significant paradigm-shift, in the field of Automatic Schema Matching.

Visual mathematical reasoning, as a fundamental visual reasoning ability, has received widespread attention from the Large Multimodal Models (LMMs) community. Existing benchmarks, such as MathVista and MathVerse, focus more on the result-oriented performance but neglect the underlying principles in knowledge acquisition and generalization. Inspired by human-like mathematical reasoning, we introduce WE-MATH, the first benchmark specifically designed to explore the problem-solving principles beyond end-to-end performance. We meticulously collect and categorize 6.5K visual math problems, spanning 67 hierarchical knowledge concepts and five layers of knowledge granularity. We decompose composite problems into sub-problems according to the required knowledge concepts and introduce a novel four-dimensional metric, namely Insufficient Knowledge (IK), Inadequate Generalization (IG), Complete Mastery (CM), and Rote Memorization (RM), to hierarchically assess inherent issues in LMMs' reasoning process. With WE-MATH, we conduct a thorough evaluation of existing LMMs in visual mathematical reasoning and reveal a negative correlation between solving steps and problem-specific performance. We confirm the IK issue of LMMs can be effectively improved via knowledge augmentation strategies. More notably, the primary challenge of GPT-4o has significantly transitioned from IK to IG, establishing it as the first LMM advancing towards the knowledge generalization stage. In contrast, other LMMs exhibit a marked inclination towards Rote Memorization - they correctly solve composite problems involving multiple knowledge concepts yet fail to answer sub-problems. We anticipate that WE-MATH will open new pathways for advancements in visual mathematical reasoning for LMMs. The WE-MATH data and evaluation code are available at https://github.com/We-Math/We-Math.

Large Language Models (LLMs) have made notable progress in mathematical reasoning, yet they often rely on single-paradigm reasoning that limits their effectiveness across diverse tasks. In this paper, we introduce Chain-of-Reasoning (CoR), a novel unified framework that integrates multiple reasoning paradigms--Natural Language Reasoning (NLR), Algorithmic Reasoning (AR), and Symbolic Reasoning (SR)--to enable synergistic collaboration. CoR generates multiple potential answers using different reasoning paradigms and synthesizes them into a coherent final solution. We propose a Progressive Paradigm Training (PPT) strategy that allows models to progressively master these paradigms, culminating in the development of CoR-Math-7B. Experimental results demonstrate that CoR-Math-7B significantly outperforms current SOTA models, achieving up to a 41.0% absolute improvement over GPT-4 in theorem proving tasks and a 7.9% improvement over RL-based methods in arithmetic tasks. These results showcase the enhanced mathematical comprehensive ability of our model, achieving significant performance gains on specific tasks and enabling zero-shot generalization across tasks.

In this work, we focus on the problem of retrieving relevant arguments for a query claim covering diverse aspects. State-of-the-art methods rely on explicit mappings between claims and premises, and thus are unable to utilize large available collections of premises without laborious and costly manual annotation. Their diversity approach relies on removing duplicates via clustering which does not directly ensure that the selected premises cover all aspects. This work introduces a new multi-step approach for the argument retrieval problem. Rather than relying on ground-truth assignments, our approach employs a machine learning model to capture semantic relationships between arguments. Beyond that, it aims to cover diverse facets of the query, instead of trying to identify duplicates explicitly. Our empirical evaluation demonstrates that our approach leads to a significant improvement in the argument retrieval task even though it requires less data.

Vehicle Routing Problems (VRP) are an extension of the Traveling Salesperson Problem and are a fundamental NP-hard challenge in combinatorial optimization. Solving VRP in real-time at large scale has become critical in numerous applications, from growing markets like last-mile delivery to emerging use-cases like interactive logistics planning. Such applications involve solving similar problem instances repeatedly, yet current state-of-the-art solvers treat each instance on its own without leveraging previous examples. We introduce a novel optimization framework that uses a reinforcement learning agent - trained on prior instances - to quickly generate initial solutions, which are then further optimized by genetic algorithms. Our framework, Evolutionary Algorithm with Reinforcement Learning Initialization (EARLI), consistently outperforms current state-of-the-art solvers across various time scales. For example, EARLI handles vehicle routing with 500 locations within 1s, 10x faster than current solvers for the same solution quality, enabling applications like real-time and interactive routing. EARLI can generalize to new data, as demonstrated on real e-commerce delivery data of a previously unseen city. Our hybrid framework presents a new way to combine reinforcement learning and genetic algorithms, paving the road for closer interdisciplinary collaboration between AI and optimization communities towards real-time optimization in diverse domains.

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, including mathematical reasoning. However, the current evaluation mostly focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing or contradictory conditions, known as ill-defined problems. To further study this problem, we develop a largescale benchmark called Problems with Missing and Contradictory conditions ( PMC) containing over 5,000 validated ill-defined mathematical problems. Our preliminary experiments through PMC reveal two challenges about existing methods: (1) traditional methods exhibit a trade-off between solving accuracy and rejection capabilities, and (2) formal methods struggle with modeling complex problems. To address these challenges, We develop Variable-Constraint Search (VCSEARCH), a trainingfree framework that leverages formal language to detect ill-defined problems, where a variableconstraint pair search strategy is incorporated to improve the modeling capability of formal language. Extensive experiments demonstrate that VCSEARCH improves the accuracy of identifying unsolvable problems by at least 12% across different LLMs, thus achieving stronger robust mathematical reasoning ability.

