Daily Papers

In this paper we introduce the SCoRe (Submodular Combinatorial Representation Learning) framework, a novel approach in representation learning that addresses inter-class bias and intra-class variance. SCoRe provides a new combinatorial viewpoint to representation learning, by introducing a family of loss functions based on set-based submodular information measures. We develop two novel combinatorial formulations for loss functions, using the Total Information and Total Correlation, that naturally minimize intra-class variance and inter-class bias. Several commonly used metric/contrastive learning loss functions like supervised contrastive loss, orthogonal projection loss, and N-pairs loss, are all instances of SCoRe, thereby underlining the versatility and applicability of SCoRe in a broad spectrum of learning scenarios. Novel objectives in SCoRe naturally model class-imbalance with up to 7.6\% improvement in classification on CIFAR-10-LT, CIFAR-100-LT, MedMNIST, 2.1% on ImageNet-LT, and 19.4% in object detection on IDD and LVIS (v1.0), demonstrating its effectiveness over existing approaches.

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.

Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and data processing inequalities. We show that several quantitative aspects of information theory can be captured by an enriched version of Markov categories, where the spaces of morphisms are equipped with a divergence or even a metric. As it is customary in information theory, mutual information can be defined as a measure of how far a joint source is from displaying independence of its components. More strikingly, Markov categories give a notion of determinism for sources and channels, and we can define entropy exactly by measuring how far a source or channel is from being deterministic. This recovers Shannon and R\'enyi entropies, as well as the Gini-Simpson index used in ecology to quantify diversity, and it can be used to give a conceptual definition of generalized entropy.

Automatic summarization is the process of reducing a text document in order to generate a summary that retains the most important points of the original document. In this work, we study two problems - i) summarizing a text document as set of keywords/caption, for image recommedation, ii) generating opinion summary which good mix of relevancy and sentiment with the text document. Intially, we present our work on an recommending images for enhancing a substantial amount of existing plain text news articles. We use probabilistic models and word similarity heuristics to generate captions and extract Key-phrases which are re-ranked using a rank aggregation framework with relevance feedback mechanism. We show that such rank aggregation and relevant feedback which are typically used in Tagging Documents, Text Information Retrieval also helps in improving image retrieval. These queries are fed to the Yahoo Search Engine to obtain relevant images 1. Our proposed method is observed to perform better than all existing baselines. Additonally, We propose a set of submodular functions for opinion summarization. Opinion summarization has built in it the tasks of summarization and sentiment detection. However, it is not easy to detect sentiment and simultaneously extract summary. The two tasks conflict in the sense that the demand of compression may drop sentiment bearing sentences, and the demand of sentiment detection may bring in redundant sentences. However, using submodularity we show how to strike a balance between the two requirements. Our functions generate summaries such that there is good correlation between document sentiment and summary sentiment along with good ROUGE score. We also compare the performances of the proposed submodular functions.

The analysis of scientific data and complex multivariate systems requires information quantities that capture relationships among multiple random variables. Recently, new information-theoretic measures have been developed to overcome the shortcomings of classical ones, such as mutual information, that are restricted to considering pairwise interactions. Among them, the concept of information synergy and redundancy is crucial for understanding the high-order dependencies between variables. One of the most prominent and versatile measures based on this concept is O-information, which provides a clear and scalable way to quantify the synergy-redundancy balance in multivariate systems. However, its practical application is limited to simplified cases. In this work, we introduce SOmegaI, which allows for the first time to compute O-information without restrictive assumptions about the system. Our experiments validate our approach on synthetic data, and demonstrate the effectiveness of SOmegaI in the context of a real-world use case.

We investigate the sets of joint probability distributions that maximize the average multi-information over a collection of margins. These functionals serve as proxies for maximizing the multi-information of a set of variables or the mutual information of two subsets of variables, at a lower computation and estimation complexity. We describe the maximizers and their relations to the maximizers of the multi-information and the mutual information.

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.

We consider the problem of subset selection where one is given multiple rankings of items and the goal is to select the highest ``quality'' subset. Score functions from the multiwinner voting literature have been used to aggregate rankings into quality scores for subsets. We study this setting of subset selection problems when, in addition, rankings may contain systemic or unconscious biases toward a group of items. For a general model of input rankings and biases, we show that requiring the selected subset to satisfy group fairness constraints can improve the quality of the selection with respect to unbiased rankings. Importantly, we show that for fairness constraints to be effective, different multiwinner score functions may require a drastically different number of rankings: While for some functions, fairness constraints need an exponential number of rankings to recover a close-to-optimal solution, for others, this dependency is only polynomial. This result relies on a novel notion of ``smoothness'' of submodular functions in this setting that quantifies how well a function can ``correctly'' assess the quality of items in the presence of bias. The results in this paper can be used to guide the choice of multiwinner score functions for the subset selection setting considered here; we additionally provide a tool to empirically enable this.

Streaming submodular maximization is a natural model for the task of selecting a representative subset from a large-scale dataset. If datapoints have sensitive attributes such as gender or race, it becomes important to enforce fairness to avoid bias and discrimination. This has spurred significant interest in developing fair machine learning algorithms. Recently, such algorithms have been developed for monotone submodular maximization under a cardinality constraint. In this paper, we study the natural generalization of this problem to a matroid constraint. We give streaming algorithms as well as impossibility results that provide trade-offs between efficiency, quality and fairness. We validate our findings empirically on a range of well-known real-world applications: exemplar-based clustering, movie recommendation, and maximum coverage in social networks.

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.

In this work, we study the problem of privately maximizing a submodular function in the streaming setting. Extensive work has been done on privately maximizing submodular functions in the general case when the function depends upon the private data of individuals. However, when the size of the data stream drawn from the domain of the objective function is large or arrives very fast, one must privately optimize the objective within the constraints of the streaming setting. We establish fundamental differentially private baselines for this problem and then derive better trade-offs between privacy and utility for the special case of decomposable submodular functions. A submodular function is decomposable when it can be written as a sum of submodular functions; this structure arises naturally when each summand function models the utility of an individual and the goal is to study the total utility of the whole population as in the well-known Combinatorial Public Projects Problem. Finally, we complement our theoretical analysis with experimental corroboration.

Byte-Pair Encoding (BPE) is a popular algorithm used for tokenizing data in NLP, despite being devised initially as a compression method. BPE appears to be a greedy algorithm at face value, but the underlying optimization problem that BPE seeks to solve has not yet been laid down. We formalize BPE as a combinatorial optimization problem. Via submodular functions, we prove that the iterative greedy version is a 1{{sigma(mu^star)}}(1-e^{-{sigma(mu^star)}})-approximation of an optimal merge sequence, where {sigma(mu^star)} is the total backward curvature with respect to the optimal merge sequence mu^star. Empirically the lower bound of the approximation is approx 0.37. We provide a faster implementation of BPE which improves the runtime complexity from Oleft(N Mright) to Oleft(N log Mright), where N is the sequence length and M is the merge count. Finally, we optimize the brute-force algorithm for optimal BPE using memoization.

Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this classic problem in the fully dynamic setting, where elements can be both inserted and deleted in real-time. Our main result is a randomized algorithm that maintains an efficient data structure with an O(k^2) amortized update time (in the number of additions and deletions) and yields a 4-approximate solution, where k is the rank of the matroid.

Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's latent space, or how fully the available latent space is being used. In this work, we define data spread and demonstrate that the commonly used measures of data spread, Average Cosine Similarity and a partition function min/max ratio I(V), do not provide reliable metrics to compare the use of latent space across models. We propose and examine eight alternative measures of data spread, all but one of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.

Many recent datasets contain a variety of different data modalities, for instance, image, question, and answer data in visual question answering (VQA). When training deep net classifiers on those multi-modal datasets, the modalities get exploited at different scales, i.e., some modalities can more easily contribute to the classification results than others. This is suboptimal because the classifier is inherently biased towards a subset of the modalities. To alleviate this shortcoming, we propose a novel regularization term based on the functional entropy. Intuitively, this term encourages to balance the contribution of each modality to the classification result. However, regularization with the functional entropy is challenging. To address this, we develop a method based on the log-Sobolev inequality, which bounds the functional entropy with the functional-Fisher-information. Intuitively, this maximizes the amount of information that the modalities contribute. On the two challenging multi-modal datasets VQA-CPv2 and SocialIQ, we obtain state-of-the-art results while more uniformly exploiting the modalities. In addition, we demonstrate the efficacy of our method on Colored MNIST.

Multimodal learning significantly benefits cancer survival prediction, especially the integration of pathological images and genomic data. Despite advantages of multimodal learning for cancer survival prediction, massive redundancy in multimodal data prevents it from extracting discriminative and compact information: (1) An extensive amount of intra-modal task-unrelated information blurs discriminability, especially for gigapixel whole slide images (WSIs) with many patches in pathology and thousands of pathways in genomic data, leading to an ``intra-modal redundancy" issue. (2) Duplicated information among modalities dominates the representation of multimodal data, which makes modality-specific information prone to being ignored, resulting in an ``inter-modal redundancy" issue. To address these, we propose a new framework, Prototypical Information Bottlenecking and Disentangling (PIBD), consisting of Prototypical Information Bottleneck (PIB) module for intra-modal redundancy and Prototypical Information Disentanglement (PID) module for inter-modal redundancy. Specifically, a variant of information bottleneck, PIB, is proposed to model prototypes approximating a bunch of instances for different risk levels, which can be used for selection of discriminative instances within modality. PID module decouples entangled multimodal data into compact distinct components: modality-common and modality-specific knowledge, under the guidance of the joint prototypical distribution. Extensive experiments on five cancer benchmark datasets demonstrated our superiority over other methods.

Vector databases typically rely on approximate nearest neighbor (ANN) search to retrieve the top-k closest vectors to a query in embedding space. While effective, this approach often yields semantically redundant results, missing the diversity and contextual richness required by applications such as retrieval-augmented generation (RAG), multi-hop QA, and memory-augmented agents. We introduce a new retrieval paradigm: semantic compression, which aims to select a compact, representative set of vectors that captures the broader semantic structure around a query. We formalize this objective using principles from submodular optimization and information geometry, and show that it generalizes traditional top-k retrieval by prioritizing coverage and diversity. To operationalize this idea, we propose graph-augmented vector retrieval, which overlays semantic graphs (e.g., kNN or knowledge-based links) atop vector spaces to enable multi-hop, context-aware search. We theoretically analyze the limitations of proximity-based retrieval under high-dimensional concentration and highlight how graph structures can improve semantic coverage. Our work outlines a foundation for meaning-centric vector search systems, emphasizing hybrid indexing, diversity-aware querying, and structured semantic retrieval. We make our implementation publicly available to foster future research in this area.

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.

We study a new connection between a technical measure called mu-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters and communities in social and information networks. The idea of mu-conductance is similar to the traditional graph conductance, but disregards sets with small volume. We derive a sequence of optimization problems including a low-rank semi-definite program from which we can derive a lower bound on the optimal mu-conductance value. These ideas give the first theoretically sound bound on the behavior of the network community profile for a wide range of cluster sizes. The algorithm scales up to graphs with hundreds of thousands of nodes and we demonstrate how our framework validates the predicted structures of real-world graphs.

Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance tradeoffs. We theoretically show that, under some conditions, estimators such as MINE exhibit variance that could grow exponentially with the true amount of underlying MI. We also empirically demonstrate that existing estimators fail to satisfy basic self-consistency properties of MI, such as data processing and additivity under independence. Based on a unified perspective of variational approaches, we develop a new estimator that focuses on variance reduction. Empirical results on standard benchmark tasks demonstrate that our proposed estimator exhibits improved bias-variance trade-offs on standard benchmark tasks.

Multimodal learning holds promise for richer information extraction by capturing dependencies across data sources. Yet, current training methods often underperform due to modality competition, a phenomenon where modalities contend for training resources leaving some underoptimized. This raises a pivotal question: how can we address training imbalances, ensure adequate optimization across all modalities, and achieve consistent performance improvements as we transition from unimodal to multimodal data? This paper proposes the Multimodal Competition Regularizer (MCR), inspired by a mutual information (MI) decomposition designed to prevent the adverse effects of competition in multimodal training. Our key contributions are: 1) A game-theoretic framework that adaptively balances modality contributions by encouraging each to maximize its informative role in the final prediction 2) Refining lower and upper bounds for each MI term to enhance the extraction of both task-relevant unique and shared information across modalities. 3) Proposing latent space permutations for conditional MI estimation, significantly improving computational efficiency. MCR outperforms all previously suggested training strategies and simple baseline, clearly demonstrating that training modalities jointly leads to important performance gains on both synthetic and large real-world datasets. We release our code and models at https://github.com/kkontras/MCR.

We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as mathematical models of contextuality in classical and quantum settings. Each information structure can be regarded as a ringed site with trivial topology; the structure ring is generated by the observables themselves and its multiplication corresponds to joint measurement. We extend Baudot and Bennequin's definition of information cohomology to this setting, as a derived functor in the category of modules over the structure ring, and show explicitly that the bar construction gives a projective resolution in that category, recovering in this way the cochain complexes previously considered in the literature. Finally, we study the particular case of a one-parameter family of coefficients made of functions of probability distributions. The only 1-cocycles are Shannon entropy or Tsallis alpha-entropy, depending on the value of the parameter.

Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this approach is advanced by stating and proving equivalent conditions for second-order stochastic dominance, a widely used way of comparing probability distributions by their spread. Furthermore, we lay foundation for the theory of comparing statistical experiments within Markov categories by stating and proving the classical Blackwell-Sherman-Stein Theorem. Our version not only offers new insight into the proof, but its abstract nature also makes the result more general, automatically specializing to the standard Blackwell-Sherman-Stein Theorem in measure-theoretic probability as well as a Bayesian version that involves prior-dependent garbling. Along the way, we define and characterize representable Markov categories, within which one can talk about Markov kernels to or from spaces of distributions. We do so by exploring the relation between Markov categories and Kleisli categories of probability monads.

Information Retrieval (IR) methods aim to identify relevant documents in response to a given query, which have gained remarkable attention due to their successful application in various natural language tasks. However, existing approaches typically consider only the textual information within the documents, which overlooks the fact that documents can contain multiple modalities, including texts, images, and tables. Further, they often segment each long document into multiple discrete passages for embedding, preventing them from capturing the overall document context and interactions between paragraphs. We argue that these two limitations lead to suboptimal document representations for retrieval. In this work, to address them, we aim to produce more comprehensive and nuanced document representations by holistically embedding documents interleaved with different modalities. Specifically, we achieve this by leveraging the capability of recent vision-language models that enable the processing and integration of text, images, and tables into a unified format and representation. Moreover, to mitigate the information loss from segmenting documents into passages, instead of representing and retrieving passages individually, we further merge the representations of segmented passages into one single document representation, while we additionally introduce a reranking strategy to decouple and identify the relevant passage within the document if necessary. Then, through extensive experiments on diverse information retrieval scenarios considering both the textual and multimodal queries, we show that our approach substantially outperforms relevant baselines, thanks to the consideration of the multimodal information interleaved within the documents in a unified way.

Recent work has sought to quantify large language model uncertainty to facilitate model control and modulate user trust. Previous works focus on measures of uncertainty that are theoretically grounded or reflect the average overt behavior of the model. In this work, we investigate a variety of uncertainty measures, in order to identify measures that correlate with human group-level uncertainty. We find that Bayesian measures and a variation on entropy measures, top-k entropy, tend to agree with human behavior as a function of model size. We find that some strong measures decrease in human-similarity with model size, but, by multiple linear regression, we find that combining multiple uncertainty measures provide comparable human-alignment with reduced size-dependency.

We introduce a Parametric Information Maximization (PIM) model for the Generalized Category Discovery (GCD) problem. Specifically, we propose a bi-level optimization formulation, which explores a parameterized family of objective functions, each evaluating a weighted mutual information between the features and the latent labels, subject to supervision constraints from the labeled samples. Our formulation mitigates the class-balance bias encoded in standard information maximization approaches, thereby handling effectively both short-tailed and long-tailed data sets. We report extensive experiments and comparisons demonstrating that our PIM model consistently sets new state-of-the-art performances in GCD across six different datasets, more so when dealing with challenging fine-grained problems.

We argue that the estimation of mutual information between high dimensional continuous random variables can be achieved by gradient descent over neural networks. We present a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size, trainable through back-prop, and strongly consistent. We present a handful of applications on which MINE can be used to minimize or maximize mutual information. We apply MINE to improve adversarially trained generative models. We also use MINE to implement Information Bottleneck, applying it to supervised classification; our results demonstrate substantial improvement in flexibility and performance in these settings.

In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.

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.

This paper addresses the problem of formalizing and quantifying the concept of "intensional inheritance" between two concepts. We begin by conceiving the intensional inheritance of W from F as the amount of information the proposition "x is F " provides about the proposition "x is W. To flesh this out, we consider concepts F and W defined by sets of properties left{F_{1}, F_{2}, ldots, F_{n}right} and left{W_{1}, W_{2}, ldots, W_{m}right} with associated degrees left{d_{1}, d_{2}, ldots, d_{n}right} and left{e_{1}, e_{2}, ldots, e_{m}right}, respectively, where the properties may overlap. We then derive formulas for the intensional inheritance using both Shannon information theory and algorithmic information theory, incorporating interaction information among properties. We examine a special case where all properties are mutually exclusive and calculate the intensional inheritance in this case in both frameworks. We also derive expressions for P(W mid F) based on the mutual information formula. Finally we consider the relationship between intensional inheritance and conventional set-theoretic "extensional" inheritance, concluding that in our information-theoretic framework, extensional inheritance emerges as a special case of intensional inheritance.

We apply category theory to extract multimodal document structure which leads us to develop information theoretic measures, content summarization and extension, and self-supervised improvement of large pretrained models. We first develop a mathematical representation of a document as a category of question-answer pairs. Second, we develop an orthogonalization procedure to divide the information contained in one or more documents into non-overlapping pieces. The structures extracted in the first and second steps lead us to develop methods to measure and enumerate the information contained in a document. We also build on those steps to develop new summarization techniques, as well as to develop a solution to a new problem viz. exegesis resulting in an extension of the original document. Our question-answer pair methodology enables a novel rate distortion analysis of summarization techniques. We implement our techniques using large pretrained models, and we propose a multimodal extension of our overall mathematical framework. Finally, we develop a novel self-supervised method using RLVR to improve large pretrained models using consistency constraints such as composability and closure under certain operations that stem naturally from our category theoretic framework.