Conformant planning is the problem of finding a sequence of actions for achieving a goal in the presence of uncertainty in the initial state or action effects. The problem has been approached as a path-finding problem in belief space where good belief representations and heuristics are critical for scaling up. In this work, a different formulation is introduced for conformant problems with deterministic actions where they are automatically converted into classical ones and solved by an off-the-shelf classical planner. The translation maps literals L and sets of assumptions t about the initial situation, into new literals KL/t that represent that L must be true if t is initially true. We lay out a general translation scheme that is sound and establish the conditions under which the translation is also complete. We show that the complexity of the complete translation is exponential in a parameter of the problem called the conformant width, which for most benchmarks is bounded. The planner based on this translation exhibits good performance in comparison with existing planners, and is the basis for T0, the best performing planner in the Conformant Track of the 2006 International Planning Competition.

The Multi-Agent Pathfinding (MAPF) problem involves finding a set of conflict-free paths for a group of agents confined to a graph. In typical MAPF scenarios, the graph and the agents' starting and ending vertices are known beforehand, allowing the use of centralized planning algorithms. However, in this study, we focus on the decentralized MAPF setting, where the agents may observe the other agents only locally and are restricted in communications with each other. Specifically, we investigate the lifelong variant of MAPF, where new goals are continually assigned to the agents upon completion of previous ones. Drawing inspiration from the successful AlphaZero approach, we propose a decentralized multi-agent Monte Carlo Tree Search (MCTS) method for MAPF tasks. Our approach utilizes the agent's observations to recreate the intrinsic Markov decision process, which is then used for planning with a tailored for multi-agent tasks version of neural MCTS. The experimental results show that our approach outperforms state-of-the-art learnable MAPF solvers. The source code is available at https://github.com/AIRI-Institute/mats-lp.

In the landscape of publicly available patent retrieval datasets, the need for explicit indomain and out-of-domain labeling, multi-jurisdiction coverage, balanced query domain representation and manageable sizes that support sub document level experiments on moderate computational resources is often overlooked. To address these gaps, we propose DAPFAM, a new open access domain-aware patent retrieval dataset constructed at the simple-family level. The dataset contains 1,247 domain balanced full text query families and 45,336 full text target families. The dataset is enriched by clear relevance judgments (forward/backward citations as positive links, random negatives), as well as explicit in-domain or out-of-domain relationships via a novel proposed labelling scheme based on via International Patent Classification (IPC) codes, resulting in 49,869 evaluation pairs. The dataset is multi jurisdictional, requires little to no preprocessing for retrieval evaluation, and remains of a size manageable for entities with limited ressources allowing for sub document level retrieval experiments without excessive computational costs. We describe our three-step data-curation pipeline, present comprehensive dataset statistics, and provide baseline experiments using lexical and neural retrieval methods. Our baseline experiments highlight significant challenges in crossdomain patent retrieval. The dataset will be publicly available (for now the access link is this repository: https://osf.io/vbyzd/?view_only=1a40242e0d1941a58aa854af3e50cf6b).

Recently, a large amount of work has focused on improving large language models' (LLMs') performance on reasoning benchmarks such as math and logic. However, past work has largely assumed that tasks are well-defined. In the real world, queries to LLMs are often underspecified, only solvable through acquiring missing information. We formalize this as a constraint satisfaction problem (CSP) with missing variable assignments. Using a special case of this formalism where only one necessary variable assignment is missing, we can rigorously evaluate an LLM's ability to identify the minimal necessary question to ask and quantify axes of difficulty levels for each problem. We present QuestBench, a set of underspecified reasoning tasks solvable by asking at most one question, which includes: (1) Logic-Q: Logical reasoning tasks with one missing proposition, (2) Planning-Q: PDDL planning problems with initial states that are partially-observed, (3) GSM-Q: Human-annotated grade school math problems with one missing variable assignment, and (4) GSME-Q: a version of GSM-Q where word problems are translated into equations by human annotators. The LLM is tasked with selecting the correct clarification question(s) from a list of options. While state-of-the-art models excel at GSM-Q and GSME-Q, their accuracy is only 40-50% on Logic-Q and Planning-Q. Analysis demonstrates that the ability to solve well-specified reasoning problems may not be sufficient for success on our benchmark: models have difficulty identifying the right question to ask, even when they can solve the fully specified version of the problem. Furthermore, in the Planning-Q domain, LLMs tend not to hedge, even when explicitly presented with the option to predict ``not sure.'' This highlights the need for deeper investigation into models' information acquisition capabilities.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

Large language model (LLM) performance on reasoning problems typically does not generalize out of distribution. Previous work has claimed that this can be mitigated by modifying prompts to include examples with chains of thought--demonstrations of solution procedures--with the intuition that it is possible to in-context teach an LLM an algorithm for solving the problem. This paper presents a case study of chain of thought on problems from Blocksworld, a classical planning domain, and examine the performance of two state-of-the-art LLMs across two axes: generality of examples given in prompt, and complexity of problems queried with each prompt. While our problems are very simple, we only find meaningful performance improvements from chain of thought prompts when those prompts are exceedingly specific to their problem class, and that those improvements quickly deteriorate as the size n of the query-specified stack grows past the size of stacks shown in the examples. Our results hint that, contrary to previous claims in the literature, CoT's performance improvements do not stem from the model learning general algorithmic procedures via demonstrations and depend on carefully engineering highly problem specific prompts. This spotlights drawbacks of chain of thought, especially because of the sharp tradeoff between possible performance gains and the amount of human labor necessary to generate examples with correct reasoning traces.

A spanning tree T of graph G is a rho-approximate universal Steiner tree (UST) for root vertex r if, for any subset of vertices S containing r, the cost of the minimal subgraph of T connecting S is within a rho factor of the minimum cost tree connecting S in G. Busch et al. (FOCS 2012) showed that every graph admits 2^{O(log n)}-approximate USTs by showing that USTs are equivalent to strong sparse partition hierarchies (up to poly-logs). Further, they posed poly-logarithmic USTs and strong sparse partition hierarchies as open questions. We settle these open questions by giving polynomial-time algorithms for computing both O(log ^ 7 n)-approximate USTs and poly-logarithmic strong sparse partition hierarchies. For graphs with constant doubling dimension or constant pathwidth we improve this to O(log n)-approximate USTs and O(1) strong sparse partition hierarchies. Our doubling dimension result is tight up to second order terms. We reduce the existence of these objects to the previously studied cluster aggregation problem and what we call dangling nets.

We introduce a large-scale dataset of math word problems and an interpretable neural math problem solver that learns to map problems to operation programs. Due to annotation challenges, current datasets in this domain have been either relatively small in scale or did not offer precise operational annotations over diverse problem types. We introduce a new representation language to model precise operation programs corresponding to each math problem that aim to improve both the performance and the interpretability of the learned models. Using this representation language, our new dataset, MathQA, significantly enhances the AQuA dataset with fully-specified operational programs. We additionally introduce a neural sequence-to-program model enhanced with automatic problem categorization. Our experiments show improvements over competitive baselines in our MathQA as well as the AQuA dataset. The results are still significantly lower than human performance indicating that the dataset poses new challenges for future research. Our dataset is available at: https://math-qa.github.io/math-QA/

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al.(2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has mathcal{O}(H^3S^2A/varepsilon^2) sample complexity thus improving the varepsilon-dependence upon existing results, where S is a number of states, A is a number of actions, H is an episode length, and varepsilon is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order mathcal{O}(poly(S,A,H)/varepsilon). Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to mathcal{O}(H^2SA/varepsilon^2), yielding a statistical separation between maximum entropy exploration and reward-free exploration.

We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing and bioinformatics, and in particular, matching graphs with inherent community structure has significance related to de-anonymization of correlated social networks. Compared to the correlated Erdos-Renyi (ER) model, where various efficient algorithms have been developed, among which a few algorithms have been proven to achieve the exact matching with constant edge correlation, no low-order polynomial algorithm has been known to achieve exact matching for the correlated SBMs with constant correlation. In this work, we propose an efficient algorithm for matching graphs with community structure, based on the comparison between partition trees rooted from each vertex, by extending the idea of Mao et al. (2021) to graphs with communities. The partition tree divides the large neighborhoods of each vertex into disjoint subsets using their edge statistics to different communities. Our algorithm is the first low-order polynomial-time algorithm achieving exact matching between two correlated SBMs with high probability in dense graphs.

Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting finite-sum structure, which generically arises in empirical variants of learning problems in these contexts. Further, methods with computable approximation errors are highly desirable, as they provide verifiable exit criteria. Motivated by these applications, we study finite-sum monotone inclusion problems, which model broad classes of equilibrium problems. Our main contributions are variants of the classical Halpern iteration that employ variance reduction to obtain improved complexity guarantees in which n component operators in the finite sum are ``on average'' either cocoercive or Lipschitz continuous and monotone, with parameter L. The resulting oracle complexity of our methods, which provide guarantees for the last iterate and for a (computable) operator norm residual, is mathcal{O}( n + nLvarepsilon^{-1}), which improves upon existing methods by a factor up to n. This constitutes the first variance reduction-type result for general finite-sum monotone inclusions and for more specific problems such as convex-concave optimization when operator norm residual is the optimality measure. We further argue that, up to poly-logarithmic factors, this complexity is unimprovable in the monotone Lipschitz setting; i.e., the provided result is near-optimal.

The Brownian sphere is a random metric space, homeomorphic to the two-dimensional sphere, which arises as the universal scaling limit of many types of random planar maps. The direct construction of the Brownian sphere is via a continuous analogue of the Cori--Vauquelin--Schaeffer (CVS) bijection. The CVS bijection maps labeled trees to planar maps, and the continuous version maps Aldous' continuum random tree with Brownian labels (the Brownian snake) to the Brownian sphere. In this work, we describe the inverse of the continuous CVS bijection, by constructing the Brownian snake as a measurable function of the Brownian sphere. Special care is needed to work with the orientation of the Brownian sphere.