The mechanisms behind the success of multi-view self-supervised learning (MVSSL) are not yet fully understood. Contrastive MVSSL methods have been studied through the lens of InfoNCE, a lower bound of the Mutual Information (MI). However, the relation between other MVSSL methods and MI remains unclear. We consider a different lower bound on the MI consisting of an entropy and a reconstruction term (ER), and analyze the main MVSSL families through its lens. Through this ER bound, we show that clustering-based methods such as DeepCluster and SwAV maximize the MI. We also re-interpret the mechanisms of distillation-based approaches such as BYOL and DINO, showing that they explicitly maximize the reconstruction term and implicitly encourage a stable entropy, and we confirm this empirically. We show that replacing the objectives of common MVSSL methods with this ER bound achieves competitive performance, while making them stable when training with smaller batch sizes or smaller exponential moving average (EMA) coefficients. Github repo: https://github.com/apple/ml-entropy-reconstruction.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

We consider a number of graph kernels and proximity measures including commute time kernel, regularized Laplacian kernel, heat kernel, exponential diffusion kernel (also called "communicability"), etc., and the corresponding distances as applied to clustering nodes in random graphs and several well-known datasets. The model of generating random graphs involves edge probabilities for the pairs of nodes that belong to the same class or different predefined classes of nodes. It turns out that in most cases, logarithmic measures (i.e., measures resulting after taking logarithm of the proximities) perform better while distinguishing underlying classes than the "plain" measures. A comparison in terms of reject curves of inter-class and intra-class distances confirms this conclusion. A similar conclusion can be made for several well-known datasets. A possible origin of this effect is that most kernels have a multiplicative nature, while the nature of distances used in cluster algorithms is an additive one (cf. the triangle inequality). The logarithmic transformation is a tool to transform the first nature to the second one. Moreover, some distances corresponding to the logarithmic measures possess a meaningful cutpoint additivity property. In our experiments, the leader is usually the logarithmic Communicability measure. However, we indicate some more complicated cases in which other measures, typically, Communicability and plain Walk, can be the winners.

Contemporary predictive models are hard to interpret as their deep nets exploit numerous complex relations between input elements. This work suggests a theoretical framework for model interpretability by measuring the contribution of relevant features to the functional entropy of the network with respect to the input. We rely on the log-Sobolev inequality that bounds the functional entropy by the functional Fisher information with respect to the covariance of the data. This provides a principled way to measure the amount of information contribution of a subset of features to the decision function. Through extensive experiments, we show that our method surpasses existing interpretability sampling-based methods on various data signals such as image, text, and audio.

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images < few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.

The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional subspaces challenging, especially for deep architectures. We argue that these difficulties come from suboptimal representation learning, where latent variables fail to balance expressivity and simplicity. This tension is closely related to the information bottleneck (IB) dilemma: constructing compressed representations that are both compact and predictive. Rethinking Koopman learning through this lens, we demonstrate that latent mutual information promotes simplicity, yet an overemphasis on simplicity may cause latent space to collapse onto a few dominant modes. In contrast, expressiveness is sustained by the von Neumann entropy, which prevents such collapse and encourages mode diversity. This insight leads us to propose an information-theoretic Lagrangian formulation that explicitly balances this tradeoff. Furthermore, we propose a new algorithm based on the Lagrangian formulation that encourages both simplicity and expressiveness, leading to a stable and interpretable Koopman representation. Beyond quantitative evaluations, we further visualize the learned manifolds under our representations, observing empirical results consistent with our theoretical predictions. Finally, we validate our approach across a diverse range of dynamical systems, demonstrating improved performance over existing Koopman learning methods. The implementation is publicly available at https://github.com/Wenxuan52/InformationKoopman.

We propose a goodness-of-fit measure for probability densities modeling observations with varying dimensionality, such as text documents of differing lengths or variable-length sequences. The proposed measure is an instance of the kernel Stein discrepancy (KSD), which has been used to construct goodness-of-fit tests for unnormalized densities. The KSD is defined by its Stein operator: current operators used in testing apply to fixed-dimensional spaces. As our main contribution, we extend the KSD to the variable-dimension setting by identifying appropriate Stein operators, and propose a novel KSD goodness-of-fit test. As with the previous variants, the proposed KSD does not require the density to be normalized, allowing the evaluation of a large class of models. Our test is shown to perform well in practice on discrete sequential data benchmarks.

Entropy and mutual information in neural networks provide rich information on the learning process, but they have proven difficult to compute reliably in high dimensions. Indeed, in noisy and high-dimensional data, traditional estimates in ambient dimensions approach a fixed entropy and are prohibitively hard to compute. To address these issues, we leverage data geometry to access the underlying manifold and reliably compute these information-theoretic measures. Specifically, we define diffusion spectral entropy (DSE) in neural representations of a dataset as well as diffusion spectral mutual information (DSMI) between different variables representing data. First, we show that they form noise-resistant measures of intrinsic dimensionality and relationship strength in high-dimensional simulated data that outperform classic Shannon entropy, nonparametric estimation, and mutual information neural estimation (MINE). We then study the evolution of representations in classification networks with supervised learning, self-supervision, or overfitting. We observe that (1) DSE of neural representations increases during training; (2) DSMI with the class label increases during generalizable learning but stays stagnant during overfitting; (3) DSMI with the input signal shows differing trends: on MNIST it increases, while on CIFAR-10 and STL-10 it decreases. Finally, we show that DSE can be used to guide better network initialization and that DSMI can be used to predict downstream classification accuracy across 962 models on ImageNet. The official implementation is available at https://github.com/ChenLiu-1996/DiffusionSpectralEntropy.

We develop tools for explicitly constructing categories enriched over generating data and that compose via ordinary scalar and matrix arithmetic arithmetic operations. We characterize meaningful size maps, weightings, and magnitude that reveal features analogous to outliers that these same notions have previously been shown to reveal in the context of metric spaces. Throughout, we provide examples of such "outlier detection" relevant to the analysis of computer programs, neural networks, cyber-physical systems, and networks of communications channels.

Making statements about the performance of trained models on tasks involving new data is one of the primary goals of machine learning, i.e., to understand the generalization power of a model. Various capacity measures try to capture this ability, but usually fall short in explaining important characteristics of models that we observe in practice. In this study, we propose the local effective dimension as a capacity measure which seems to correlate well with generalization error on standard data sets. Importantly, we prove that the local effective dimension bounds the generalization error and discuss the aptness of this capacity measure for machine learning models.

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.

We propose TAROT, a targeted data selection framework grounded in optimal transport theory. Previous targeted data selection methods primarily rely on influence-based greedy heuristics to enhance domain-specific performance. While effective on limited, unimodal data (i.e., data following a single pattern), these methods struggle as target data complexity increases. Specifically, in multimodal distributions, these heuristics fail to account for multiple inherent patterns, leading to suboptimal data selection. This work identifies two primary factors contributing to this limitation: (i) the disproportionate impact of dominant feature components in high-dimensional influence estimation, and (ii) the restrictive linear additive assumptions inherent in greedy selection strategies. To address these challenges, TAROT incorporates whitened feature distance to mitigate dominant feature bias, providing a more reliable measure of data influence. Building on this, TAROT uses whitened feature distance to quantify and minimize the optimal transport distance between the selected data and target domains. Notably, this minimization also facilitates the estimation of optimal selection ratios. We evaluate TAROT across multiple tasks, including semantic segmentation, motion prediction, and instruction tuning. Results consistently show that TAROT outperforms state-of-the-art methods, highlighting its versatility across various deep learning tasks. Code is available at https://github.com/vita-epfl/TAROT.

We introduce the Structured Knowledge Accumulation (SKA) framework, which reinterprets entropy as a dynamic, layer-wise measure of knowledge alignment in neural networks. Instead of relying on traditional gradient-based optimization, SKA defines entropy in terms of knowledge vectors and their influence on decision probabilities across multiple layers. This formulation naturally leads to the emergence of activation functions such as the sigmoid as a consequence of entropy minimization. Unlike conventional backpropagation, SKA allows each layer to optimize independently by aligning its knowledge representation with changes in decision probabilities. As a result, total network entropy decreases in a hierarchical manner, allowing knowledge structures to evolve progressively. This approach provides a scalable, biologically plausible alternative to gradient-based learning, bridging information theory and artificial intelligence while offering promising applications in resource-constrained and parallel computing environments.

Integrating and processing information from various sources or modalities are critical for obtaining a comprehensive and accurate perception of the real world in autonomous systems and cyber-physical systems. Drawing inspiration from neuroscience, we develop the Information-Theoretic Hierarchical Perception (ITHP) model, which utilizes the concept of information bottleneck. Different from most traditional fusion models that incorporate all modalities identically in neural networks, our model designates a prime modality and regards the remaining modalities as detectors in the information pathway, serving to distill the flow of information. Our proposed perception model focuses on constructing an effective and compact information flow by achieving a balance between the minimization of mutual information between the latent state and the input modal state, and the maximization of mutual information between the latent states and the remaining modal states. This approach leads to compact latent state representations that retain relevant information while minimizing redundancy, thereby substantially enhancing the performance of multimodal representation learning. Experimental evaluations on the MUStARD, CMU-MOSI, and CMU-MOSEI datasets demonstrate that our model consistently distills crucial information in multimodal learning scenarios, outperforming state-of-the-art benchmarks. Remarkably, on the CMU-MOSI dataset, ITHP surpasses human-level performance in the multimodal sentiment binary classification task across all evaluation metrics (i.e., Binary Accuracy, F1 Score, Mean Absolute Error, and Pearson Correlation).

Most existing debiasing methods for multimodal models, including causal intervention and inference methods, utilize approximate heuristics to represent the biases, such as shallow features from early stages of training or unimodal features for multimodal tasks like VQA, etc., which may not be accurate. In this paper, we study bias arising from confounders in a causal graph for multimodal data and examine a novel approach that leverages causally-motivated information minimization to learn the confounder representations. Robust predictive features contain diverse information that helps a model generalize to out-of-distribution data. Hence, minimizing the information content of features obtained from a pretrained biased model helps learn the simplest predictive features that capture the underlying data distribution. We treat these features as confounder representations and use them via methods motivated by causal theory to remove bias from models. We find that the learned confounder representations indeed capture dataset biases, and the proposed debiasing methods improve out-of-distribution (OOD) performance on multiple multimodal datasets without sacrificing in-distribution performance. Additionally, we introduce a novel metric to quantify the sufficiency of spurious features in models' predictions that further demonstrates the effectiveness of our proposed methods. Our code is available at: https://github.com/Vaidehi99/CausalInfoMin

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its tremendous empirical success, the rigorous theoretical understanding of why unsupervised pretraining generally helps remains rather limited -- most existing results are restricted to particular methods or approaches for unsupervised pretraining with specialized structural assumptions. This paper studies a generic framework, where the unsupervised representation learning task is specified by an abstract class of latent variable models Phi and the downstream task is specified by a class of prediction functions Psi. We consider a natural approach of using Maximum Likelihood Estimation (MLE) for unsupervised pretraining and Empirical Risk Minimization (ERM) for learning downstream tasks. We prove that, under a mild ''informative'' condition, our algorithm achieves an excess risk of mathcal{O}(mathcal{C_Phi/m} + mathcal{C_Psi/n}) for downstream tasks, where C_Phi, C_Psi are complexity measures of function classes Phi, Psi, and m, n are the number of unlabeled and labeled data respectively. Comparing to the baseline of mathcal{O}(mathcal{C_{Phi circ Psi}/n}) achieved by performing supervised learning using only the labeled data, our result rigorously shows the benefit of unsupervised pretraining when m gg n and C_{Phicirc Psi} > C_Psi. This paper further shows that our generic framework covers a wide range of approaches for unsupervised pretraining, including factor models, Gaussian mixture models, and contrastive learning.

The burgeoning presence of multimodal content-sharing platforms propels the development of personalized recommender systems. Previous works usually suffer from data sparsity and cold-start problems, and may fail to adequately explore semantic user-product associations from multimodal data. To address these issues, we propose a novel Multi-Modal Hypergraph Contrastive Learning (MMHCL) framework for user recommendation. For a comprehensive information exploration from user-product relations, we construct two hypergraphs, i.e. a user-to-user (u2u) hypergraph and an item-to-item (i2i) hypergraph, to mine shared preferences among users and intricate multimodal semantic resemblance among items, respectively. This process yields denser second-order semantics that are fused with first-order user-item interaction as complementary to alleviate the data sparsity issue. Then, we design a contrastive feature enhancement paradigm by applying synergistic contrastive learning. By maximizing/minimizing the mutual information between second-order (e.g. shared preference pattern for users) and first-order (information of selected items for users) embeddings of the same/different users and items, the feature distinguishability can be effectively enhanced. Compared with using sparse primary user-item interaction only, our MMHCL obtains denser second-order hypergraphs and excavates more abundant shared attributes to explore the user-product associations, which to a certain extent alleviates the problems of data sparsity and cold-start. Extensive experiments have comprehensively demonstrated the effectiveness of our method. Our code is publicly available at: https://github.com/Xu107/MMHCL.

Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inference process that maps complex systems into a simplified representational space and models large jumps in time. To achieve this, we propose Time-lagged Information Bottleneck (T-IB), a principled objective rooted in information theory, which aims to capture relevant temporal features while discarding high-frequency information to simplify the simulation task and minimize the inference error. Our experiments demonstrate that T-IB learns information-optimal representations for accurately modeling the statistical properties and dynamics of the original process at a selected time lag, outperforming existing time-lagged dimensionality reduction methods.

Maximizing a monotone submodular function is a fundamental task in machine learning, economics, and statistics. In this paper, we present two communication-efficient decentralized online algorithms for the monotone continuous DR-submodular maximization problem, both of which reduce the number of per-function gradient evaluations and per-round communication complexity from T^{3/2} to 1. The first one, One-shot Decentralized Meta-Frank-Wolfe (Mono-DMFW), achieves a (1-1/e)-regret bound of O(T^{4/5}). As far as we know, this is the first one-shot and projection-free decentralized online algorithm for monotone continuous DR-submodular maximization. Next, inspired by the non-oblivious boosting function zhang2022boosting, we propose the Decentralized Online Boosting Gradient Ascent (DOBGA) algorithm, which attains a (1-1/e)-regret of O(T). To the best of our knowledge, this is the first result to obtain the optimal O(T) against a (1-1/e)-approximation with only one gradient inquiry for each local objective function per step. Finally, various experimental results confirm the effectiveness of the proposed methods.

We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from neighborhoods of different sizes are either pooled (AE) or encoded distinctly in a multi-scale approach (MUSAE). Capturing attribute-neighborhood relationships over multiple scales is useful for a diverse range of applications, including latent feature identification across disconnected networks with similar attributes. We prove theoretically that matrices of node-feature pointwise mutual information are implicitly factorized by the embeddings. Experiments show that our algorithms are robust, computationally efficient and outperform comparable models on social networks and web graphs.

Tangles were originally introduced as a concept to formalize regions of high connectivity in graphs. In recent years, they have also been discovered as a link between structural graph theory and data science: when interpreting similarity in data sets as connectivity between points, finding clusters in the data essentially amounts to finding tangles in the underlying graphs. This paper further explores the potential of tangles in data sets as a means for a formal study of clusters. Real-world data often follow a normal distribution. Accounting for this, we develop a quantitative theory of tangles in data sets drawn from Gaussian mixtures. To this end, we equip the data with a graph structure that models similarity between the points and allows us to apply tangle theory to the data. We provide explicit conditions under which tangles associated with the marginal Gaussian distributions exist asymptotically almost surely. This can be considered as a sufficient formal criterion for the separabability of clusters in the data.

We define and investigate the problem of c-approximate window search: approximate nearest neighbor search where each point in the dataset has a numeric label, and the goal is to find nearest neighbors to queries within arbitrary label ranges. Many semantic search problems, such as image and document search with timestamp filters, or product search with cost filters, are natural examples of this problem. We propose and theoretically analyze a modular tree-based framework for transforming an index that solves the traditional c-approximate nearest neighbor problem into a data structure that solves window search. On standard nearest neighbor benchmark datasets equipped with random label values, adversarially constructed embeddings, and image search embeddings with real timestamps, we obtain up to a 75times speedup over existing solutions at the same level of recall.

Few neural architectures lend themselves to provable learning with gradient based methods. One popular model is the single-index model, in which labels are produced by composing an unknown linear projection with a possibly unknown scalar link function. Learning this model with SGD is relatively well-understood, whereby the so-called information exponent of the link function governs a polynomial sample complexity rate. However, extending this analysis to deeper or more complicated architectures remains challenging. In this work, we consider single index learning in the setting of symmetric neural networks. Under analytic assumptions on the activation and maximum degree assumptions on the link function, we prove that gradient flow recovers the hidden planted direction, represented as a finitely supported vector in the feature space of power sum polynomials. We characterize a notion of information exponent adapted to our setting that controls the efficiency of learning.

In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relational database schema; in fact an olog can serve as a data repository if desired. Unlike database schemas, which are generally difficult to create or modify, ologs are designed to be user-friendly enough that authoring or reconfiguring an olog is a matter of course rather than a difficult chore. It is hoped that learning to author ologs is much simpler than learning a database definition language, despite their similarity. We describe ologs carefully and illustrate with many examples. As an application we show that any primitive recursive function can be described by an olog. We also show that ologs can be aligned or connected together into a larger network using functors. The various methods of information flow and institutions can then be used to integrate local and global world-views. We finish by providing several different avenues for future research.

The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning. In this paper, we focus on circular probability measures, i.e., probability measures supported on the unit circle, and introduce a new computationally efficient metric for these measures, denoted as Linear Circular Optimal Transport (LCOT). The proposed metric comes with an explicit linear embedding that allows one to apply Machine Learning (ML) algorithms to the embedded measures and seamlessly modify the underlying metric for the ML algorithm to LCOT. We show that the proposed metric is rooted in the Circular Optimal Transport (COT) and can be considered the linearization of the COT metric with respect to a fixed reference measure. We provide a theoretical analysis of the proposed metric and derive the computational complexities for pairwise comparison of circular probability measures. Lastly, through a set of numerical experiments, we demonstrate the benefits of LCOT in learning representations of circular measures.

With the increasing numbers of publicly available models, there are probably pretrained, online models for most tasks users require. However, current model search methods are rudimentary, essentially a text-based search in the documentation, thus users cannot find the relevant models. This paper presents ProbeLog, a method for retrieving classification models that can recognize a target concept, such as "Dog", without access to model metadata or training data. Differently from previous probing methods, ProbeLog computes a descriptor for each output dimension (logit) of each model, by observing its responses on a fixed set of inputs (probes). Our method supports both logit-based retrieval ("find more logits like this") and zero-shot, text-based retrieval ("find all logits corresponding to dogs"). As probing-based representations require multiple costly feedforward passes through the model, we develop a method, based on collaborative filtering, that reduces the cost of encoding repositories by 3x. We demonstrate that ProbeLog achieves high retrieval accuracy, both in real-world and fine-grained search tasks and is scalable to full-size repositories.