The deployment and training of neural networks on edge computing devices pose many challenges. The low memory nature of edge devices is often one of the biggest limiting factors encountered in the deployment of large neural network models. Tensor rematerialization or recompute is a way to address high memory requirements for neural network training and inference. In this paper we consider the problem of execution time minimization of compute graphs subject to a memory budget. In particular, we develop a new constraint programming formulation called Moccasin with only O(n) integer variables, where n is the number of nodes in the compute graph. This is a significant improvement over the works in the recent literature that propose formulations with O(n^2) Boolean variables. We present numerical studies that show that our approach is up to an order of magnitude faster than recent work especially for large-scale graphs.

Proving geometric theorems constitutes a hallmark of visual reasoning combining both intuitive and logical skills. Therefore, automated theorem proving of Olympiad-level geometry problems is considered a notable milestone in human-level automated reasoning. The introduction of AlphaGeometry, a neuro-symbolic model trained with 100 million synthetic samples, marked a major breakthrough. It solved 25 of 30 International Mathematical Olympiad (IMO) problems whereas the reported baseline based on Wu's method solved only ten. In this note, we revisit the IMO-AG-30 Challenge introduced with AlphaGeometry, and find that Wu's method is surprisingly strong. Wu's method alone can solve 15 problems, and some of them are not solved by any of the other methods. This leads to two key findings: (i) Combining Wu's method with the classic synthetic methods of deductive databases and angle, ratio, and distance chasing solves 21 out of 30 methods by just using a CPU-only laptop with a time limit of 5 minutes per problem. Essentially, this classic method solves just 4 problems less than AlphaGeometry and establishes the first fully symbolic baseline strong enough to rival the performance of an IMO silver medalist. (ii) Wu's method even solves 2 of the 5 problems that AlphaGeometry failed to solve. Thus, by combining AlphaGeometry with Wu's method we set a new state-of-the-art for automated theorem proving on IMO-AG-30, solving 27 out of 30 problems, the first AI method which outperforms an IMO gold medalist.

OpenStreetMap (OSM) is currently the richest publicly available information source on geographic entities (e.g., buildings and roads) worldwide. However, using OSM entities in machine learning models and other applications is challenging due to the large scale of OSM, the extreme heterogeneity of entity annotations, and a lack of a well-defined ontology to describe entity semantics and properties. This paper presents GeoVectors - a unique, comprehensive world-scale linked open corpus of OSM entity embeddings covering the entire OSM dataset and providing latent representations of over 980 million geographic entities in 180 countries. The GeoVectors corpus captures semantic and geographic dimensions of OSM entities and makes these entities directly accessible to machine learning algorithms and semantic applications. We create a semantic description of the GeoVectors corpus, including identity links to the Wikidata and DBpedia knowledge graphs to supply context information. Furthermore, we provide a SPARQL endpoint - a semantic interface that offers direct access to the semantic and latent representations of geographic entities in OSM.

Inventory Routing Problem (IRP) is a crucial challenge in supply chain management as it involves optimizing efficient route selection while considering the uncertainty of inventory demand planning. To solve IRPs, usually a two-stage approach is employed, where demand is predicted using machine learning techniques first, and then an optimization algorithm is used to minimize routing costs. Our experiment shows machine learning models fall short of achieving perfect accuracy because inventory levels are influenced by the dynamic business environment, which, in turn, affects the optimization problem in the next stage, resulting in sub-optimal decisions. In this paper, we formulate and propose a decision-focused learning-based approach to solving real-world IRPs. This approach directly integrates inventory prediction and routing optimization within an end-to-end system potentially ensuring a robust supply chain strategy.

This paper develops a new mathematical-statistical approach to analyze a class of Flajolet-Martin algorithms (FMa), and provides analytical confidence intervals for the number F0 of distinct elements in a stream, based on Chernoff bounds. The class of FMa has reached a significant popularity in bigdata stream learning, and the attention of the literature has mainly been based on algorithmic aspects, basically complexity optimality, while the statistical analysis of these class of algorithms has been often faced heuristically. The analysis provided here shows deep connections with mathematical special functions and with extreme value theory. The latter connection may help in explaining heuristic considerations, while the first opens many numerical issues, faced at the end of the present paper. Finally, the algorithms are tested on an anonymized real data stream and MonteCarlo simulations are provided to support our analytical choice in this context.

In this paper, we propose a new class of metric for table structure recognition (TSR) evaluation, called grid table similarity (GriTS). Unlike prior metrics, GriTS evaluates the correctness of a predicted table directly in its natural form as a matrix. To create a similarity measure between matrices, we generalize the two-dimensional largest common substructure (2D-LCS) problem, which is NP-hard, to the 2D most similar substructures (2D-MSS) problem and propose a polynomial-time heuristic for solving it. This algorithm produces both an upper and a lower bound on the true similarity between matrices. We show using evaluation on a large real-world dataset that in practice there is almost no difference between these bounds. We compare GriTS to other metrics and empirically validate that matrix similarity exhibits more desirable behavior than alternatives for TSR performance evaluation. Finally, GriTS unifies all three subtasks of cell topology recognition, cell location recognition, and cell content recognition within the same framework, which simplifies the evaluation and enables more meaningful comparisons across different types of TSR approaches. Code will be released at https://github.com/microsoft/table-transformer.