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.

Numerous deep learning algorithms have been inspired by and understood via the notion of information bottleneck, where unnecessary information is (often implicitly) minimized while task-relevant information is maximized. However, a rigorous argument for justifying why it is desirable to control information bottlenecks has been elusive. In this paper, we provide the first rigorous learning theory for justifying the benefit of information bottleneck in deep learning by mathematically relating information bottleneck to generalization errors. Our theory proves that controlling information bottleneck is one way to control generalization errors in deep learning, although it is not the only or necessary way. We investigate the merit of our new mathematical findings with experiments across a range of architectures and learning settings. In many cases, generalization errors are shown to correlate with the degree of information bottleneck: i.e., the amount of the unnecessary information at hidden layers. This paper provides a theoretical foundation for current and future methods through the lens of information bottleneck. Our new generalization bounds scale with the degree of information bottleneck, unlike the previous bounds that scale with the number of parameters, VC dimension, Rademacher complexity, stability or robustness. Our code is publicly available at: https://github.com/xu-ji/information-bottleneck

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.

Sequential recommendations have drawn significant attention in modeling the user's historical behaviors to predict the next item. With the booming development of multimodal data (e.g., image, text) on internet platforms, sequential recommendation also benefits from the incorporation of multimodal data. Most methods introduce modal features of items as side information and simply concatenates them to learn unified user interests. Nevertheless, these methods encounter the limitation in modeling multimodal differences. We argue that user interests and item relationships vary across different modalities. To address this problem, we propose a novel Multimodal Difference Learning framework for Sequential Recommendation, MDSRec for brevity. Specifically, we first explore the differences in item relationships by constructing modal-aware item relation graphs with behavior signal to enhance item representations. Then, to capture the differences in user interests across modalities, we design a interest-centralized attention mechanism to independently model user sequence representations in different modalities. Finally, we fuse the user embeddings from multiple modalities to achieve accurate item recommendation. Experimental results on five real-world datasets demonstrate the superiority of MDSRec over state-of-the-art baselines and the efficacy of multimodal difference learning.

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.

A critical barrier to learning an accurate decision rule for outlier detection is the scarcity of outlier data. As such, practitioners often turn to the use of similar but imperfect outlier data from which they might transfer information to the target outlier detection task. Despite the recent empirical success of transfer learning approaches in outlier detection, a fundamental understanding of when and how knowledge can be transferred from a source to a target outlier detection task remains elusive. In this work, we adopt the traditional framework of Neyman-Pearson classification -- which formalizes supervised outlier detection -- with the added assumption that one has access to some related but imperfect outlier data. Our main results are as follows: We first determine the information-theoretic limits of the problem under a measure of discrepancy that extends some existing notions from traditional balanced classification; interestingly, unlike in balanced classification, seemingly very dissimilar sources can provide much information about a target, thus resulting in fast transfer. We then show that, in principle, these information-theoretic limits are achievable by adaptive procedures, i.e., procedures with no a priori information on the discrepancy between source and target outlier distributions.

With the development of Artificial Intelligence (AI) and Internet of Things (IoT) technologies, network communications based on the Shannon-Nyquist theorem gradually reveal their limitations due to the neglect of semantic information in the transmitted content. Semantic communication (SemCom) provides a solution for extracting information meanings from the transmitted content. The semantic information can be successfully interpreted by a receiver with the help of a shared knowledge base (KB). This paper proposes a two-stage hierarchical qualification and validation model for natural language-based machine-to-machine (M2M) SemCom. The approach can be applied in various applications, such as autonomous driving and edge computing. In the proposed model, we quantitatively measure the degree of understanding (DoU) between two communication parties at the word and sentence levels. The DoU is validated and ensured at each level before moving to the next step. The model's effectiveness is verified through a series of experiments, and the results show that the quantification and validation method proposed in this paper can significantly improve the DoU of inter-machine SemCom.

Associating unstructured data with structured information is crucial for real-world tasks that require relevance search. However, existing graph learning benchmarks often overlook the rich semantic information associate with each node. To bridge such gap, we introduce the Multimodal Graph Benchmark (MM-GRAPH), the first comprehensive multi-modal graph benchmark that incorporates both textual and visual information. MM-GRAPH surpasses previous efforts, which have primarily focused on text-attributed graphs with various connectivity patterns. MM-GRAPH consists of five graph learning datasets of various scales that are appropriate for different learning tasks. Their multimodal node features, enabling a more comprehensive evaluation of graph learning algorithms in real-world scenarios. To facilitate research on multimodal graph learning, we further provide an extensive study on the performance of various graph neural networks in the presence of features from various modalities. MM-GRAPH aims to foster research on multimodal graph learning and drive the development of more advanced and robust graph learning algorithms. By providing a diverse set of datasets and benchmarks, MM-GRAPH enables researchers to evaluate and compare their models in realistic settings, ultimately leading to improved performance on real-world applications that rely on multimodal graph data.

The Sliced-Wasserstein distance (SW) is a computationally efficient and theoretically grounded alternative to the Wasserstein distance. Yet, the literature on its statistical properties -- or, more accurately, its generalization properties -- with respect to the distribution of slices, beyond the uniform measure, is scarce. To bring new contributions to this line of research, we leverage the PAC-Bayesian theory and a central observation that SW may be interpreted as an average risk, the quantity PAC-Bayesian bounds have been designed to characterize. We provide three types of results: i) PAC-Bayesian generalization bounds that hold on what we refer as adaptive Sliced-Wasserstein distances, i.e. SW defined with respect to arbitrary distributions of slices (among which data-dependent distributions), ii) a principled procedure to learn the distribution of slices that yields maximally discriminative SW, by optimizing our theoretical bounds, and iii) empirical illustrations of our theoretical findings.

This paper investigates a novel lossy compression framework operating under logarithmic loss, designed to handle situations where the reconstruction distribution diverges from the source distribution. This framework is especially relevant for applications that require joint compression and retrieval, and in scenarios involving distributional shifts due to processing. We show that the proposed formulation extends the classical minimum entropy coupling framework by integrating a bottleneck, allowing for a controlled degree of stochasticity in the coupling. We explore the decomposition of the Minimum Entropy Coupling with Bottleneck (MEC-B) into two distinct optimization problems: Entropy-Bounded Information Maximization (EBIM) for the encoder, and Minimum Entropy Coupling (MEC) for the decoder. Through extensive analysis, we provide a greedy algorithm for EBIM with guaranteed performance, and characterize the optimal solution near functional mappings, yielding significant theoretical insights into the structural complexity of this problem. Furthermore, we illustrate the practical application of MEC-B through experiments in Markov Coding Games (MCGs) under rate limits. These games simulate a communication scenario within a Markov Decision Process, where an agent must transmit a compressed message from a sender to a receiver through its actions. Our experiments highlight the trade-offs between MDP rewards and receiver accuracy across various compression rates, showcasing the efficacy of our method compared to conventional compression baseline.

We explore local vs. global evolution of knowledge systems through the framework of socio-epistemic networks (SEN), applying two complementary methods to a corpus of scientific texts. The framework comprises three interconnected layers-social, semiotic (material), and semantic-proposing a multilayered approach to understanding structural developments of knowledge. To analyse diachronic changes on the semantic layer, we first use information-theoretic measures based on relative entropy to detect semantic shifts, assess their significance, and identify key driving features. Second, variations in document embedding densities reveal changes in semantic neighbourhoods, tracking how concentration of similar documents increase, remain stable, or disperse. This enables us to trace document trajectories based on content (topics) or metadata (authorship, institution). Case studies of Joseph Silk and Hans-J\"urgen Treder illustrate how individual scholar's work aligns with broader disciplinary shifts in general relativity and gravitation research, demonstrating the applications, limitations, and further potential of this approach.

Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been extensively used in the most diverse types of problems, also motivating some respective generalizations. The present work addresses further generalizations of this index, including its modification into a coincidence index capable of accounting also for the level of relative interiority between the two compared entities, as well as respective extensions for sets in continuous vector spaces, the generalization to multiset addition, densities and generic scalar fields, as well as a means to quantify the joint interdependence between two random variables. The also interesting possibility to take into account more than two sets has also been addressed, including the description of an index capable of quantifying the level of chaining between three structures. Several of the described and suggested eneralizations have been illustrated with respect to numeric case examples. It is also posited that these indices can play an important role while analyzing and integrating datasets in modeling approaches and pattern recognition activities, including as a measurement of clusters similarity or separation and as a resource for representing and analyzing complex networks.

Retrieval-augmented generation (RAG) faces challenges related to factual correctness, source attribution, and response completeness. The LiveRAG Challenge hosted at SIGIR'25 aims to advance RAG research using a fixed corpus and a shared, open-source LLM. We propose a modular pipeline that operates on information nuggets-minimal, atomic units of relevant information extracted from retrieved documents. This multistage pipeline encompasses query rewriting, passage retrieval and reranking, nugget detection and clustering, cluster ranking and summarization, and response fluency enhancement. This design inherently promotes grounding in specific facts, facilitates source attribution, and ensures maximum information inclusion within length constraints. In this challenge, we extend our focus to also address the retrieval component of RAG, building upon our prior work on multi-faceted query rewriting. Furthermore, for augmented generation, we concentrate on improving context curation capabilities, maximizing the breadth of information covered in the response while ensuring pipeline efficiency. Our results show that combining original queries with a few sub-query rewrites boosts recall, while increasing the number of documents used for reranking and generation beyond a certain point reduces effectiveness, without improving response quality.

Relational data augmentation is a powerful technique for enhancing data analytics and improving machine learning models by incorporating columns from external datasets. However, it is challenging to efficiently discover relevant external tables to join with a given input table. Existing approaches rely on data discovery systems to identify joinable tables from external sources, typically based on overlap or containment. However, the sheer number of tables obtained from these systems results in irrelevant joins that need to be performed; this can be computationally expensive or even infeasible in practice. We address this limitation by proposing the use of efficient mutual information (MI) estimation for finding relevant joinable tables. We introduce a new sketching method that enables efficient evaluation of relationship discovery queries by estimating MI without materializing the joins and returning a smaller set of tables that are more likely to be relevant. We also demonstrate the effectiveness of our approach at approximating MI in extensive experiments using synthetic and real-world datasets.

Wikipedia relies on an extensive review process to verify that the content of each individual page is unbiased and presents a neutral point of view. Less attention has been paid to possible biases in the hyperlink structure of Wikipedia, which has a significant influence on the user's exploration process when visiting more than one page. The evaluation of hyperlink bias is challenging because it depends on the global view rather than the text of individual pages. In this paper, we focus on the influence of the interconnect topology between articles describing complementary aspects of polarizing topics. We introduce a novel measure of exposure to diverse information to quantify users' exposure to different aspects of a topic throughout an entire surfing session, rather than just one click ahead. We apply this measure to six polarizing topics (e.g., gun control and gun right), and we identify cases in which the network topology significantly limits the exposure of users to diverse information on the topic, encouraging users to remain in a knowledge bubble. Our findings demonstrate the importance of evaluating Wikipedia's network structure in addition to the extensive review of individual articles.

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.

Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to best quantify predictive uncertainty. In this work, we revisit core concepts to propose a framework for information-theoretic measures of predictive uncertainty. Our proposed framework categorizes predictive uncertainty measures according to two factors: (I) The predicting model (II) The approximation of the true predictive distribution. Examining all possible combinations of these two factors, we derive a set of predictive uncertainty measures that includes both known and newly introduced ones. We extensively evaluate these measures across a broad set of tasks, identifying conditions under which certain measures excel. Our findings show the importance of aligning the choice of uncertainty measure with the predicting model on in-distribution (ID) data, the limitations of epistemic uncertainty measures for out-of-distribution (OOD) data, and that the disentanglement between measures varies substantially between ID and OOD data. Together, these insights provide a more comprehensive understanding of predictive uncertainty measures, revealing their implicit assumptions and relationships.

Fairness and relevance are two important aspects of recommender systems (RSs). Typically, they are evaluated either (i) separately by individual measures of fairness and relevance, or (ii) jointly using a single measure that accounts for fairness with respect to relevance. However, approach (i) often does not provide a reliable joint estimate of the goodness of the models, as it has two different best models: one for fairness and another for relevance. Approach (ii) is also problematic because these measures tend to be ad-hoc and do not relate well to traditional relevance measures, like NDCG. Motivated by this, we present a new approach for jointly evaluating fairness and relevance in RSs: Distance to Pareto Frontier (DPFR). Given some user-item interaction data, we compute their Pareto frontier for a pair of existing relevance and fairness measures, and then use the distance from the frontier as a measure of the jointly achievable fairness and relevance. Our approach is modular and intuitive as it can be computed with existing measures. Experiments with 4 RS models, 3 re-ranking strategies, and 6 datasets show that existing metrics have inconsistent associations with our Pareto-optimal solution, making DPFR a more robust and theoretically well-founded joint measure for assessing fairness and relevance. Our code: https://github.com/theresiavr/DPFR-recsys-evaluation

How might one test the hypothesis that networks were sampled from the same distribution? Here, we compare two statistical tests that use subgraph counts to address this question. The first uses the empirical subgraph densities themselves as estimates of those of the underlying distribution. The second test uses a new approach that converts these subgraph densities into estimates of the graph cumulants of the distribution (without any increase in computational complexity). We demonstrate -- via theory, simulation, and application to real data -- the superior statistical power of using graph cumulants. In summary, when analyzing data using subgraph/motif densities, we suggest using the corresponding graph cumulants instead.

We develop a simulation framework for studying misinformation spread within online social networks that blends agent-based modeling and natural language processing techniques. While many other agent-based simulations exist in this space, questions over their fidelity and generalization to existing networks in part hinders their ability to provide actionable insights. To partially address these concerns, we create a 'digital clone' of a known misinformation sharing network by downloading social media histories for over ten thousand of its users. We parse these histories to both extract the structure of the network and model the nuanced ways in which information is shared and spread among its members. Unlike many other agent-based methods in this space, information sharing between users in our framework is sensitive to topic of discussion, user preferences, and online community dynamics. To evaluate the fidelity of our method, we seed our cloned network with a set of posts recorded in the base network and compare propagation dynamics between the two, observing reasonable agreement across the twin networks over a variety of metrics. Lastly, we explore how the cloned network may serve as a flexible, low-cost testbed for misinformation countermeasure evaluation and red teaming analysis. We hope the tools explored here augment existing efforts in the space and unlock new opportunities for misinformation countermeasure evaluation, a field that may become increasingly important to consider with the anticipated rise of misinformation campaigns fueled by generative artificial intelligence.

In this paper, the problem of semantic information extraction for resource constrained text data transmission is studied. In the considered model, a sequence of text data need to be transmitted within a communication resource-constrained network, which only allows limited data transmission. Thus, at the transmitter, the original text data is extracted with natural language processing techniques. Then, the extracted semantic information is captured in a knowledge graph. An additional probability dimension is introduced in this graph to capture the importance of each information. This semantic information extraction problem is posed as an optimization framework whose goal is to extract most important semantic information for transmission. To find an optimal solution for this problem, a Floyd's algorithm based solution coupled with an efficient sorting mechanism is proposed. Numerical results testify the effectiveness of the proposed algorithm with regards to two novel performance metrics including semantic uncertainty and semantic similarity.

Retrieval-Augmented Generation (RAG) has shown substantial promise in improving factual accuracy by grounding model responses with external knowledge relevant to queries. However, most existing RAG approaches are limited to a text-only corpus, and while recent efforts have extended RAG to other modalities such as images and videos, they typically operate over a single modality-specific corpus. In contrast, real-world queries vary widely in the type of knowledge they require, which a single type of knowledge source cannot address. To address this, we introduce UniversalRAG, a novel RAG framework designed to retrieve and integrate knowledge from heterogeneous sources with diverse modalities and granularities. Specifically, motivated by the observation that forcing all modalities into a unified representation space derived from a single combined corpus causes a modality gap, where the retrieval tends to favor items from the same modality as the query, we propose a modality-aware routing mechanism that dynamically identifies the most appropriate modality-specific corpus and performs targeted retrieval within it. Also, beyond modality, we organize each modality into multiple granularity levels, enabling fine-tuned retrieval tailored to the complexity and scope of the query. We validate UniversalRAG on 8 benchmarks spanning multiple modalities, showing its superiority over modality-specific and unified baselines.

Given a database of bit strings A_1,ldots,A_min {0,1}^n, a fundamental data structure task is to estimate the distances between a given query Bin {0,1}^n with all the strings in the database. In addition, one might further want to ensure the integrity of the database by releasing these distance statistics in a secure manner. In this work, we propose differentially private (DP) data structures for this type of tasks, with a focus on Hamming and edit distance. On top of the strong privacy guarantees, our data structures are also time- and space-efficient. In particular, our data structure is epsilon-DP against any sequence of queries of arbitrary length, and for any query B such that the maximum distance to any string in the database is at most k, we output m distance estimates. Moreover, - For Hamming distance, our data structure answers any query in widetilde O(mk+n) time and each estimate deviates from the true distance by at most widetilde O(k/e^{epsilon/log k}); - For edit distance, our data structure answers any query in widetilde O(mk^2+n) time and each estimate deviates from the true distance by at most widetilde O(k/e^{epsilon/(log k log n)}). For moderate k, both data structures support sublinear query operations. We obtain these results via a novel adaptation of the randomized response technique as a bit flipping procedure, applied to the sketched strings.

Conventional multimodal recommender systems predominantly leverage Bayesian Personalized Ranking (BPR) optimization to learn item representations by amalgamating item identity (ID) embeddings with multimodal features. Nevertheless, our empirical and theoretical findings unequivocally demonstrate a pronounced optimization gradient bias in favor of acquiring representations from multimodal features over item ID embeddings. As a consequence, item ID embeddings frequently exhibit suboptimal characteristics despite the convergence of multimodal feature parameters. Given the rich informational content inherent in multimodal features, in this paper, we propose a novel model (i.e., LIRDRec) that learns item representations directly from these features to augment recommendation performance. Recognizing that features derived from each modality may capture disparate yet correlated aspects of items, we propose a multimodal transformation mechanism, integrated with modality-specific encoders, to effectively fuse features from all modalities. Moreover, to differentiate the influence of diverse modality types, we devise a progressive weight copying fusion module within LIRDRec. This module incrementally learns the weight assigned to each modality in synthesizing the final user or item representations. Finally, we utilize the powerful visual understanding of Multimodal Large Language Models (MLLMs) to convert the item images into texts and extract semantics embeddings upon the texts via LLMs. Empirical evaluations conducted on five real-world datasets validate the superiority of our approach relative to competing baselines. It is worth noting the proposed model, equipped with embeddings extracted from MLLMs and LLMs, can further improve the recommendation accuracy of NDCG@20 by an average of 4.21% compared to the original embeddings.