MDPs with low-rank transitions -- that is, the transition matrix can be factored into the product of two matrices, left and right -- is a highly representative structure that enables tractable learning. The left matrix enables expressive function approximation for value-based learning and has been studied extensively. In this work, we instead investigate sample-efficient learning with density features, i.e., the right matrix, which induce powerful models for state-occupancy distributions. This setting not only sheds light on leveraging unsupervised learning in RL, but also enables plug-in solutions for convex RL. In the offline setting, we propose an algorithm for off-policy estimation of occupancies that can handle non-exploratory data. Using this as a subroutine, we further devise an online algorithm that constructs exploratory data distributions in a level-by-level manner. As a central technical challenge, the additive error of occupancy estimation is incompatible with the multiplicative definition of data coverage. In the absence of strong assumptions like reachability, this incompatibility easily leads to exponential error blow-up, which we overcome via novel technical tools. Our results also readily extend to the representation learning setting, when the density features are unknown and must be learned from an exponentially large candidate set.

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its reconstruction error via connections to higher-order singular values. Specifically, we introduce a novel Tucker packing problem, which we prove is NP-hard, and give a polynomial-time approximation scheme based on a reduction to the 2-dimensional knapsack problem with a matroid constraint. We also generalize our techniques to tree tensor network decompositions. We implement our algorithm using an integer programming solver, and show that its solution quality is competitive with (and sometimes better than) the greedy algorithm that uses the true Tucker decomposition loss at each step, while also running up to 1000x faster.

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often effective to incorporate global topological features, which are typically extracted by persistent homology. In the calculation of persistent homology for a point cloud, we choose a filtration for the point cloud, an increasing sequence of spaces. Since the performance of machine learning methods combined with persistent homology is highly affected by the choice of a filtration, we need to tune it depending on data and tasks. In this paper, we propose a framework that learns a filtration adaptively with the use of neural networks. In order to make the resulting persistent homology isometry-invariant, we develop a neural network architecture with such invariance. Additionally, we show a theoretical result on a finite-dimensional approximation of filtration functions, which justifies the proposed network architecture. Experimental results demonstrated the efficacy of our framework in several classification tasks.

We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and information present from past problems to rapidly predict and solve new problems. Otherwise, standard methods ignore the knowledge of the past solutions and suboptimally re-solve each problem from scratch. We instantiate Meta OT models in discrete and continuous settings between grayscale images, spherical data, classification labels, and color palettes and use them to improve the computational time of standard OT solvers. Our source code is available at http://github.com/facebookresearch/meta-ot

A key to knowledge graph embedding (KGE) is to choose a proper representation space, e.g., point-wise Euclidean space and complex vector space. In this paper, we propose a unified perspective of embedding and introduce uncertainty into KGE from the view of group theory. Our model can incorporate existing models (i.e., generality), ensure the computation is tractable (i.e., efficiency) and enjoy the expressive power of complex random variables (i.e., expressiveness). The core idea is that we embed entities/relations as elements of a symmetric group, i.e., permutations of a set. Permutations of different sets can reflect different properties of embedding. And the group operation of symmetric groups is easy to compute. In specific, we show that the embedding of many existing models, point vectors, can be seen as elements of a symmetric group. To reflect uncertainty, we first embed entities/relations as permutations of a set of random variables. A permutation can transform a simple random variable into a complex random variable for greater expressiveness, called a normalizing flow. We then define scoring functions by measuring the similarity of two normalizing flows, namely NFE. We construct several instantiating models and prove that they are able to learn logical rules. Experimental results demonstrate the effectiveness of introducing uncertainty and our model. The code is available at https://github.com/changyi7231/NFE.

Designing a single model to address multiple tasks has been a long-standing objective in artificial intelligence. Recently, large language models have demonstrated exceptional capability in solving different tasks within the language domain. However, a unified model for various graph tasks remains underexplored, primarily due to the challenges unique to the graph learning domain. First, graph data from different areas carry distinct attributes and follow different distributions. Such discrepancy makes it hard to represent graphs in a single representation space. Second, tasks on graphs diversify into node, link, and graph tasks, requiring distinct embedding strategies. Finally, an appropriate graph prompting paradigm for in-context learning is unclear. We propose One for All (OFA), the first general framework that can use a single graph model to address the above challenges. Specifically, OFA proposes text-attributed graphs to unify different graph data by describing nodes and edges with natural language and uses language models to encode the diverse and possibly cross-domain text attributes to feature vectors in the same embedding space. Furthermore, OFA introduces the concept of nodes-of-interest to standardize different tasks with a single task representation. For in-context learning on graphs, OFA introduces a novel graph prompting paradigm that appends prompting substructures to the input graph, which enables it to address varied tasks without fine-tuning. We train the OFA model using graph data from multiple domains (including citation networks, molecular graphs, knowledge graphs, etc.) simultaneously and evaluate its ability in supervised, few-shot, and zero-shot learning scenarios. OFA performs well across different tasks, making it the first general-purpose across-domains classification model on graphs.