Due to the convenience of mobile devices, the online games have become an important part for user entertainments in reality, creating a demand for friend recommendation in online games. However, none of existing approaches can effectively incorporate the multi-modal user features (e.g., images and texts) with the structural information in the friendship graph, due to the following limitations: (1) some of them ignore the high-order structural proximity between users, (2) some fail to learn the pairwise relevance between users at modality-specific level, and (3) some cannot capture both the local and global user preferences on different modalities. By addressing these issues, in this paper, we propose an end-to-end model FROG that better models the user preferences on potential friends. Comprehensive experiments on both offline evaluation and online deployment at Tencent have demonstrated the superiority of FROG over existing approaches.

Combining several (sample approximations of) distributions, which we term sub-posteriors, into a single distribution proportional to their product, is a common challenge. Occurring, for instance, in distributed 'big data' problems, or when working under multi-party privacy constraints. Many existing approaches resort to approximating the individual sub-posteriors for practical necessity, then find either an analytical approximation or sample approximation of the resulting (product-pooled) posterior. The quality of the posterior approximation for these approaches is poor when the sub-posteriors fall out-with a narrow range of distributional form, such as being approximately Gaussian. Recently, a Fusion approach has been proposed which finds an exact Monte Carlo approximation of the posterior, circumventing the drawbacks of approximate approaches. Unfortunately, existing Fusion approaches have a number of computational limitations, particularly when unifying a large number of sub-posteriors. In this paper, we generalise the theory underpinning existing Fusion approaches, and embed the resulting methodology within a recursive divide-and-conquer sequential Monte Carlo paradigm. This ultimately leads to a competitive Fusion approach, which is robust to increasing numbers of sub-posteriors.

Sequential recommendation (SR) systems have evolved significantly over the past decade, transitioning from traditional collaborative filtering to deep learning approaches and, more recently, to large language models (LLMs). While the adoption of LLMs has driven substantial advancements, these models inherently lack collaborative filtering information, relying primarily on textual content data neglecting other modalities and thus failing to achieve optimal recommendation performance. To address this limitation, we propose Molar, a Multimodal large language sequential recommendation framework that integrates multiple content modalities with ID information to capture collaborative signals effectively. Molar employs an MLLM to generate unified item representations from both textual and non-textual data, facilitating comprehensive multimodal modeling and enriching item embeddings. Additionally, it incorporates collaborative filtering signals through a post-alignment mechanism, which aligns user representations from content-based and ID-based models, ensuring precise personalization and robust performance. By seamlessly combining multimodal content with collaborative filtering insights, Molar captures both user interests and contextual semantics, leading to superior recommendation accuracy. Extensive experiments validate that Molar significantly outperforms traditional and LLM-based baselines, highlighting its strength in utilizing multimodal data and collaborative signals for sequential recommendation tasks. The source code is available at https://anonymous.4open.science/r/Molar-8B06/.

Multimedia content in social media platforms provides significant information during disaster events. The types of information shared include reports of injured or deceased people, infrastructure damage, and missing or found people, among others. Although many studies have shown the usefulness of both text and image content for disaster response purposes, the research has been mostly focused on analyzing only the text modality in the past. In this paper, we propose to use both text and image modalities of social media data to learn a joint representation using state-of-the-art deep learning techniques. Specifically, we utilize convolutional neural networks to define a multimodal deep learning architecture with a modality-agnostic shared representation. Extensive experiments on real-world disaster datasets show that the proposed multimodal architecture yields better performance than models trained using a single modality (e.g., either text or image).

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in learning a family of sub-Gaussian probability distributions. We introduce a notion of complexity for probability distributions in terms of their relative density with respect to the standard Gaussian measure. We prove that if the log-relative density can be locally approximated by a neural network whose parameters can be suitably bounded, then the distribution generated by empirical score matching approximates the target distribution in total variation with a dimension-independent rate. We illustrate our theory through examples, which include certain mixtures of Gaussians. An essential ingredient of our proof is to derive a dimension-free deep neural network approximation rate for the true score function associated with the forward process, which is interesting in its own right.

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for sampling random graph homomorphisms and establish bounds on their mixing times and the concentration of their time averages. Based on our sampling algorithms, we propose a novel framework for network data analysis that circumvents some of the drawbacks in methods based on independent and neighborhood sampling. Various time averages of the MCMC trajectory give us various computable observables, including well-known ones such as homomorphism density and average clustering coefficient and their generalizations. Furthermore, we show that these network observables are stable with respect to a suitably renormalized cut distance between networks. We provide various examples and simulations demonstrating our framework through synthetic networks. We also demonstrate the performance of our framework on the tasks of network clustering and subgraph classification on the Facebook100 dataset and on Word Adjacency Networks of a set of classic novels.

In order to develop machine learning and deep learning models that take into account the guidelines and principles of trustworthy AI, a novel information theoretic trustworthy AI framework is introduced. A unified approach to "privacy-preserving interpretable and transferable learning" is considered for studying and optimizing the tradeoffs between privacy, interpretability, and transferability aspects. A variational membership-mapping Bayesian model is used for the analytical approximations of the defined information theoretic measures for privacy-leakage, interpretability, and transferability. The approach consists of approximating the information theoretic measures via maximizing a lower-bound using variational optimization. The study presents a unified information theoretic approach to study different aspects of trustworthy AI in a rigorous analytical manner. The approach is demonstrated through numerous experiments on benchmark datasets and a real-world biomedical application concerned with the detection of mental stress on individuals using heart rate variability analysis.

We introduce a new analytical framework to quantify the changes in a machine learning algorithm's output distribution following the inclusion of a few data points in its training set, a notion we define as leave-one-out distinguishability (LOOD). This problem is key to measuring data **memorization** and **information leakage** in machine learning, and the **influence** of training data points on model predictions. We illustrate how our method broadens and refines existing empirical measures of memorization and privacy risks associated with training data. We use Gaussian processes to model the randomness of machine learning algorithms, and validate LOOD with extensive empirical analysis of information leakage using membership inference attacks. Our theoretical framework enables us to investigate the causes of information leakage and where the leakage is high. For example, we analyze the influence of activation functions, on data memorization. Additionally, our method allows us to optimize queries that disclose the most significant information about the training data in the leave-one-out setting. We illustrate how optimal queries can be used for accurate **reconstruction** of training data.

Cross-modal metric learning is a prominent research topic that bridges the semantic heterogeneity between vision and language. Existing methods frequently utilize simple cosine or complex distance metrics to transform the pairwise features into a similarity score, which suffers from an inadequate or inefficient capability for distance measurements. Consequently, we propose a Generalized Structural Sparse Function to dynamically capture thorough and powerful relationships across modalities for pair-wise similarity learning while remaining concise but efficient. Specifically, the distance metric delicately encapsulates two formats of diagonal and block-diagonal terms, automatically distinguishing and highlighting the cross-channel relevancy and dependency inside a structured and organized topology. Hence, it thereby empowers itself to adapt to the optimal matching patterns between the paired features and reaches a sweet spot between model complexity and capability. Extensive experiments on cross-modal and two extra uni-modal retrieval tasks (image-text retrieval, person re-identification, fine-grained image retrieval) have validated its superiority and flexibility over various popular retrieval frameworks. More importantly, we further discover that it can be seamlessly incorporated into multiple application scenarios, and demonstrates promising prospects from Attention Mechanism to Knowledge Distillation in a plug-and-play manner. Our code is publicly available at: https://github.com/Paranioar/GSSF.

Existing information retrieval (IR) models often assume a homogeneous format, limiting their applicability to diverse user needs, such as searching for images with text descriptions, searching for a news article with a headline image, or finding a similar photo with a query image. To approach such different information-seeking demands, we introduce UniIR, a unified instruction-guided multimodal retriever capable of handling eight distinct retrieval tasks across modalities. UniIR, a single retrieval system jointly trained on ten diverse multimodal-IR datasets, interprets user instructions to execute various retrieval tasks, demonstrating robust performance across existing datasets and zero-shot generalization to new tasks. Our experiments highlight that multi-task training and instruction tuning are keys to UniIR's generalization ability. Additionally, we construct the M-BEIR, a multimodal retrieval benchmark with comprehensive results, to standardize the evaluation of universal multimodal information retrieval.

Unsupervised keyphrase prediction has gained growing interest in recent years. However, existing methods typically rely on heuristically defined importance scores, which may lead to inaccurate informativeness estimation. In addition, they lack consideration for time efficiency. To solve these problems, we propose ERU-KG, an unsupervised keyphrase generation (UKG) model that consists of an informativeness and a phraseness module. The former estimates the relevance of keyphrase candidates, while the latter generate those candidates. The informativeness module innovates by learning to model informativeness through references (e.g., queries, citation contexts, and titles) and at the term-level, thereby 1) capturing how the key concepts of documents are perceived in different contexts and 2) estimating informativeness of phrases more efficiently by aggregating term informativeness, removing the need for explicit modeling of the candidates. ERU-KG demonstrates its effectiveness on keyphrase generation benchmarks by outperforming unsupervised baselines and achieving on average 89\% of the performance of a supervised model for top 10 predictions. Additionally, to highlight its practical utility, we evaluate the model on text retrieval tasks and show that keyphrases generated by ERU-KG are effective when employed as query and document expansions. Furthermore, inference speed tests reveal that ERU-KG is the fastest among baselines of similar model sizes. Finally, our proposed model can switch between keyphrase generation and extraction by adjusting hyperparameters, catering to diverse application requirements.

We investigate the online bandit learning of the monotone multi-linear DR-submodular functions, designing the algorithm BanditMLSM that attains O(T^{2/3}log T) of (1-1/e)-regret. Then we reduce submodular bandit with partition matroid constraint and bandit sequential monotone maximization to the online bandit learning of the monotone multi-linear DR-submodular functions, attaining O(T^{2/3}log T) of (1-1/e)-regret in both problems, which improve the existing results. To the best of our knowledge, we are the first to give a sublinear regret algorithm for the submodular bandit with partition matroid constraint. A special case of this problem is studied by Streeter et al.(2009). They prove a O(T^{4/5}) (1-1/e)-regret upper bound. For the bandit sequential submodular maximization, the existing work proves an O(T^{2/3}) regret with a suboptimal 1/2 approximation ratio (Niazadeh et al. 2021).

Neural embedding models have become a fundamental component of modern information retrieval (IR) pipelines. These models produce a single embedding x in R^d per data-point, allowing for fast retrieval via highly optimized maximum inner product search (MIPS) algorithms. Recently, beginning with the landmark ColBERT paper, multi-vector models, which produce a set of embedding per data point, have achieved markedly superior performance for IR tasks. Unfortunately, using these models for IR is computationally expensive due to the increased complexity of multi-vector retrieval and scoring. In this paper, we introduce MUVERA (MUlti-VEctor Retrieval Algorithm), a retrieval mechanism which reduces multi-vector similarity search to single-vector similarity search. This enables the usage of off-the-shelf MIPS solvers for multi-vector retrieval. MUVERA asymmetrically generates Fixed Dimensional Encodings (FDEs) of queries and documents, which are vectors whose inner product approximates multi-vector similarity. We prove that FDEs give high-quality epsilon-approximations, thus providing the first single-vector proxy for multi-vector similarity with theoretical guarantees. Empirically, we find that FDEs achieve the same recall as prior state-of-the-art heuristics while retrieving 2-5times fewer candidates. Compared to prior state of the art implementations, MUVERA achieves consistently good end-to-end recall and latency across a diverse set of the BEIR retrieval datasets, achieving an average of 10% improved recall with 90% lower latency.

Extracting low-dimensional summary statistics from large datasets is essential for efficient (likelihood-free) inference. We characterize different classes of summaries and demonstrate their importance for correctly analysing dimensionality reduction algorithms. We demonstrate that minimizing the expected posterior entropy (EPE) under the prior predictive distribution of the model subsumes many existing methods. They are equivalent to or are special or limiting cases of minimizing the EPE. We offer a unifying framework for obtaining informative summaries, provide concrete recommendations for practitioners, and propose a practical method to obtain high-fidelity summaries whose utility we demonstrate for both benchmark and practical examples.

We present a systematic investigation of Multi-modal Retrieval Augmented Multi-modal Generation (M^2RAG), a novel task that enables foundation models to process multi-modal web content and generate multi-modal responses, which exhibits better information density and readability. Despite its potential impact, M^2RAG remains understudied, lacking comprehensive analysis and high-quality data resources. To address this gap, we establish a comprehensive benchmark through a rigorous data curation pipeline, and employ text-modal metrics and multi-modal metrics based on foundation models for evaluation. We further propose several strategies for foundation models to process M^2RAG effectively and construct a training set by filtering high-quality samples using designed metrics. Our extensive experiments demonstrate the reliability of our proposed metrics, a landscape of model performance within our designed strategies, and show that our fine-tuned 7B-8B models outperform the state-of-the-art GPT-4o model. Additionally, we perform fine-grained analyses across diverse domains and validate the effectiveness of our designs in data curation pipeline. All resources, including codes, datasets, and model weights, will be publicly released.

Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and cannot integrate new data points. To address these drawbacks, we propose InfoOT, an information-theoretic extension of optimal transport that maximizes the mutual information between domains while minimizing geometric distances. The resulting objective can still be formulated as a (generalized) optimal transport problem, and can be efficiently solved by projected gradient descent. This formulation yields a new projection method that is robust to outliers and generalizes to unseen samples. Empirically, InfoOT improves the quality of alignments across benchmarks in domain adaptation, cross-domain retrieval, and single-cell alignment.

Integrating information from different reference data sources is a major challenge for Retrieval-Augmented Generation (RAG) systems because each knowledge source adopts a unique data structure and follows different conventions. Retrieving from multiple knowledge sources with one fixed strategy usually leads to under-exploitation of information. To mitigate this drawback, inspired by Mix-of-Expert, we introduce Mix-of-Granularity (MoG), a method that dynamically determines the optimal granularity of a knowledge database based on input queries using a router. The router is efficiently trained with a newly proposed loss function employing soft labels. We further extend MoG to Mix-of-Granularity-Graph (MoGG), where reference documents are pre-processed into graphs, enabling the retrieval of relevant information from distantly situated chunks. Extensive experiments demonstrate that both MoG and MoGG effectively predict optimal granularity levels, significantly enhancing the performance of the RAG system in downstream tasks. The code of both MoG and MoGG will be made public.

A fundamental question in modern machine learning is why large, over-parameterized models, such as deep neural networks and transformers, tend to generalize well, even when their number of parameters far exceeds the number of training samples. We investigate this phenomenon through the lens of information theory, grounded in universal learning theory. Specifically, we study a Bayesian mixture learner with log-loss and (almost) uniform prior over an expansive hypothesis class. Our key result shows that the learner's regret is not determined by the overall size of the hypothesis class, but rather by the cumulative probability of all models that are close, in Kullback-Leibler divergence distance, to the true data-generating process. We refer to this cumulative probability as the weight of the hypothesis. This leads to a natural notion of model simplicity: simple models are those with large weight and thus require fewer samples to generalize, while complex models have small weight and need more data. This perspective provides a rigorous and intuitive explanation for why over-parameterized models often avoid overfitting: the presence of simple hypotheses allows the posterior to concentrate on them when supported by the data. We further bridge theory and practice by recalling that stochastic gradient descent with Langevin dynamics samples from the correct posterior distribution, enabling our theoretical learner to be approximated using standard machine learning methods combined with ensemble learning. Our analysis yields non-uniform regret bounds and aligns with key practical concepts such as flat minima and model distillation. The results apply broadly across online, batch, and supervised learning settings, offering a unified and principled understanding of the generalization behavior of modern AI systems.

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

We carry out an information-theoretical analysis of a two-layer neural network trained from input-output pairs generated by a teacher network with matching architecture, in overparametrized regimes. Our results come in the form of bounds relating i) the mutual information between training data and network weights, or ii) the Bayes-optimal generalization error, to the same quantities but for a simpler (generalized) linear model for which explicit expressions are rigorously known. Our bounds, which are expressed in terms of the number of training samples, input dimension and number of hidden units, thus yield fundamental performance limits for any neural network (and actually any learning procedure) trained from limited data generated according to our two-layer teacher neural network model. The proof relies on rigorous tools from spin glasses and is guided by ``Gaussian equivalence principles'' lying at the core of numerous recent analyses of neural networks. With respect to the existing literature, which is either non-rigorous or restricted to the case of the learning of the readout weights only, our results are information-theoretic (i.e. are not specific to any learning algorithm) and, importantly, cover a setting where all the network parameters are trained.

Multimodal foundation models that can holistically process text alongside images, video, audio, and other sensory modalities are increasingly used in a variety of real-world applications. However, it is challenging to characterize and study progress in multimodal foundation models, given the range of possible modeling decisions, tasks, and domains. In this paper, we introduce Holistic Evaluation of Multimodal Models (HEMM) to systematically evaluate the capabilities of multimodal foundation models across a set of 3 dimensions: basic skills, information flow, and real-world use cases. Basic multimodal skills are internal abilities required to solve problems, such as learning interactions across modalities, fine-grained alignment, multi-step reasoning, and the ability to handle external knowledge. Information flow studies how multimodal content changes during a task through querying, translation, editing, and fusion. Use cases span domain-specific challenges introduced in real-world multimedia, affective computing, natural sciences, healthcare, and human-computer interaction applications. Through comprehensive experiments across the 30 tasks in HEMM, we (1) identify key dataset dimensions (e.g., basic skills, information flows, and use cases) that pose challenges to today's models, and (2) distill performance trends regarding how different modeling dimensions (e.g., scale, pre-training data, multimodal alignment, pre-training, and instruction tuning objectives) influence performance. Our conclusions regarding challenging multimodal interactions, use cases, and tasks requiring reasoning and external knowledge, the benefits of data and model scale, and the impacts of instruction tuning yield actionable insights for future work in multimodal foundation models.

We consider distributed linear bandits where M agents learn collaboratively to minimize the overall cumulative regret incurred by all agents. Information exchange is facilitated by a central server, and both the uplink and downlink communications are carried over channels with fixed capacity, which limits the amount of information that can be transmitted in each use of the channels. We investigate the regret-communication trade-off by (i) establishing information-theoretic lower bounds on the required communications (in terms of bits) for achieving a sublinear regret order; (ii) developing an efficient algorithm that achieves the minimum sublinear regret order offered by centralized learning using the minimum order of communications dictated by the information-theoretic lower bounds. For sparse linear bandits, we show a variant of the proposed algorithm offers better regret-communication trade-off by leveraging the sparsity of the problem.