Training monolingual language models for low and mid-resource languages is made challenging by limited and often inadequate pretraining data. In this study, we propose a novel model conversion strategy to address this issue, adapting high-resources monolingual language models to a new target language. By generalizing over a word translation dictionary encompassing both the source and target languages, we map tokens from the target tokenizer to semantically similar tokens from the source language tokenizer. This one-to-many token mapping improves tremendously the initialization of the embedding table for the target language. We conduct experiments to convert high-resource models to mid- and low-resource languages, namely Dutch and Frisian. These converted models achieve a new state-of-the-art performance on these languages across all sorts of downstream tasks. By reducing significantly the amount of data and time required for training state-of-the-art models, our novel model conversion strategy has the potential to benefit many languages worldwide.

Business Intelligence (BI) is crucial in modern enterprises and billion-dollar business. Traditionally, technical experts like database administrators would manually prepare BI-models (e.g., in star or snowflake schemas) that join tables in data warehouses, before less-technical business users can run analytics using end-user dashboarding tools. However, the popularity of self-service BI (e.g., Tableau and Power-BI) in recent years creates a strong demand for less technical end-users to build BI-models themselves. We develop an Auto-BI system that can accurately predict BI models given a set of input tables, using a principled graph-based optimization problem we propose called k-Min-Cost-Arborescence (k-MCA), which holistically considers both local join prediction and global schema-graph structures, leveraging a graph-theoretical structure called arborescence. While we prove k-MCA is intractable and inapproximate in general, we develop novel algorithms that can solve k-MCA optimally, which is shown to be efficient in practice with sub-second latency and can scale to the largest BI-models we encounter (with close to 100 tables). Auto-BI is rigorously evaluated on a unique dataset with over 100K real BI models we harvested, as well as on 4 popular TPC benchmarks. It is shown to be both efficient and accurate, achieving over 0.9 F1-score on both real and synthetic benchmarks.

We propose Hydra-MDP, a novel paradigm employing multiple teachers in a teacher-student model. This approach uses knowledge distillation from both human and rule-based teachers to train the student model, which features a multi-head decoder to learn diverse trajectory candidates tailored to various evaluation metrics. With the knowledge of rule-based teachers, Hydra-MDP learns how the environment influences the planning in an end-to-end manner instead of resorting to non-differentiable post-processing. This method achieves the 1^{st} place in the Navsim challenge, demonstrating significant improvements in generalization across diverse driving environments and conditions. More details by visiting https://github.com/NVlabs/Hydra-MDP.

Recently, Qiao, Duan, and Cheng~(2019) proposed a distributed nearest-neighbor classification method, in which a massive dataset is split into smaller groups, each processed with a k-nearest-neighbor classifier, and the final class label is predicted by a majority vote among these groupwise class labels. This paper shows that the distributed algorithm with k=1 over a sufficiently large number of groups attains a minimax optimal error rate up to a multiplicative logarithmic factor under some regularity conditions, for both regression and classification problems. Roughly speaking, distributed 1-nearest-neighbor rules with M groups has a performance comparable to standard Theta(M)-nearest-neighbor rules. In the analysis, alternative rules with a refined aggregation method are proposed and shown to attain exact minimax optimal rates.

In this case study, the renowned Travelling Salesmen problem has been studied. Travelling Salesman problem is a most demanding computational problem in Computer Science. The Travelling Salesmen problem has been solved by two different ways using Hopfield Network. The main theory of the problem is to find distance and connectedness between nodes in a graph having edges between the nodes. The basic algorithm used for this problem is Djikstra's Algorithm. But till now , a number of such algorithms have evolved. Among them(some other algorithms) , are distinct and have been proved to solve the travelling salesmen problem by graph theory.

Algorithm configuration (AC) is concerned with the automated search of the most suitable parameter configuration of a parametrized algorithm. There is currently a wide variety of AC problem variants and methods proposed in the literature. Existing reviews do not take into account all derivatives of the AC problem, nor do they offer a complete classification scheme. To this end, we introduce taxonomies to describe the AC problem and features of configuration methods, respectively. We review existing AC literature within the lens of our taxonomies, outline relevant design choices of configuration approaches, contrast methods and problem variants against each other, and describe the state of AC in industry. Finally, our review provides researchers and practitioners with a look at future research directions in the field of AC.

In this paper, we revisit one of the simplest problems in data structures: the task of inserting elements into an open-addressed hash table so that elements can later be retrieved with as few probes as possible. We show that, even without reordering elements over time, it is possible to construct a hash table that achieves far better expected search complexities (both amortized and worst-case) than were previously thought possible. Along the way, we disprove the central conjecture left by Yao in his seminal paper ``Uniform Hashing is Optimal''. All of our results come with matching lower bounds.

Despite the considerable progress in automatic abdominal multi-organ segmentation from CT/MRI scans in recent years, a comprehensive evaluation of the models' capabilities is hampered by the lack of a large-scale benchmark from diverse clinical scenarios. Constraint by the high cost of collecting and labeling 3D medical data, most of the deep learning models to date are driven by datasets with a limited number of organs of interest or samples, which still limits the power of modern deep models and makes it difficult to provide a fully comprehensive and fair estimate of various methods. To mitigate the limitations, we present AMOS, a large-scale, diverse, clinical dataset for abdominal organ segmentation. AMOS provides 500 CT and 100 MRI scans collected from multi-center, multi-vendor, multi-modality, multi-phase, multi-disease patients, each with voxel-level annotations of 15 abdominal organs, providing challenging examples and test-bed for studying robust segmentation algorithms under diverse targets and scenarios. We further benchmark several state-of-the-art medical segmentation models to evaluate the status of the existing methods on this new challenging dataset. We have made our datasets, benchmark servers, and baselines publicly available, and hope to inspire future research. Information can be found at https://amos22.grand-challenge.org.

In recent years, persistent homology (PH) has been successfully applied to real-world data in many different settings. Despite significant computational advances, PH algorithms do not yet scale to large datasets preventing interesting applications. One approach to address computational issues posed by PH is to select a set of landmarks by subsampling from the data. Currently, these landmark points are chosen either at random or using the maxmin algorithm. Neither is ideal as random selection tends to favour dense areas of the data while the maxmin algorithm is very sensitive to noise. Here, we propose a novel approach to select landmarks specifically for PH that preserves coarse topological information of the original dataset. Our method is motivated by the Mayer-Vietoris sequence and requires only local PH computation thus enabling efficient computation. We test our landmarks on artificial datasets which contain different levels of noise and compare them to standard landmark selection techniques. We demonstrate that our landmark selection outperforms standard methods as well as a subsampling technique based on an outlier-robust version of the k--means algorithm for low sampling densities in noisy data with respect to robustness to outliers.

Scaling laws for inference compute in multi-agent systems remain under-explored compared to single-agent scenarios. This work aims to bridge this gap by investigating the problem of data synthesis through multi-agent sampling, where synthetic responses are generated by sampling from multiple distinct language models. Effective model coordination is crucial for successful multi-agent collaboration. Unlike previous approaches that rely on fixed workflows, we treat model coordination as a multi-step decision-making process, optimizing generation structures dynamically for each input question. We introduce Tree Search-based Orchestrated Agents~(TOA), where the workflow evolves iteratively during the sequential sampling process. To achieve this, we leverage Monte Carlo Tree Search (MCTS), integrating a reward model to provide real-time feedback and accelerate exploration. Our experiments on alignment, machine translation, and mathematical reasoning demonstrate that multi-agent sampling significantly outperforms single-agent sampling as inference compute scales. TOA is the most compute-efficient approach, achieving SOTA performance on WMT and a 71.8\% LC win rate on AlpacaEval. Moreover, fine-tuning with our synthesized alignment data surpasses strong preference learning methods on challenging benchmarks such as Arena-Hard and AlpacaEval.

We study multi-agent reinforcement learning (MARL) for the general-sum Markov Games (MGs) under the general function approximation. In order to find the minimum assumption for sample-efficient learning, we introduce a novel complexity measure called the Multi-Agent Decoupling Coefficient (MADC) for general-sum MGs. Using this measure, we propose the first unified algorithmic framework that ensures sample efficiency in learning Nash Equilibrium, Coarse Correlated Equilibrium, and Correlated Equilibrium for both model-based and model-free MARL problems with low MADC. We also show that our algorithm provides comparable sublinear regret to the existing works. Moreover, our algorithm combines an equilibrium-solving oracle with a single objective optimization subprocedure that solves for the regularized payoff of each deterministic joint policy, which avoids solving constrained optimization problems within data-dependent constraints (Jin et al. 2020; Wang et al. 2023) or executing sampling procedures with complex multi-objective optimization problems (Foster et al. 2023), thus being more amenable to empirical implementation.

LLMs exhibit advanced reasoning capabilities, offering the potential to transform natural language questions into mathematical models. However, existing open-source datasets in operations research domain lack detailed annotations of the modeling process, such as variable definitions, focusing solely on objective values, which hinders reinforcement learning applications. To address this, we release the StructuredOR dataset, annotated with comprehensive labels that capture the complete mathematical modeling process. We further propose BPP-Search, a algorithm that integrates reinforcement learning into a tree-of-thought structure using Beam search, a Process reward model, and a pairwise Preference algorithm. This approach enables efficient exploration of tree structures, avoiding exhaustive search while improving accuracy. Extensive experiments on StructuredOR, NL4OPT, and MAMO-ComplexLP datasets show that BPP-Search significantly outperforms state-of-the-art methods. In tree-based reasoning, BPP-Search excels in accuracy and efficiency, enabling faster retrieval of correct solutions.

Traditional Learning-To-Rank (LETOR) approaches, including pairwise methods like RankNet and LambdaMART, often fall short by solely focusing on pairwise comparisons, leading to sub-optimal global rankings. Conversely, deep learning based listwise methods, while aiming to optimise entire lists, require complex tuning and yield only marginal improvements over robust pairwise models. To overcome these limitations, we introduce Travelling Salesman Problem Rank (TSPRank), a hybrid pairwise-listwise ranking method. TSPRank reframes the ranking problem as a Travelling Salesman Problem (TSP), a well-known combinatorial optimisation challenge that has been extensively studied for its numerous solution algorithms and applications. This approach enables the modelling of pairwise relationships and leverages combinatorial optimisation to determine the listwise ranking. This approach can be directly integrated as an additional component into embeddings generated by existing backbone models to enhance ranking performance. Our extensive experiments across three backbone models on diverse tasks, including stock ranking, information retrieval, and historical events ordering, demonstrate that TSPRank significantly outperforms both pure pairwise and listwise methods. Our qualitative analysis reveals that TSPRank's main advantage over existing methods is its ability to harness global information better while ranking. TSPRank's robustness and superior performance across different domains highlight its potential as a versatile and effective LETOR solution.