To develop a trustworthy AI system, which aim to identify the input regions that most influence the models decisions. The primary task of existing attribution methods lies in efficiently and accurately identifying the relationships among input-prediction interactions. Particularly when the input data is discrete, such as images, analyzing the relationship between inputs and outputs poses a significant challenge due to the combinatorial explosion. In this paper, we propose a novel and efficient black-box attribution mechanism, LiMA (Less input is More faithful for Attribution), which reformulates the attribution of important regions as an optimization problem for submodular subset selection. First, to accurately assess interactions, we design a submodular function that quantifies subset importance and effectively captures their impact on decision outcomes. Then, efficiently ranking input sub-regions by their importance for attribution, we improve optimization efficiency through a novel bidirectional greedy search algorithm. LiMA identifies both the most and least important samples while ensuring an optimal attribution boundary that minimizes errors. Extensive experiments on eight foundation models demonstrate that our method provides faithful interpretations with fewer regions and exhibits strong generalization, shows an average improvement of 36.3% in Insertion and 39.6% in Deletion. Our method also outperforms the naive greedy search in attribution efficiency, being 1.6 times faster. Furthermore, when explaining the reasons behind model prediction errors, the average highest confidence achieved by our method is, on average, 86.1% higher than that of state-of-the-art attribution algorithms. The code is available at https://github.com/RuoyuChen10/LIMA.

We propose a filtering feature selection framework that considers subsets of features as paths in a graph, where a node is a feature and an edge indicates pairwise (customizable) relations among features, dealing with relevance and redundancy principles. By two different interpretations (exploiting properties of power series of matrices and relying on Markov chains fundamentals) we can evaluate the values of paths (i.e., feature subsets) of arbitrary lengths, eventually go to infinite, from which we dub our framework Infinite Feature Selection (Inf-FS). Going to infinite allows to constrain the computational complexity of the selection process, and to rank the features in an elegant way, that is, considering the value of any path (subset) containing a particular feature. We also propose a simple unsupervised strategy to cut the ranking, so providing the subset of features to keep. In the experiments, we analyze diverse settings with heterogeneous features, for a total of 11 benchmarks, comparing against 18 widely-known comparative approaches. The results show that Inf-FS behaves better in almost any situation, that is, when the number of features to keep are fixed a priori, or when the decision of the subset cardinality is part of the process.

Mathematical researchers, especially those in early-career positions, face critical decisions about topic specialization with limited information about the collaborative environments of different research areas. The aim of this paper is to study how the popularity of a research topic is associated with the structure of that topic's collaboration network, as observed by a suite of measures capturing organizational structure at several scales. We apply these measures to 1,938 algorithmically discovered topics across 121,391 papers sourced from arXiv metadata during the period 2020--2025. Our analysis, which controls for the confounding effects of network size, reveals a structural dichotomy--we find that popular topics organize into modular "schools of thought," while niche topics maintain hierarchical core-periphery structures centered around established experts. This divide is not an artifact of scale, but represents a size-independent structural pattern correlated with popularity. We also document a "constraint reversal": after controlling for size, researchers in popular fields face greater structural constraints on collaboration opportunities, contrary to conventional expectations. Our findings suggest that topic selection is an implicit choice between two fundamentally different collaborative environments, each with distinct implications for a researcher's career. To make these structural patterns transparent to the research community, we developed the Math Research Compass (https://mathresearchcompass.com), an interactive platform providing data on topic popularity and collaboration patterns across mathematical topics.

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.

The design of modern recommender systems relies on understanding which parts of the feature space are relevant for solving a given recommendation task. However, real-world data sets in this domain are often characterized by their large size, sparsity, and noise, making it challenging to identify meaningful signals. Feature ranking represents an efficient branch of algorithms that can help address these challenges by identifying the most informative features and facilitating the automated search for more compact and better-performing models (AutoML). We introduce OutRank, a system for versatile feature ranking and data quality-related anomaly detection. OutRank was built with categorical data in mind, utilizing a variant of mutual information that is normalized with regard to the noise produced by features of the same cardinality. We further extend the similarity measure by incorporating information on feature similarity and combined relevance. The proposed approach's feasibility is demonstrated by speeding up the state-of-the-art AutoML system on a synthetic data set with no performance loss. Furthermore, we considered a real-life click-through-rate prediction data set where it outperformed strong baselines such as random forest-based approaches. The proposed approach enables exploration of up to 300% larger feature spaces compared to AutoML-only approaches, enabling faster search for better models on off-the-shelf hardware.

Finding the mode of a high dimensional probability distribution D is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when D is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known. In this work, we significantly generalize a result of (LeeLiMusco:2021) on mode approximation for Gaussian mixture models. We develop randomized dimensionality reduction methods for mixtures involving a broader class of kernels, including the popular logistic, sigmoid, and generalized Gaussian kernels. As in Lee et al.'s work, our dimensionality reduction results yield quasi-polynomial algorithms for mode finding with multiplicative accuracy (1-epsilon) for any epsilon > 0. Moreover, when combined with gradient descent, they yield efficient practical heuristics for the problem. In addition to our positive results, we prove a hardness result for box kernels, showing that there is no polynomial time algorithm for finding the mode of a kernel density estimate, unless P = NP. Obtaining similar hardness results for kernels used in practice (like Gaussian or logistic kernels) is an interesting future direction.

Multimodal information retrieval (MIR) faces inherent challenges due to the heterogeneity of data sources and the complexity of cross-modal alignment. While previous studies have identified modal gaps in feature spaces, a systematic approach to address these challenges remains unexplored. In this work, we introduce UNITE, a universal framework that tackles these challenges through two critical yet underexplored aspects: data curation and modality-aware training configurations. Our work provides the first comprehensive analysis of how modality-specific data properties influence downstream task performance across diverse scenarios. Moreover, we propose Modal-Aware Masked Contrastive Learning (MAMCL) to mitigate the competitive relationships among the instances of different modalities. Our framework achieves state-of-the-art results on multiple multimodal retrieval benchmarks, outperforming existing methods by notable margins. Through extensive experiments, we demonstrate that strategic modality curation and tailored training protocols are pivotal for robust cross-modal representation learning. This work not only advances MIR performance but also provides a foundational blueprint for future research in multimodal systems. Our project is available at https://friedrichor.github.io/projects/UNITE.

With the emergence of data marketplaces, the demand for methods to assess the value of data has increased significantly. While numerous techniques have been proposed for this purpose, none have specifically addressed graphs as the main data modality. Graphs are widely used across various fields, ranging from chemical molecules to social networks. In this study, we break down graphs into two main components: structural and featural, and we focus on evaluating data without relying on specific task-related metrics, making it applicable in practical scenarios where validation requirements may be lacking. We introduce a novel framework called blind message passing, which aligns the seller's and buyer's graphs using a shared node permutation based on graph matching. This allows us to utilize the graph Wasserstein distance to quantify the differences in the structural distribution of graph datasets, called the structural disparities. We then consider featural aspects of buyers' and sellers' graphs for data valuation and capture their statistical similarities and differences, referred to as relevance and diversity, respectively. Our approach ensures that buyers and sellers remain unaware of each other's datasets. Our experiments on real datasets demonstrate the effectiveness of our approach in capturing the relevance, diversity, and structural disparities of seller data for buyers, particularly in graph-based data valuation scenarios.

Molecular knowledge resides within three different modalities of information sources: molecular structures, biomedical documents, and knowledge bases. Effective incorporation of molecular knowledge from these modalities holds paramount significance in facilitating biomedical research. However, existing multimodal molecular foundation models exhibit limitations in capturing intricate connections between molecular structures and texts, and more importantly, none of them attempt to leverage a wealth of molecular expertise derived from knowledge graphs. In this study, we introduce MolFM, a multimodal molecular foundation model designed to facilitate joint representation learning from molecular structures, biomedical texts, and knowledge graphs. We propose cross-modal attention between atoms of molecular structures, neighbors of molecule entities and semantically related texts to facilitate cross-modal comprehension. We provide theoretical analysis that our cross-modal pre-training captures local and global molecular knowledge by minimizing the distance in the feature space between different modalities of the same molecule, as well as molecules sharing similar structures or functions. MolFM achieves state-of-the-art performance on various downstream tasks. On cross-modal retrieval, MolFM outperforms existing models with 12.13% and 5.04% absolute gains under the zero-shot and fine-tuning settings, respectively. Furthermore, qualitative analysis showcases MolFM's implicit ability to provide grounding from molecular substructures and knowledge graphs. Code and models are available on https://github.com/BioFM/OpenBioMed.

Controllable music generation with deep generative models has become increasingly reliant on disentanglement learning techniques. However, current disentanglement metrics, such as mutual information gap (MIG), are often inadequate and misleading when used for evaluating latent representations in the presence of interdependent semantic attributes often encountered in real-world music datasets. In this work, we propose a dependency-aware information metric as a drop-in replacement for MIG that accounts for the inherent relationship between semantic attributes.

Does the People's Republic of China (PRC) interfere with European elections through ethnic Chinese diaspora media? This question forms the basis of an ongoing research project exploring how PRC narratives about European elections are represented in Chinese diaspora media, and thus the objectives of PRC news media manipulation. In order to study diaspora media efficiently and at scale, it is necessary to use techniques derived from quantitative text analysis, such as topic modelling. In this paper, we present a pipeline for studying information dynamics in Chinese media. Firstly, we present KeyNMF, a new approach to static and dynamic topic modelling using transformer-based contextual embedding models. We provide benchmark evaluations to demonstrate that our approach is competitive on a number of Chinese datasets and metrics. Secondly, we integrate KeyNMF with existing methods for describing information dynamics in complex systems. We apply this pipeline to data from five news sites, focusing on the period of time leading up to the 2024 European parliamentary elections. Our methods and results demonstrate the effectiveness of KeyNMF for studying information dynamics in Chinese media and lay groundwork for further work addressing the broader research questions.

Information Retrieval using dense low-dimensional representations recently became popular and showed out-performance to traditional sparse-representations like BM25. However, no previous work investigated how dense representations perform with large index sizes. We show theoretically and empirically that the performance for dense representations decreases quicker than sparse representations for increasing index sizes. In extreme cases, this can even lead to a tipping point where at a certain index size sparse representations outperform dense representations. We show that this behavior is tightly connected to the number of dimensions of the representations: The lower the dimension, the higher the chance for false positives, i.e. returning irrelevant documents.

Keeping track of all relevant recent publications and experimental results for a research area is a challenging task. Prior work has demonstrated the efficacy of information extraction models in various scientific areas. Recently, several datasets have been released for the yet understudied materials science domain. However, these datasets focus on sub-problems such as parsing synthesis procedures or on sub-domains, e.g., solid oxide fuel cells. In this resource paper, we present MuLMS, a new dataset of 50 open-access articles, spanning seven sub-domains of materials science. The corpus has been annotated by domain experts with several layers ranging from named entities over relations to frame structures. We present competitive neural models for all tasks and demonstrate that multi-task training with existing related resources leads to benefits.

Multimodal learning combines multiple data modalities, broadening the types and complexity of data our models can utilize: for example, from plain text to image-caption pairs. Most multimodal learning algorithms focus on modeling simple one-to-one pairs of data from two modalities, such as image-caption pairs, or audio-text pairs. However, in most real-world settings, entities of different modalities interact with each other in more complex and multifaceted ways, going beyond one-to-one mappings. We propose to represent these complex relationships as graphs, allowing us to capture data with any number of modalities, and with complex relationships between modalities that can flexibly vary from one sample to another. Toward this goal, we propose Multimodal Graph Learning (MMGL), a general and systematic framework for capturing information from multiple multimodal neighbors with relational structures among them. In particular, we focus on MMGL for generative tasks, building upon pretrained Language Models (LMs), aiming to augment their text generation with multimodal neighbor contexts. We study three research questions raised by MMGL: (1) how can we infuse multiple neighbor information into the pretrained LMs, while avoiding scalability issues? (2) how can we infuse the graph structure information among multimodal neighbors into the LMs? and (3) how can we finetune the pretrained LMs to learn from the neighbor context in a parameter-efficient manner? We conduct extensive experiments to answer these three questions on MMGL and analyze the empirical results to pave the way for future MMGL research.

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.

As the field of representation learning grows, there has been a proliferation of different loss functions to solve different classes of problems. We introduce a single information-theoretic equation that generalizes a large collection of modern loss functions in machine learning. In particular, we introduce a framework that shows that several broad classes of machine learning methods are precisely minimizing an integrated KL divergence between two conditional distributions: the supervisory and learned representations. This viewpoint exposes a hidden information geometry underlying clustering, spectral methods, dimensionality reduction, contrastive learning, and supervised learning. This framework enables the development of new loss functions by combining successful techniques from across the literature. We not only present a wide array of proofs, connecting over 23 different approaches, but we also leverage these theoretical results to create state-of-the-art unsupervised image classifiers that achieve a +8% improvement over the prior state-of-the-art on unsupervised classification on ImageNet-1K. We also demonstrate that I-Con can be used to derive principled debiasing methods which improve contrastive representation learners.

Universal multimodal embedding models have achieved great success in capturing semantic relevance between queries and candidates. However, current methods either condense queries and candidates into a single vector, potentially limiting the expressiveness for fine-grained information, or produce too many vectors that are prohibitively expensive for multi-vector retrieval. In this work, we introduce MetaEmbed, a new framework for multimodal retrieval that rethinks how multimodal embeddings are constructed and interacted with at scale. During training, a fixed number of learnable Meta Tokens are appended to the input sequence. At test-time, their last-layer contextualized representations serve as compact yet expressive multi-vector embeddings. Through the proposed Matryoshka Multi-Vector Retrieval training, MetaEmbed learns to organize information by granularity across multiple vectors. As a result, we enable test-time scaling in multimodal retrieval, where users can balance retrieval quality against efficiency demands by selecting the number of tokens used for indexing and retrieval interactions. Extensive evaluations on the Massive Multimodal Embedding Benchmark (MMEB) and the Visual Document Retrieval Benchmark (ViDoRe) confirm that MetaEmbed achieves state-of-the-art retrieval performance while scaling robustly to models with 32B parameters.

Data quality and diversity are key to the construction of effective instruction-tuning datasets. % With the increasing availability of open-source instruction-tuning datasets, it is advantageous to automatically select high-quality and diverse subsets from a vast amount of data. % Existing methods typically prioritize instance quality and use heuristic rules to maintain diversity. % However, this absence of a comprehensive view of the entire collection often leads to suboptimal results. % Moreover, heuristic rules generally focus on distance or clustering within the embedding space, which fails to accurately capture the intent of complex instructions in the semantic space. % To bridge this gap, we propose a unified method for quantifying the information content of datasets. This method models the semantic space by constructing a label graph and quantifies diversity based on the distribution of information within the graph. % Based on such a measurement, we further introduce an efficient sampling method that selects data samples iteratively to Maximize the Information Gain (MIG) in semantic space. % Experiments on various datasets and base models demonstrate that MIG consistently outperforms state-of-the-art methods. % Notably, the model fine-tuned with 5\% Tulu3 data sampled by MIG achieves comparable performance to the official SFT model trained on the full dataset, with improvements of +5.73\% on AlpacaEval and +6.89\% on Wildbench.

Mixture of Experts (MoE), an ensemble of specialized models equipped with a router that dynamically distributes each input to appropriate experts, has achieved successful results in the field of machine learning. However, theoretical understanding of this architecture is falling behind due to its inherent complexity. In this paper, we theoretically study the sample and runtime complexity of MoE following the stochastic gradient descent (SGD) when learning a regression task with an underlying cluster structure of single index models. On the one hand, we prove that a vanilla neural network fails in detecting such a latent organization as it can only process the problem as a whole. This is intrinsically related to the concept of information exponent which is low for each cluster, but increases when we consider the entire task. On the other hand, we show that a MoE succeeds in dividing this problem into easier subproblems by leveraging the ability of each expert to weakly recover the simpler function corresponding to an individual cluster. To the best of our knowledge, this work is among the first to explore the benefits of the MoE framework by examining its SGD dynamics in the context of nonlinear regression.

Optimal Transport is a useful metric to compare probability distributions and to compute a pairing given a ground cost. Its entropic regularization variant (eOT) is crucial to have fast algorithms and reflect fuzzy/noisy matchings. This work focuses on Inverse Optimal Transport (iOT), the problem of inferring the ground cost from samples drawn from a coupling that solves an eOT problem. It is a relevant problem that can be used to infer unobserved/missing links, and to obtain meaningful information about the structure of the ground cost yielding the pairing. On one side, iOT benefits from convexity, but on the other side, being ill-posed, it requires regularization to handle the sampling noise. This work presents an in-depth theoretical study of the l1 regularization to model for instance Euclidean costs with sparse interactions between features. Specifically, we derive a sufficient condition for the robust recovery of the sparsity of the ground cost that can be seen as a far reaching generalization of the Lasso's celebrated Irrepresentability Condition. To provide additional insight into this condition, we work out in detail the Gaussian case. We show that as the entropic penalty varies, the iOT problem interpolates between a graphical Lasso and a classical Lasso, thereby establishing a connection between iOT and graph estimation, an important problem in ML.

Deep neural networks have demonstrated remarkable performance in supervised learning tasks but require large amounts of labeled data. Self-supervised learning offers an alternative paradigm, enabling the model to learn from data without explicit labels. Information theory has been instrumental in understanding and optimizing deep neural networks. Specifically, the information bottleneck principle has been applied to optimize the trade-off between compression and relevant information preservation in supervised settings. However, the optimal information objective in self-supervised learning remains unclear. In this paper, we review various approaches to self-supervised learning from an information-theoretic standpoint and present a unified framework that formalizes the self-supervised information-theoretic learning problem. We integrate existing research into a coherent framework, examine recent self-supervised methods, and identify research opportunities and challenges. Moreover, we discuss empirical measurement of information-theoretic quantities and their estimators. This paper offers a comprehensive review of the intersection between information theory, self-supervised learning, and deep neural networks.

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.

Recent advances in artificial intelligence reveal the limits of purely predictive systems and call for a shift toward causal and collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce the relativity of causal knowledge, which posits structural causal models (SCMs) are inherently imperfect, subjective representations embedded within networks of relationships. By leveraging category theory, we arrange SCMs into a functor category and show that their observational and interventional probability measures naturally form convex structures. This result allows us to encode non-intervened SCMs with convex spaces of probability measures. Next, using sheaf theory, we construct the network sheaf and cosheaf of causal knowledge. These structures enable the transfer of causal knowledge across the network while incorporating interventional consistency and the perspective of the subjects, ultimately leading to the formal, mathematical definition of relative causal knowledge.

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.

Multimodal recommendation systems have attracted increasing attention for their improved performance by leveraging items' multimodal information. Prior methods often build modality-specific item-item semantic graphs from raw modality features and use them as supplementary structures alongside the user-item interaction graph to enhance user preference learning. However, these semantic graphs suffer from semantic deficiencies, including (1) insufficient modeling of collaborative signals among items and (2) structural distortions introduced by noise in raw modality features, ultimately compromising performance. To address these issues, we first extract collaborative signals from the interaction graph and infuse them into each modality-specific item semantic graph to enhance semantic modeling. Then, we design a modulus-based personalized embedding perturbation mechanism that injects perturbations with modulus-guided personalized intensity into embeddings to generate contrastive views. This enables the model to learn noise-robust representations through contrastive learning, thereby reducing the effect of structural noise in semantic graphs. Besides, we propose a dual representation alignment mechanism that first aligns multiple semantic representations via a designed Anchor-based InfoNCE loss using behavior representations as anchors, and then aligns behavior representations with the fused semantics by standard InfoNCE, to ensure representation consistency. Extensive experiments on four benchmark datasets validate the effectiveness of our framework.

We study the problem of detecting the correlation between two Gaussian databases XinR^{ntimes d} and Y^{ntimes d}, each composed of n users with d features. This problem is relevant in the analysis of social media, computational biology, etc. We formulate this as a hypothesis testing problem: under the null hypothesis, these two databases are statistically independent. Under the alternative, however, there exists an unknown permutation sigma over the set of n users (or, row permutation), such that X is rho-correlated with Y^sigma, a permuted version of Y. We determine sharp thresholds at which optimal testing exhibits a phase transition, depending on the asymptotic regime of n and d. Specifically, we prove that if rho^2dto0, as dtoinfty, then weak detection (performing slightly better than random guessing) is statistically impossible, irrespectively of the value of n. This compliments the performance of a simple test that thresholds the sum all entries of X^TY. Furthermore, when d is fixed, we prove that strong detection (vanishing error probability) is impossible for any rho<rho^star, where rho^star is an explicit function of d, while weak detection is again impossible as long as rho^2dto0. These results close significant gaps in current recent related studies.

To deduce new facts on a knowledge graph (KG), a link predictor learns from the graph structure and collects local evidence to find the answer to a given query. However, existing methods suffer from a severe scalability problem due to the utilization of the whole KG for prediction, which hinders their promise on large scale KGs and cannot be directly addressed by vanilla sampling methods. In this work, we propose the one-shot-subgraph link prediction to achieve efficient and adaptive prediction. The design principle is that, instead of directly acting on the whole KG, the prediction procedure is decoupled into two steps, i.e., (i) extracting only one subgraph according to the query and (ii) predicting on this single, query dependent subgraph. We reveal that the non-parametric and computation-efficient heuristics Personalized PageRank (PPR) can effectively identify the potential answers and supporting evidence. With efficient subgraph-based prediction, we further introduce the automated searching of the optimal configurations in both data and model spaces. Empirically, we achieve promoted efficiency and leading performances on five large-scale benchmarks. The code is publicly available at: https://github.com/tmlr-group/one-shot-subgraph.

Deep recommender systems rely heavily on large embedding tables to handle high-cardinality categorical features such as user/item identifiers, and face significant memory constraints at scale. To tackle this challenge, hashing techniques are often employed to map multiple entities to the same embedding and thus reduce the size of the embedding tables. Concurrently, graph-based collaborative signals have emerged as powerful tools in recommender systems, yet their potential for optimizing embedding table reduction remains unexplored. This paper introduces GraphHash, the first graph-based approach that leverages modularity-based bipartite graph clustering on user-item interaction graphs to reduce embedding table sizes. We demonstrate that the modularity objective has a theoretical connection to message-passing, which provides a foundation for our method. By employing fast clustering algorithms, GraphHash serves as a computationally efficient proxy for message-passing during preprocessing and a plug-and-play graph-based alternative to traditional ID hashing. Extensive experiments show that GraphHash substantially outperforms diverse hashing baselines on both retrieval and click-through-rate prediction tasks. In particular, GraphHash achieves on average a 101.52% improvement in recall when reducing the embedding table size by more than 75%, highlighting the value of graph-based collaborative information for model reduction. Our code is available at https://github.com/snap-research/GraphHash.

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.

The rapid spread of multimodal misinformation on social media calls for more effective and robust detection methods. Recent advances leveraging multimodal large language models (MLLMs) have shown the potential in addressing this challenge. However, it remains unclear exactly where the bottleneck of existing approaches lies (evidence retrieval v.s. reasoning), hindering the further advances in this field. On the dataset side, existing benchmarks either contain outdated events, leading to evaluation bias due to discrepancies with contemporary social media scenarios as MLLMs can simply memorize these events, or artificially synthetic, failing to reflect real-world misinformation patterns. Additionally, it lacks comprehensive analyses of MLLM-based model design strategies. To address these issues, we introduce XFacta, a contemporary, real-world dataset that is better suited for evaluating MLLM-based detectors. We systematically evaluate various MLLM-based misinformation detection strategies, assessing models across different architectures and scales, as well as benchmarking against existing detection methods. Building on these analyses, we further enable a semi-automatic detection-in-the-loop framework that continuously updates XFacta with new content to maintain its contemporary relevance. Our analysis provides valuable insights and practices for advancing the field of multimodal misinformation detection. The code and data have been released.

Enhancing the intelligibility and interpretability of machine learning is a crucial task in responding to the demand for Explicability as an AI principle, and in promoting the better social implementation of AI. The aim of our research is to contribute to this improvement by reformulating machine learning models through the lens of category theory, thereby developing a semantic framework for structuring and understanding AI systems. Our categorical modeling in this paper clarifies and formalizes the structural interplay between residuals and parameters in supervised learning. The present paper focuses on the multiple linear regression model, which represents the most basic form of supervised learning. By defining two concrete categories corresponding to parameters and data, along with an adjoint pair of functors between them, we introduce our categorical formulation of supervised learning. We show that the essential structure of this framework is captured by what we call the Gauss-Markov Adjunction. Within this setting, the dual flow of information can be explicitly described as a correspondence between variations in parameters and residuals. The ordinary least squares estimator for the parameters and the minimum residual are related via the preservation of limits by the right adjoint functor. Furthermore, we position this formulation as an instance of extended denotational semantics for supervised learning, and propose applying a semantic perspective developed in theoretical computer science as a formal foundation for Explicability in AI.

Medical decision-making requires integrating diverse medical information, from imaging to clinical narratives. These medical modalities are often acquired in a many-to-many manner. However, current medical vision-language pretraining models (Med-VLPMs) fail to directly account for this many-to-many mapping in their model training and embeddings. To address this, we present Probabilistic Modality-Enhanced Diagnosis (ProbMED), a multimodal Med-VLPM that employs probabilistic contrastive learning to model distributions over embeddings rather than deterministic estimates. ProbMED aligns four distinct modalities -- chest X-rays, electrocardiograms, echocardiograms, and clinical text -- into a unified probabilistic embedding space. We use InfoNCE loss with Hellinger distance to integrate inter-modality distributions. We introduce a probabilistic synthetic sampling loss that captures modality-specific mean and variance to improve intra-modality binding. Extensive experiments across 13 medical datasets demonstrate that our model outperforms current Med-VLPMs in cross-modality retrieval, zero-shot, and few-shot classification. We also demonstrate the robust integration of multiple modalities for prognostication, showing improved intra- and inter-medical modality binding.

With information consumption via online video streaming becoming increasingly popular, misinformation video poses a new threat to the health of the online information ecosystem. Though previous studies have made much progress in detecting misinformation in text and image formats, video-based misinformation brings new and unique challenges to automatic detection systems: 1) high information heterogeneity brought by various modalities, 2) blurred distinction between misleading video manipulation and ubiquitous artistic video editing, and 3) new patterns of misinformation propagation due to the dominant role of recommendation systems on online video platforms. To facilitate research on this challenging task, we conduct this survey to present advances in misinformation video detection research. We first analyze and characterize the misinformation video from three levels including signals, semantics, and intents. Based on the characterization, we systematically review existing works for detection from features of various modalities to techniques for clue integration. We also introduce existing resources including representative datasets and widely used tools. Besides summarizing existing studies, we discuss related areas and outline open issues and future directions to encourage and guide more research on misinformation video detection. Our corresponding public repository is available at https://github.com/ICTMCG/Awesome-Misinfo-Video-Detection.

The rise in loosely-structured data available through text, images, and other modalities has called for new ways of querying them. Multimedia Information Retrieval has filled this gap and has witnessed exciting progress in recent years. Tasks such as search and retrieval of extensive multimedia archives have undergone massive performance improvements, driven to a large extent by recent developments in multimodal deep learning. However, methods in this field remain limited in the kinds of queries they support and, in particular, their inability to answer database-like queries. For this reason, inspired by recent work on neural databases, we propose a new framework, which we name Multimodal Neural Databases (MMNDBs). MMNDBs can answer complex database-like queries that involve reasoning over different input modalities, such as text and images, at scale. In this paper, we present the first architecture able to fulfill this set of requirements and test it with several baselines, showing the limitations of currently available models. The results show the potential of these new techniques to process unstructured data coming from different modalities, paving the way for future research in the area. Code to replicate the experiments will be released at https://github.com/GiovanniTRA/MultimodalNeuralDatabases

Dynamic feature selection, where we sequentially query features to make accurate predictions with a minimal budget, is a promising paradigm to reduce feature acquisition costs and provide transparency into a model's predictions. The problem is challenging, however, as it requires both predicting with arbitrary feature sets and learning a policy to identify valuable selections. Here, we take an information-theoretic perspective and prioritize features based on their mutual information with the response variable. The main challenge is implementing this policy, and we design a new approach that estimates the mutual information in a discriminative rather than generative fashion. Building on our approach, we then introduce several further improvements: allowing variable feature budgets across samples, enabling non-uniform feature costs, incorporating prior information, and exploring modern architectures to handle partial inputs. Our experiments show that our method provides consistent gains over recent methods across a variety of datasets.

In this work, we introduce Multiple Embedding Model for EHR (MEME), an approach that views Electronic Health Records (EHR) as multimodal data. This approach incorporates "pseudo-notes", textual representations of tabular EHR concepts such as diagnoses and medications, and allows us to effectively employ Large Language Models (LLMs) for EHR representation. This framework also adopts a multimodal approach, embedding each EHR modality separately. We demonstrate the effectiveness of MEME by applying it to several tasks within the Emergency Department across multiple hospital systems. Our findings show that MEME surpasses the performance of both single modality embedding methods and traditional machine learning approaches. However, we also observe notable limitations in generalizability across hospital institutions for all tested models.

By leveraging the retrieval of information from external knowledge databases, Large Language Models (LLMs) exhibit enhanced capabilities for accomplishing many knowledge-intensive tasks. However, due to the inherent flaws of current retrieval systems, there might exist irrelevant information within those retrieving top-ranked passages. In this work, we present a comprehensive investigation into the robustness of LLMs to different types of irrelevant information under various conditions. We initially introduce a framework to construct high-quality irrelevant information that ranges from semantically unrelated, partially related, and related to questions. Furthermore, our analysis demonstrates that the constructed irrelevant information not only scores highly on similarity metrics, being highly retrieved by existing systems, but also bears semantic connections to the context. Our investigation reveals that current LLMs still face challenges in discriminating highly semantically related information and can be easily distracted by these irrelevant yet misleading contents. Besides, we also find that current solutions for handling irrelevant information have limitations in improving the robustness of LLMs to such distractions. Resources are available at https://github.com/Di-viner/LLM-Robustness-to-Irrelevant-Information.

The study of network robustness is a critical tool in the characterization and sense making of complex interconnected systems such as infrastructure, communication and social networks. While significant research has been conducted in all of these areas, gaps in the surveying literature still exist. Answers to key questions are currently scattered across multiple scientific fields and numerous papers. In this survey, we distill key findings across numerous domains and provide researchers crucial access to important information by--(1) summarizing and comparing recent and classical graph robustness measures; (2) exploring which robustness measures are most applicable to different categories of networks (e.g., social, infrastructure; (3) reviewing common network attack strategies, and summarizing which attacks are most effective across different network topologies; and (4) extensive discussion on selecting defense techniques to mitigate attacks across a variety of networks. This survey guides researchers and practitioners in navigating the expansive field of network robustness, while summarizing answers to key questions. We conclude by highlighting current research directions and open problems.

We study the problem of adaptively identifying patient subpopulations that benefit from a given treatment during a confirmatory clinical trial. This type of adaptive clinical trial has been thoroughly studied in biostatistics, but has been allowed only limited adaptivity so far. Here, we aim to relax classical restrictions on such designs and investigate how to incorporate ideas from the recent machine learning literature on adaptive and online experimentation to make trials more flexible and efficient. We find that the unique characteristics of the subpopulation selection problem -- most importantly that (i) one is usually interested in finding subpopulations with any treatment benefit (and not necessarily the single subgroup with largest effect) given a limited budget and that (ii) effectiveness only has to be demonstrated across the subpopulation on average -- give rise to interesting challenges and new desiderata when designing algorithmic solutions. Building on these findings, we propose AdaGGI and AdaGCPI, two meta-algorithms for subpopulation construction. We empirically investigate their performance across a range of simulation scenarios and derive insights into their (dis)advantages across different settings.

Pairwise clustering, in general, partitions a set of items via a known similarity function. In our treatment, clustering is modeled as a transductive prediction problem. Thus rather than beginning with a known similarity function, the function instead is hidden and the learner only receives a random sample consisting of a subset of the pairwise similarities. An additional set of pairwise side-information may be given to the learner, which then determines the inductive bias of our algorithms. We measure performance not based on the recovery of the hidden similarity function, but instead on how well we classify each item. We give tight bounds on the number of misclassifications. We provide two algorithms. The first algorithm SACA is a simple agglomerative clustering algorithm which runs in near linear time, and which serves as a baseline for our analyses. Whereas the second algorithm, RGCA, enables the incorporation of side-information which may lead to improved bounds at the cost of a longer running time.

Multimodal recommender systems utilizing multimodal features (e.g., images and textual descriptions) typically show better recommendation accuracy than general recommendation models based solely on user-item interactions. Generally, prior work fuses multimodal features into item ID embeddings to enrich item representations, thus failing to capture the latent semantic item-item structures. In this context, LATTICE proposes to learn the latent structure between items explicitly and achieves state-of-the-art performance for multimodal recommendations. However, we argue the latent graph structure learning of LATTICE is both inefficient and unnecessary. Experimentally, we demonstrate that freezing its item-item structure before training can also achieve competitive performance. Based on this finding, we propose a simple yet effective model, dubbed as FREEDOM, that FREEzes the item-item graph and DenOises the user-item interaction graph simultaneously for Multimodal recommendation. Theoretically, we examine the design of FREEDOM through a graph spectral perspective and demonstrate that it possesses a tighter upper bound on the graph spectrum. In denoising the user-item interaction graph, we devise a degree-sensitive edge pruning method, which rejects possibly noisy edges with a high probability when sampling the graph. We evaluate the proposed model on three real-world datasets and show that FREEDOM can significantly outperform current strongest baselines. Compared with LATTICE, FREEDOM achieves an average improvement of 19.07% in recommendation accuracy while reducing its memory cost up to 6times on large graphs. The source code is available at: https://github.com/enoche/FREEDOM.

Data used for analytics and machine learning often take the form of tables with categorical entries. We introduce a family of lossless compression algorithms for such data that proceed in four steps: (i) Estimate latent variables associated to rows and columns; (ii) Partition the table in blocks according to the row/column latents; (iii) Apply a sequential (e.g. Lempel-Ziv) coder to each of the blocks; (iv) Append a compressed encoding of the latents. We evaluate it on several benchmark datasets, and study optimal compression in a probabilistic model for that tabular data, whereby latent values are independent and table entries are conditionally independent given the latent values. We prove that the model has a well defined entropy rate and satisfies an asymptotic equipartition property. We also prove that classical compression schemes such as Lempel-Ziv and finite-state encoders do not achieve this rate. On the other hand, the latent estimation strategy outlined above achieves the optimal rate.

Current multimodal information retrieval studies mainly focus on single-image inputs, which limits real-world applications involving multiple images and text-image interleaved content. In this work, we introduce the text-image interleaved retrieval (TIIR) task, where the query and document are interleaved text-image sequences, and the model is required to understand the semantics from the interleaved context for effective retrieval. We construct a TIIR benchmark based on naturally interleaved wikiHow tutorials, where a specific pipeline is designed to generate interleaved queries. To explore the task, we adapt several off-the-shelf retrievers and build a dense baseline by interleaved multimodal large language model (MLLM). We then propose a novel Matryoshka Multimodal Embedder (MME), which compresses the number of visual tokens at different granularity, to address the challenge of excessive visual tokens in MLLM-based TIIR models. Experiments demonstrate that simple adaption of existing models does not consistently yield effective results. Our MME achieves significant improvements over the baseline by substantially fewer visual tokens. We provide extensive analysis and will release the dataset and code to facilitate future research.

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning algorithms as functors that map pseudometric spaces to optimization objectives and that factor through hierarchical clustering functors. We then use this characterization to prove refinement bounds on manifold learning loss functions and construct a hierarchy of manifold learning algorithms based on their equivariants. We express several popular manifold learning algorithms as functors at different levels of this hierarchy, including Metric Multidimensional Scaling, IsoMap, and UMAP. Next, we use interleaving distance to study the stability of a broad class of manifold learning algorithms. We present bounds on how closely the embeddings these algorithms produce from noisy data approximate the embeddings they would learn from noiseless data. Finally, we use our framework to derive a set of novel manifold learning algorithms, which we experimentally demonstrate are competitive with the state of the art.

We utilize a recently developed topic modeling method called SeNMFk, extending the standard Non-negative Matrix Factorization (NMF) methods by incorporating the semantic structure of the text, and adding a robust system for determining the number of topics. With SeNMFk, we were able to extract coherent topics validated by human experts. From these topics, a few are relatively general and cover broad concepts, while the majority can be precisely mapped to specific scientific effects or measurement techniques. The topics also differ by ubiquity, with only three topics prevalent in almost 40 percent of the abstract, while each specific topic tends to dominate a small subset of the abstracts. These results demonstrate the ability of SeNMFk to produce a layered and nuanced analysis of large scientific corpora.

We show that existing unsupervised methods on large language model (LLM) activations do not discover knowledge -- instead they seem to discover whatever feature of the activations is most prominent. The idea behind unsupervised knowledge elicitation is that knowledge satisfies a consistency structure, which can be used to discover knowledge. We first prove theoretically that arbitrary features (not just knowledge) satisfy the consistency structure of a particular leading unsupervised knowledge-elicitation method, contrast-consistent search (Burns et al. - arXiv:2212.03827). We then present a series of experiments showing settings in which unsupervised methods result in classifiers that do not predict knowledge, but instead predict a different prominent feature. We conclude that existing unsupervised methods for discovering latent knowledge are insufficient, and we contribute sanity checks to apply to evaluating future knowledge elicitation methods. Conceptually, we hypothesise that the identification issues explored here, e.g. distinguishing a model's knowledge from that of a simulated character's, will persist for future unsupervised methods.