The concept of causal abstraction got recently popularised to demystify the opaque decision-making processes of machine learning models; in short, a neural network can be abstracted as a higher-level algorithm if there exists a function which allows us to map between them. Notably, most interpretability papers implement these maps as linear functions, motivated by the linear representation hypothesis: the idea that features are encoded linearly in a model's representations. However, this linearity constraint is not required by the definition of causal abstraction. In this work, we critically examine the concept of causal abstraction by considering arbitrarily powerful alignment maps. In particular, we prove that under reasonable assumptions, any neural network can be mapped to any algorithm, rendering this unrestricted notion of causal abstraction trivial and uninformative. We complement these theoretical findings with empirical evidence, demonstrating that it is possible to perfectly map models to algorithms even when these models are incapable of solving the actual task; e.g., on an experiment using randomly initialised language models, our alignment maps reach 100% interchange-intervention accuracy on the indirect object identification task. This raises the non-linear representation dilemma: if we lift the linearity constraint imposed to alignment maps in causal abstraction analyses, we are left with no principled way to balance the inherent trade-off between these maps' complexity and accuracy. Together, these results suggest an answer to our title's question: causal abstraction is not enough for mechanistic interpretability, as it becomes vacuous without assumptions about how models encode information. Studying the connection between this information-encoding assumption and causal abstraction should lead to exciting future work.

Geometric ability is a significant challenge for large language models (LLMs) due to the need for advanced spatial comprehension and abstract thinking. Existing datasets primarily evaluate LLMs on their final answers, but they cannot truly measure their true understanding of geometric structures, as LLMs can arrive at correct answers by coincidence. To fill this gap, we introduce the GeomRel dataset, designed to evaluate LLMs' understanding of geometric structures by isolating the core step of geometric relationship identification in problem-solving. Using this benchmark, we conduct thorough evaluations of diverse LLMs and identify key limitations in understanding geometric structures. We further propose the Geometry Chain-of-Thought (GeoCoT) method, which enhances LLMs' ability to identify geometric relationships, resulting in significant performance improvements.

A major barrier to deploying current machine learning models lies in their non-reliability to dataset shifts. To resolve this problem, most existing studies attempted to transfer stable information to unseen environments. Particularly, independent causal mechanisms-based methods proposed to remove mutable causal mechanisms via the do-operator. Compared to previous methods, the obtained stable predictors are more effective in identifying stable information. However, a key question remains: which subset of this whole stable information should the model transfer, in order to achieve optimal generalization ability? To answer this question, we present a comprehensive minimax analysis from a causal perspective. Specifically, we first provide a graphical condition for the whole stable set to be optimal. When this condition fails, we surprisingly find with an example that this whole stable set, although can fully exploit stable information, is not the optimal one to transfer. To identify the optimal subset under this case, we propose to estimate the worst-case risk with a novel optimization scheme over the intervention functions on mutable causal mechanisms. We then propose an efficient algorithm to search for the subset with minimal worst-case risk, based on a newly defined equivalence relation between stable subsets. Compared to the exponential cost of exhaustively searching over all subsets, our searching strategy enjoys a polynomial complexity. The effectiveness and efficiency of our methods are demonstrated on synthetic data and the diagnosis of Alzheimer's disease.

We study the matrix models pi:C(S_N^+)to M_N(C(X)) which are flat, in the sense that the standard generators of C(S_N^+) are mapped to rank 1 projections. Our first result is a generalization of the Pauli matrix construction at N=4, using finite groups and 2-cocycles. Our second result is the construction of a universal representation of C(S_N^+), inspired from the Sinkhorn algorithm, that we conjecture to be inner faithful.

The Text-to-SQL(Text2SQL) task aims to convert natural language queries into executable SQL queries. Thanks to the application of large language models (LLMs), significant progress has been made in this field. However, challenges such as model scalability, limited generation space, and coherence issues in SQL generation still persist. To address these issues, we propose SQL-o1, a Self-Reward-based heuristic search method designed to enhance the reasoning ability of LLMs in SQL query generation. SQL-o1 combines Monte Carlo Tree Search (MCTS) for heuristic process-level search and constructs a Schema-Aware dataset to help the model better understand database schemas. Extensive experiments on the Bird and Spider datasets demonstrate that SQL-o1 improves execution accuracy by 10.8\% on the complex Bird dataset compared to the latest baseline methods, even outperforming GPT-4-based approaches. Additionally, SQL-o1 excels in few-shot learning scenarios and shows strong cross-model transferability. Our code is publicly available at:https://github.com/ShuaiLyu0110/SQL-o1.