Data diversity is crucial for the instruction tuning of large language models. Existing studies have explored various diversity-aware data selection methods to construct high-quality datasets and enhance model performance. However, the fundamental problem of precisely defining and measuring data diversity remains underexplored, limiting clear guidance for data engineering. To address this, we systematically analyze 11 existing diversity measurement methods by evaluating their correlation with model performance through extensive fine-tuning experiments. Our results indicate that a reliable diversity measure should properly account for both inter-sample differences and the information distribution in the sample space. Building on this, we propose NovelSum, a new diversity metric based on sample-level "novelty." Experiments on both simulated and real-world data show that NovelSum accurately captures diversity variations and achieves a 0.97 correlation with instruction-tuned model performance, highlighting its value in guiding data engineering practices. With NovelSum as an optimization objective, we further develop a greedy, diversity-oriented data selection strategy that outperforms existing approaches, validating both the effectiveness and practical significance of our metric.

We propose a direct estimation method for R\'{e}nyi and f-divergence measures based on a new graph theoretical interpretation. Suppose that we are given two sample sets X and Y, respectively with N and M samples, where eta:=M/N is a constant value. Considering the k-nearest neighbor (k-NN) graph of Y in the joint data set (X,Y), we show that the average powered ratio of the number of X points to the number of Y points among all k-NN points is proportional to R\'{e}nyi divergence of X and Y densities. A similar method can also be used to estimate f-divergence measures. We derive bias and variance rates, and show that for the class of gamma-H\"{o}lder smooth functions, the estimator achieves the MSE rate of O(N^{-2gamma/(gamma+d)}). Furthermore, by using a weighted ensemble estimation technique, for density functions with continuous and bounded derivatives of up to the order d, and some extra conditions at the support set boundary, we derive an ensemble estimator that achieves the parametric MSE rate of O(1/N). Our estimators are more computationally tractable than other competing estimators, which makes them appealing in many practical applications.

Prediction problems often admit competing models that perform almost equally well. This effect challenges key assumptions in machine learning when competing models assign conflicting predictions. In this paper, we define predictive multiplicity as the ability of a prediction problem to admit competing models with conflicting predictions. We introduce formal measures to evaluate the severity of predictive multiplicity and develop integer programming tools to compute them exactly for linear classification problems. We apply our tools to measure predictive multiplicity in recidivism prediction problems. Our results show that real-world datasets may admit competing models that assign wildly conflicting predictions, and motivate the need to measure and report predictive multiplicity in model development.

Large multimodal models (LMMs) have recently shown great progress in text-rich image understanding, yet they still struggle with complex, multi-page, visually-rich documents. Traditional methods using document parsers for retrieval-augmented generation suffer from performance and efficiency limitations, while directly presenting all pages to LMMs leads to inefficiencies, especially with lengthy documents. In this work, we present a novel framework named LoRA-Contextualizing Adaptation of Large multimodal models (LoCAL), which broadens the capabilities of any LMM to support long-document understanding. We demonstrate that LMMs can effectively serve as multimodal retrievers, fetching relevant pages to answer user questions based on these pages. LoCAL is implemented with two specific LMM adapters: one for evidence page retrieval and another for question answering. Empirical results show state-of-the-art performance on public benchmarks, demonstrating the effectiveness of LoCAL.

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order probability distributions, i.e., predictions in the form of distributions on probability distributions. A completely conclusive solution has not yet been found, however, as shown by recent criticisms of commonly used uncertainty measures associated with second-order distributions, identifying undesirable theoretical properties of these measures. In light of these criticisms, we propose a set of formal criteria that meaningful uncertainty measures for predictive uncertainty based on second-order distributions should obey. Moreover, we provide a general framework for developing uncertainty measures to account for these criteria, and offer an instantiation based on the Wasserstein distance, for which we prove that all criteria are satisfied.

To answer a question, language models often need to integrate prior knowledge learned during pretraining and new information presented in context. We hypothesize that models perform this integration in a predictable way across different questions and contexts: models will rely more on prior knowledge for questions about entities (e.g., persons, places, etc.) that they are more familiar with due to higher exposure in the training corpus, and be more easily persuaded by some contexts than others. To formalize this problem, we propose two mutual information-based metrics to measure a model's dependency on a context and on its prior about an entity: first, the persuasion score of a given context represents how much a model depends on the context in its decision, and second, the susceptibility score of a given entity represents how much the model can be swayed away from its original answer distribution about an entity. Following well-established measurement modeling methods, we empirically test for the validity and reliability of these metrics. Finally, we explore and find a relationship between the scores and the model's expected familiarity with an entity, and provide two use cases to illustrate their benefits.

The pervasive influence of misinformation has far-reaching and detrimental effects on both individuals and society. The COVID-19 pandemic has witnessed an alarming surge in the dissemination of medical misinformation. However, existing datasets pertaining to misinformation predominantly focus on textual information, neglecting the inclusion of visual elements, and tend to center solely on COVID-19-related misinformation, overlooking misinformation surrounding other diseases. Furthermore, the potential of Large Language Models (LLMs), such as the ChatGPT developed in late 2022, in generating misinformation has been overlooked in previous works. To overcome these limitations, we present Med-MMHL, a novel multi-modal misinformation detection dataset in a general medical domain encompassing multiple diseases. Med-MMHL not only incorporates human-generated misinformation but also includes misinformation generated by LLMs like ChatGPT. Our dataset aims to facilitate comprehensive research and development of methodologies for detecting misinformation across diverse diseases and various scenarios, including human and LLM-generated misinformation detection at the sentence, document, and multi-modal levels. To access our dataset and code, visit our GitHub repository: https://github.com/styxsys0927/Med-MMHL.

Academic survey writing, which distills vast literature into a coherent and insightful narrative, remains a labor-intensive and intellectually demanding task. While recent approaches, such as general DeepResearch agents and survey-specialized methods, can generate surveys automatically (a.k.a. LLM4Survey), their outputs often fall short of human standards and there lacks a rigorous, reader-aligned benchmark for thoroughly revealing their deficiencies. To fill the gap, we propose a fine-grained, quiz-driven evaluation framework SurveyBench, featuring (1) typical survey topics source from recent 11,343 arXiv papers and corresponding 4,947 high-quality surveys; (2) a multifaceted metric hierarchy that assesses the outline quality (e.g., coverage breadth, logical coherence), content quality (e.g., synthesis granularity, clarity of insights), and non-textual richness; and (3) a dual-mode evaluation protocol that includes content-based and quiz-based answerability tests, explicitly aligned with readers' informational needs. Results show SurveyBench effectively challenges existing LLM4Survey approaches (e.g., on average 21% lower than human in content-based evaluation).

The advent of Large Language Models (LLMs) has paved the way for AI search engines, e.g., SearchGPT, showcasing a new paradigm in human-internet interaction. However, most current AI search engines are limited to text-only settings, neglecting the multimodal user queries and the text-image interleaved nature of website information. Recently, Large Multimodal Models (LMMs) have made impressive strides. Yet, whether they can function as AI search engines remains under-explored, leaving the potential of LMMs in multimodal search an open question. To this end, we first design a delicate pipeline, MMSearch-Engine, to empower any LMMs with multimodal search capabilities. On top of this, we introduce MMSearch, a comprehensive evaluation benchmark to assess the multimodal search performance of LMMs. The curated dataset contains 300 manually collected instances spanning 14 subfields, which involves no overlap with the current LMMs' training data, ensuring the correct answer can only be obtained within searching. By using MMSearch-Engine, the LMMs are evaluated by performing three individual tasks (requery, rerank, and summarization), and one challenging end-to-end task with a complete searching process. We conduct extensive experiments on closed-source and open-source LMMs. Among all tested models, GPT-4o with MMSearch-Engine achieves the best results, which surpasses the commercial product, Perplexity Pro, in the end-to-end task, demonstrating the effectiveness of our proposed pipeline. We further present error analysis to unveil current LMMs still struggle to fully grasp the multimodal search tasks, and conduct ablation study to indicate the potential of scaling test-time computation for AI search engine. We hope MMSearch may provide unique insights to guide the future development of multimodal AI search engine. Project Page: https://mmsearch.github.io

Currently, high-dimensional data is ubiquitous in data science, which necessitates the development of techniques to decompose and interpret such multidimensional (aka tensor) datasets. Finding a low dimensional representation of the data, that is, its inherent structure, is one of the approaches that can serve to understand the dynamics of low dimensional latent features hidden in the data. Nonnegative RESCAL is one such technique, particularly well suited to analyze self-relational data, such as dynamic networks found in international trade flows. Nonnegative RESCAL computes a low dimensional tensor representation by finding the latent space containing multiple modalities. Estimating the dimensionality of this latent space is crucial for extracting meaningful latent features. Here, to determine the dimensionality of the latent space with nonnegative RESCAL, we propose a latent dimension determination method which is based on clustering of the solutions of multiple realizations of nonnegative RESCAL decompositions. We demonstrate the performance of our model selection method on synthetic data and then we apply our method to decompose a network of international trade flows data from International Monetary Fund and validate the resulting features against empirical facts from economic literature.

In this paper we introduce Feature Gradients, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e., in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N . This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Crucially, our algorithm is capable of finding higher-order correlations between features and targets for both the N > D and N < D regimes, as opposed to approaches that do not consider such interactions and/or only consider one regime. We provide experimental demonstration of the algorithm in small and large sample-and feature-size settings.

An established measure of the expressive power of a given ReLU neural network is the number of linear regions into which it partitions the input space. There exist many different, non-equivalent definitions of what a linear region actually is. We systematically assess which papers use which definitions and discuss how they relate to each other. We then analyze the computational complexity of counting the number of such regions for the various definitions. Generally, this turns out to be an intractable problem. We prove NP- and #P-hardness results already for networks with one hidden layer and strong hardness of approximation results for two or more hidden layers. Finally, on the algorithmic side, we demonstrate that counting linear regions can at least be achieved in polynomial space for some common definitions.

We introduce a theoretical framework for sampling from unnormalized densities based on a smoothing scheme that uses an isotropic Gaussian kernel with a single fixed noise scale. We prove one can decompose sampling from a density (minimal assumptions made on the density) into a sequence of sampling from log-concave conditional densities via accumulation of noisy measurements with equal noise levels. Our construction is unique in that it keeps track of a history of samples, making it non-Markovian as a whole, but it is lightweight algorithmically as the history only shows up in the form of a running empirical mean of samples. Our sampling algorithm generalizes walk-jump sampling (Saremi & Hyv\"arinen, 2019). The "walk" phase becomes a (non-Markovian) chain of (log-concave) Markov chains. The "jump" from the accumulated measurements is obtained by empirical Bayes. We study our sampling algorithm quantitatively using the 2-Wasserstein metric and compare it with various Langevin MCMC algorithms. We also report a remarkable capacity of our algorithm to "tunnel" between modes of a distribution.

In the marketing field, understanding consumer heterogeneity, which is the internal or psychological difference among consumers that cannot be captured by behavioral logs, has long been a critical challenge. However, a number of consumers today usually post their evaluation on the specific product on the online platform, which can be the valuable source of such unobservable differences among consumers. Several previous studies have shown the validity of the analysis on text modality, but on the other hand, such analyses may not necessarily demonstrate sufficient predictive accuracy for text alone, as they may not include information readily available from cross-sectional data, such as consumer profile data. In addition, recent advances in machine learning techniques, such as large-scale language models (LLMs) and multimodal learning have made it possible to deal with the various kind of dataset simultaneously, including textual data and the traditional cross-sectional data, and the joint representations can be effectively obtained from multiple modalities. Therefore, this study constructs a product evaluation model that takes into account consumer heterogeneity by multimodal learning of online product reviews and consumer profile information. We also compare multiple models using different modalities or hyper-parameters to demonstrate the robustness of multimodal learning in marketing analysis.

Multimodal recommendation systems are increasingly becoming foundational technologies for e-commerce and content platforms, enabling personalized services by jointly modeling users' historical behaviors and the multimodal features of items (e.g., visual and textual). However, most existing methods rely on either static fusion strategies or graph-based local interaction modeling, facing two critical limitations: (1) insufficient ability to model fine-grained cross-modal associations, leading to suboptimal fusion quality; and (2) a lack of global distribution-level consistency, causing representational bias. To address these, we propose MambaRec, a novel framework that integrates local feature alignment and global distribution regularization via attention-guided learning. At its core, we introduce the Dilated Refinement Attention Module (DREAM), which uses multi-scale dilated convolutions with channel-wise and spatial attention to align fine-grained semantic patterns between visual and textual modalities. This module captures hierarchical relationships and context-aware associations, improving cross-modal semantic modeling. Additionally, we apply Maximum Mean Discrepancy (MMD) and contrastive loss functions to constrain global modality alignment, enhancing semantic consistency. This dual regularization reduces mode-specific deviations and boosts robustness. To improve scalability, MambaRec employs a dimensionality reduction strategy to lower the computational cost of high-dimensional multimodal features. Extensive experiments on real-world e-commerce datasets show that MambaRec outperforms existing methods in fusion quality, generalization, and efficiency. Our code has been made publicly available at https://github.com/rkl71/MambaRec.

In modern machine learning problems we deal with datasets that are either distributed by nature or potentially large for which distributing the computations is usually a standard way to proceed, since centralized algorithms are in general ineffective. We propose a distributed learning approach for mixtures of experts (MoE) models with an aggregation strategy to construct a reduction estimator from local estimators fitted parallelly to distributed subsets of the data. The aggregation is based on an optimal minimization of an expected transportation divergence between the large MoE composed of local estimators and the unknown desired MoE model. We show that the provided reduction estimator is consistent as soon as the local estimators to be aggregated are consistent, and its construction is performed by a proposed majorization-minimization (MM) algorithm that is computationally effective. We study the statistical and numerical properties for the proposed reduction estimator on experiments that demonstrate its performance compared to namely the global estimator constructed in a centralized way from the full dataset. For some situations, the computation time is more than ten times faster, for a comparable performance. Our source codes are publicly available on Github.

State-of-the-art retrieval models typically address a straightforward search scenario, where retrieval tasks are fixed (e.g., finding a passage to answer a specific question) and only a single modality is supported for both queries and retrieved results. This paper introduces techniques for advancing information retrieval with multimodal large language models (MLLMs), enabling a broader search scenario, termed universal multimodal retrieval, where multiple modalities and diverse retrieval tasks are accommodated. To this end, we first study fine-tuning an MLLM as a bi-encoder retriever on 10 datasets with 16 retrieval tasks. Our empirical results show that the fine-tuned MLLM retriever is capable of understanding challenging queries, composed of both text and image, but underperforms a smaller CLIP retriever in cross-modal retrieval tasks due to modality bias from MLLMs. To address the issue, we propose modality-aware hard negative mining to mitigate the modality bias exhibited by MLLM retrievers. Second, we propose to continually fine-tune the universal multimodal retriever to enhance its text retrieval capability while maintaining multimodal retrieval capability. As a result, our model, MM-Embed, achieves state-of-the-art performance on the multimodal retrieval benchmark M-BEIR, which spans multiple domains and tasks, while also surpassing the state-of-the-art text retrieval model, NV-Embed-v1, on MTEB retrieval benchmark. Finally, we explore to prompt the off-the-shelf MLLMs as the zero-shot rerankers to refine the ranking of the candidates from the multimodal retriever. We find that through prompt-and-reranking, MLLMs can further improve multimodal retrieval when the user queries (e.g., text-image composed queries) are more complex and challenging to understand. These findings also pave the way to advance universal multimodal retrieval in the future.

Knowledge Graph Embedding (KGE) models are used to learn continuous representations of entities and relations. A key task in the literature is predicting missing links between entities. However, Knowledge Graphs are not just sets of links but also have semantics underlying their structure. Semantics is crucial in several downstream tasks, such as query answering or reasoning. We introduce the subgraph inference task, where a model has to generate likely and semantically valid subgraphs. We propose IntelliGraphs, a set of five new Knowledge Graph datasets. The IntelliGraphs datasets contain subgraphs with semantics expressed in logical rules for evaluating subgraph inference. We also present the dataset generator that produced the synthetic datasets. We designed four novel baseline models, which include three models based on traditional KGEs. We evaluate their expressiveness and show that these models cannot capture the semantics. We believe this benchmark will encourage the development of machine learning models that emphasize semantic understanding.

Multimodal information extraction (MIE) gains significant attention as the popularity of multimedia content increases. However, current MIE methods often resort to using task-specific model structures, which results in limited generalizability across tasks and underutilizes shared knowledge across MIE tasks. To address these issues, we propose UMIE, a unified multimodal information extractor to unify three MIE tasks as a generation problem using instruction tuning, being able to effectively extract both textual and visual mentions. Extensive experiments show that our single UMIE outperforms various state-of-the-art (SoTA) methods across six MIE datasets on three tasks. Furthermore, in-depth analysis demonstrates UMIE's strong generalization in the zero-shot setting, robustness to instruction variants, and interpretability. Our research serves as an initial step towards a unified MIE model and initiates the exploration into both instruction tuning and large language models within the MIE domain. Our code, data, and model are available at https://github.com/ZUCC-AI/UMIE

Even for a conservative estimate, 80% of enterprise data reside in unstructured files, stored in data lakes that accommodate heterogeneous formats. Classical search engines can no longer meet information seeking needs, especially when the task is to browse and explore for insight formulation. In other words, there are no obvious search keywords to use. Knowledge graphs, due to their natural visual appeals that reduce the human cognitive load, become the winning candidate for heterogeneous data integration and knowledge representation. In this paper, we introduce Docs2KG, a novel framework designed to extract multimodal information from diverse and heterogeneous unstructured documents, including emails, web pages, PDF files, and Excel files. Dynamically generates a unified knowledge graph that represents the extracted key information, Docs2KG enables efficient querying and exploration of document data lakes. Unlike existing approaches that focus on domain-specific data sources or pre-designed schemas, Docs2KG offers a flexible and extensible solution that can adapt to various document structures and content types. The proposed framework unifies data processing supporting a multitude of downstream tasks with improved domain interpretability. Docs2KG is publicly accessible at https://docs2kg.ai4wa.com, and a demonstration video is available at https://docs2kg.ai4wa.com/Video.

Retrieval-augmented generation integrates the capabilities of large language models with relevant information retrieved from an extensive corpus, yet encounters challenges when confronted with real-world noisy data. One recent solution is to train a filter module to find relevant content but only achieve suboptimal noise compression. In this paper, we propose to introduce the information bottleneck theory into retrieval-augmented generation. Our approach involves the filtration of noise by simultaneously maximizing the mutual information between compression and ground output, while minimizing the mutual information between compression and retrieved passage. In addition, we derive the formula of information bottleneck to facilitate its application in novel comprehensive evaluations, the selection of supervised fine-tuning data, and the construction of reinforcement learning rewards. Experimental results demonstrate that our approach achieves significant improvements across various question answering datasets, not only in terms of the correctness of answer generation but also in the conciseness with 2.5% compression rate.

Large Multimodal Models(LMMs) face notable challenges when encountering multimodal knowledge conflicts, particularly under retrieval-augmented generation(RAG) frameworks where the contextual information from external sources may contradict the model's internal parametric knowledge, leading to unreliable outputs. However, existing benchmarks fail to reflect such realistic conflict scenarios. Most focus solely on intra-memory conflicts, while context-memory and inter-context conflicts remain largely investigated. Furthermore, commonly used factual knowledge-based evaluations are often overlooked, and existing datasets lack a thorough investigation into conflict detection capabilities. To bridge this gap, we propose MMKC-Bench, a benchmark designed to evaluate factual knowledge conflicts in both context-memory and inter-context scenarios. MMKC-Bench encompasses three types of multimodal knowledge conflicts and includes 1,573 knowledge instances and 3,381 images across 23 broad types, collected through automated pipelines with human verification. We evaluate three representative series of LMMs on both model behavior analysis and conflict detection tasks. Our findings show that while current LMMs are capable of recognizing knowledge conflicts, they tend to favor internal parametric knowledge over external evidence. We hope MMKC-Bench will foster further research in multimodal knowledge conflict and enhance the development of multimodal RAG systems. The source code is available at https://github.com/MLLMKCBENCH/MLLMKC.

This paper has been accepted in the NeurIPS 2024 D & B Track. Harmful memes have proliferated on the Chinese Internet, while research on detecting Chinese harmful memes significantly lags behind due to the absence of reliable datasets and effective detectors. To this end, we focus on the comprehensive detection of Chinese harmful memes. We construct ToxiCN MM, the first Chinese harmful meme dataset, which consists of 12,000 samples with fine-grained annotations for various meme types. Additionally, we propose a baseline detector, Multimodal Knowledge Enhancement (MKE), incorporating contextual information of meme content generated by the LLM to enhance the understanding of Chinese memes. During the evaluation phase, we conduct extensive quantitative experiments and qualitative analyses on multiple baselines, including LLMs and our MKE. The experimental results indicate that detecting Chinese harmful memes is challenging for existing models while demonstrating the effectiveness of MKE. The resources for this paper are available at https://github.com/DUT-lujunyu/ToxiCN_MM.

Recent advances in maximizing mutual information (MI) between the source and target have demonstrated its effectiveness in text generation. However, previous works paid little attention to modeling the backward network of MI (i.e., dependency from the target to the source), which is crucial to the tightness of the variational information maximization lower bound. In this paper, we propose Adversarial Mutual Information (AMI): a text generation framework which is formed as a novel saddle point (min-max) optimization aiming to identify joint interactions between the source and target. Within this framework, the forward and backward networks are able to iteratively promote or demote each other's generated instances by comparing the real and synthetic data distributions. We also develop a latent noise sampling strategy that leverages random variations at the high-level semantic space to enhance the long term dependency in the generation process. Extensive experiments based on different text generation tasks demonstrate that the proposed AMI framework can significantly outperform several strong baselines, and we also show that AMI has potential to lead to a tighter lower bound of maximum mutual information for the variational information maximization problem.

Advanced Multimodal Large Language Models (MLLMs) struggle with recent Knowledge-based VQA tasks, such as INFOSEEK and Encyclopedic-VQA, due to their limited and frozen knowledge scope, often leading to ambiguous and inaccurate responses. Thus, multimodal Retrieval-Augmented Generation (mRAG) is naturally introduced to provide MLLMs with comprehensive and up-to-date knowledge, effectively expanding the knowledge scope. However, current mRAG methods have inherent drawbacks, including: 1) Performing retrieval even when external knowledge is not needed. 2) Lacking of identification of evidence that supports the query. 3) Increasing model complexity due to additional information filtering modules or rules. To address these shortcomings, we propose a novel generalized framework called multimodal Retrieval-Reflection-Augmented Generation (mR^2AG), which achieves adaptive retrieval and useful information localization to enable answers through two easy-to-implement reflection operations, preventing high model complexity. In mR^2AG, Retrieval-Reflection is designed to distinguish different user queries and avoids redundant retrieval calls, and Relevance-Reflection is introduced to guide the MLLM in locating beneficial evidence of the retrieved content and generating answers accordingly. In addition, mR^2AG can be integrated into any well-trained MLLM with efficient fine-tuning on the proposed mR^2AG Instruction-Tuning dataset (mR^2AG-IT). mR^2AG significantly outperforms state-of-the-art MLLMs (e.g., GPT-4v/o) and RAG-based MLLMs on INFOSEEK and Encyclopedic-VQA, while maintaining the exceptional capabilities of base MLLMs across a wide range of Visual-dependent tasks.

We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is "dimension-free" in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.

Interference is ubiquitous when conducting causal experiments over networks. Except for certain network structures, causal inference on the network in the presence of interference is difficult due to the entanglement between the treatment assignments and the interference levels. In this article, we conduct causal inference under interference on an observed, sparse but connected network, and we propose a novel design of experiments based on an independent set. Compared to conventional designs, the independent-set design focuses on an independent subset of data and controls their interference exposures through the assignments to the rest (auxiliary set). We provide a lower bound on the size of the independent set from a greedy algorithm , and justify the theoretical performance of estimators under the proposed design. Our approach is capable of estimating both spillover effects and treatment effects. We justify its superiority over conventional methods and illustrate the empirical performance through simulations.

There is increasing interest in the use of multimodal data in various web applications, such as digital advertising and e-commerce. Typical methods for extracting important information from multimodal data rely on a mid-fusion architecture that combines the feature representations from multiple encoders. However, as the number of modalities increases, several potential problems with the mid-fusion model structure arise, such as an increase in the dimensionality of the concatenated multimodal features and missing modalities. To address these problems, we propose a new concept that considers multimodal inputs as a set of sequences, namely, deep multimodal sequence sets (DM^2S^2). Our set-aware concept consists of three components that capture the relationships among multiple modalities: (a) a BERT-based encoder to handle the inter- and intra-order of elements in the sequences, (b) intra-modality residual attention (IntraMRA) to capture the importance of the elements in a modality, and (c) inter-modality residual attention (InterMRA) to enhance the importance of elements with modality-level granularity further. Our concept exhibits performance that is comparable to or better than the previous set-aware models. Furthermore, we demonstrate that the visualization of the learned InterMRA and IntraMRA weights can provide an interpretation of the prediction results.

Seminal research in the field of graph neural networks (GNNs) has revealed a direct correspondence between the expressive capabilities of GNNs and the k-dimensional Weisfeiler-Leman (kWL) test, a widely-recognized method for verifying graph isomorphism. This connection has reignited interest in comprehending the specific graph properties effectively distinguishable by the kWL test. A central focus of research in this field revolves around determining the least dimensionality k, for which kWL can discern graphs with different number of occurrences of a pattern graph P. We refer to such a least k as the WL-dimension of this pattern counting problem. This inquiry traditionally delves into two distinct counting problems related to patterns: subgraph counting and induced subgraph counting. Intriguingly, despite their initial appearance as separate challenges with seemingly divergent approaches, both of these problems are interconnected components of a more comprehensive problem: "graph motif parameters". In this paper, we provide a precise characterization of the WL-dimension of labeled graph motif parameters. As specific instances of this result, we obtain characterizations of the WL-dimension of the subgraph counting and induced subgraph counting problem for every labeled pattern P. We additionally demonstrate that in cases where the kWL test distinguishes between graphs with varying occurrences of a pattern P, the exact number of occurrences of P can be computed uniformly using only local information of the last layer of a corresponding GNN. We finally delve into the challenge of recognizing the WL-dimension of various graph parameters. We give a polynomial time algorithm for determining the WL-dimension of the subgraph counting problem for given pattern P, answering an open question from previous work.

Diversity is an important criterion for many areas of machine learning (ML), including generative modeling and dataset curation. Yet little work has gone into understanding, formalizing, and measuring diversity in ML. In this paper, we address the diversity evaluation problem by proposing the Vendi Score, which connects and extends ideas from ecology and quantum statistical mechanics to ML. The Vendi Score is defined as the exponential of the Shannon entropy of the eigenvalues of a similarity matrix. This matrix is induced by a user-defined similarity function applied to the sample to be evaluated for diversity. In taking a similarity function as input, the Vendi Score enables its user to specify any desired form of diversity. Importantly, unlike many existing metrics in ML, the Vendi Score doesn't require a reference dataset or distribution over samples or labels, it is therefore general and applicable to any generative model, decoding algorithm, and dataset from any domain where similarity can be defined. We showcased the Vendi Score on molecular generative modeling, a domain where diversity plays an important role in enabling the discovery of novel molecules. We found that the Vendi Score addresses shortcomings of the current diversity metric of choice in that domain. We also applied the Vendi Score to generative models of images and decoding algorithms of text and found it confirms known results about diversity in those domains. Furthermore, we used the Vendi Score to measure mode collapse, a known limitation of generative adversarial networks (GANs). In particular, the Vendi Score revealed that even GANs that capture all the modes of a labeled dataset can be less diverse than the original dataset. Finally, the interpretability of the Vendi Score allowed us to diagnose several benchmark ML datasets for diversity, opening the door for diversity-informed data augmentation.

Given a sample of size N, it is often useful to select a subsample of smaller size n<N to be used for statistical estimation or learning. Such a data selection step is useful to reduce the requirements of data labeling and the computational complexity of learning. We assume to be given N unlabeled samples {{boldsymbol x}_i}_{ile N}, and to be given access to a `surrogate model' that can predict labels y_i better than random guessing. Our goal is to select a subset of the samples, to be denoted by {{boldsymbol x}_i}_{iin G}, of size |G|=n<N. We then acquire labels for this set and we use them to train a model via regularized empirical risk minimization. By using a mixture of numerical experiments on real and synthetic data, and mathematical derivations under low- and high- dimensional asymptotics, we show that: (i)~Data selection can be very effective, in particular beating training on the full sample in some cases; (ii)~Certain popular choices in data selection methods (e.g. unbiased reweighted subsampling, or influence function-based subsampling) can be substantially suboptimal.

We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels defined on the nodes of a graph. Our algorithm enjoys subquadratic time complexity with respect to the number of nodes, overcoming the notoriously prohibitive cubic scaling of exact graph kernel evaluation. It can also be trivially distributed across machines, permitting learning on much larger networks. At the heart of the algorithm is a modulation function which upweights or downweights the contribution from different random walks depending on their lengths. We show that by parameterising it with a neural network we can obtain u-GRFs that give higher-quality kernel estimates or perform efficient, scalable kernel learning. We provide robust theoretical analysis and support our findings with experiments including pointwise estimation of fixed graph kernels, solving non-homogeneous graph ordinary differential equations, node clustering and kernel regression on triangular meshes.

Graph Neural Networks (GNNs) are neural models that leverage the dependency structure in graphical data via message passing among the graph nodes. GNNs have emerged as pivotal architectures in analyzing graph-structured data, and their expansive application in sensitive domains requires a comprehensive understanding of their decision-making processes -- necessitating a framework for GNN explainability. An explanation function for GNNs takes a pre-trained GNN along with a graph as input, to produce a `sufficient statistic' subgraph with respect to the graph label. A main challenge in studying GNN explainability is to provide fidelity measures that evaluate the performance of these explanation functions. This paper studies this foundational challenge, spotlighting the inherent limitations of prevailing fidelity metrics, including Fid_+, Fid_-, and Fid_Delta. Specifically, a formal, information-theoretic definition of explainability is introduced and it is shown that existing metrics often fail to align with this definition across various statistical scenarios. The reason is due to potential distribution shifts when subgraphs are removed in computing these fidelity measures. Subsequently, a robust class of fidelity measures are introduced, and it is shown analytically that they are resilient to distribution shift issues and are applicable in a wide range of scenarios. Extensive empirical analysis on both synthetic and real datasets are provided to illustrate that the proposed metrics are more coherent with gold standard metrics. The source code is available at https://trustai4s-lab.github.io/fidelity.

Many methods in differentially private model training rely on computing the similarity between a query point (such as public or synthetic data) and private data. We abstract out this common subroutine and study the following fundamental algorithmic problem: Given a similarity function f and a large high-dimensional private dataset X subset R^d, output a differentially private (DP) data structure which approximates sum_{x in X} f(x,y) for any query y. We consider the cases where f is a kernel function, such as f(x,y) = e^{-|x-y|_2^2/sigma^2} (also known as DP kernel density estimation), or a distance function such as f(x,y) = |x-y|_2, among others. Our theoretical results improve upon prior work and give better privacy-utility trade-offs as well as faster query times for a wide range of kernels and distance functions. The unifying approach behind our results is leveraging `low-dimensional structures' present in the specific functions f that we study, using tools such as provable dimensionality reduction, approximation theory, and one-dimensional decomposition of the functions. Our algorithms empirically exhibit improved query times and accuracy over prior state of the art. We also present an application to DP classification. Our experiments demonstrate that the simple methodology of classifying based on average similarity is orders of magnitude faster than prior DP-SGD based approaches for comparable accuracy.

Vector embeddings have been tasked with an ever-increasing set of retrieval tasks over the years, with a nascent rise in using them for reasoning, instruction-following, coding, and more. These new benchmarks push embeddings to work for any query and any notion of relevance that could be given. While prior works have pointed out theoretical limitations of vector embeddings, there is a common assumption that these difficulties are exclusively due to unrealistic queries, and those that are not can be overcome with better training data and larger models. In this work, we demonstrate that we may encounter these theoretical limitations in realistic settings with extremely simple queries. We connect known results in learning theory, showing that the number of top-k subsets of documents capable of being returned as the result of some query is limited by the dimension of the embedding. We empirically show that this holds true even if we restrict to k=2, and directly optimize on the test set with free parameterized embeddings. We then create a realistic dataset called LIMIT that stress tests models based on these theoretical results, and observe that even state-of-the-art models fail on this dataset despite the simple nature of the task. Our work shows the limits of embedding models under the existing single vector paradigm and calls for future research to develop methods that can resolve this fundamental limitation.

We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically involves an underlying projection process that maps the original hypergraph onto a graph, and is common in graph-based analysis. While hypergraph projection can potentially lead to loss of higher-order relations, there exists very limited studies on the consequences of doing so, as well as its remediation. This work fills this gap by doing two things: (1) we develop analysis based on graph and set theory, showing two ubiquitous patterns of hyperedges that are root to structural information loss in all hypergraph projections; we also quantify the combinatorial impossibility of recovering the lost higher-order structures if no extra help is provided; (2) we still seek to recover the lost higher-order structures in hypergraph projection, and in light of (1)'s findings we propose to relax the problem into a learning-based setting. Under this setting, we develop a learning-based hypergraph reconstruction method based on an important statistic of hyperedge distributions that we find. Our reconstruction method is evaluated on 8 real-world datasets under different settings, and exhibits consistently good performance. We also demonstrate benefits of the reconstructed hypergraphs via use cases of protein rankings and link predictions.

Bootstrap aggregating (bagging) is an effective ensemble protocol, which is believed can enhance robustness by its majority voting mechanism. Recent works further prove the sample-wise robustness certificates for certain forms of bagging (e.g. partition aggregation). Beyond these particular forms, in this paper, we propose the first collective certification for general bagging to compute the tight robustness against the global poisoning attack. Specifically, we compute the maximum number of simultaneously changed predictions via solving a binary integer linear programming (BILP) problem. Then we analyze the robustness of vanilla bagging and give the upper bound of the tolerable poison budget. Based on this analysis, we propose hash bagging to improve the robustness of vanilla bagging almost for free. This is achieved by modifying the random subsampling in vanilla bagging to a hash-based deterministic subsampling, as a way of controlling the influence scope for each poisoning sample universally. Our extensive experiments show the notable advantage in terms of applicability and robustness.

Cancer has relational information residing at varying scales, modalities, and resolutions of the acquired data, such as radiology, pathology, genomics, proteomics, and clinical records. Integrating diverse data types can improve the accuracy and reliability of cancer diagnosis and treatment. There can be disease-related information that is too subtle for humans or existing technological tools to discern visually. Traditional methods typically focus on partial or unimodal information about biological systems at individual scales and fail to encapsulate the complete spectrum of the heterogeneous nature of data. Deep neural networks have facilitated the development of sophisticated multimodal data fusion approaches that can extract and integrate relevant information from multiple sources. Recent deep learning frameworks such as Graph Neural Networks (GNNs) and Transformers have shown remarkable success in multimodal learning. This review article provides an in-depth analysis of the state-of-the-art in GNNs and Transformers for multimodal data fusion in oncology settings, highlighting notable research studies and their findings. We also discuss the foundations of multimodal learning, inherent challenges, and opportunities for integrative learning in oncology. By examining the current state and potential future developments of multimodal data integration in oncology, we aim to demonstrate the promising role that multimodal neural networks can play in cancer prevention, early detection, and treatment through informed oncology practices in personalized settings.

To be informative, an evaluation must measure how well systems generalize to realistic unseen data. We identify limitations of and propose improvements to current evaluations of text-to-SQL systems. First, we compare human-generated and automatically generated questions, characterizing properties of queries necessary for real-world applications. To facilitate evaluation on multiple datasets, we release standardized and improved versions of seven existing datasets and one new text-to-SQL dataset. Second, we show that the current division of data into training and test sets measures robustness to variations in the way questions are asked, but only partially tests how well systems generalize to new queries; therefore, we propose a complementary dataset split for evaluation of future work. Finally, we demonstrate how the common practice of anonymizing variables during evaluation removes an important challenge of the task. Our observations highlight key difficulties, and our methodology enables effective measurement of future development.

We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels (cc-universal) on the metric spaces, which results in reproducing kernel Hilbert spaces for the predictor and response that are rich enough to characterize the conditional independence that determines sufficient dimension reduction. For univariate distributions, we construct the universal kernel using the Wasserstein distance, while for multivariate distributions, we resort to the sliced Wasserstein distance. The sliced Wasserstein distance ensures that the metric space possesses similar topological properties to the Wasserstein space while also offering significant computation benefits. Numerical results based on synthetic data show that our method outperforms possible competing methods. The method is also applied to several data sets, including fertility and mortality data and Calgary temperature data.

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples (x,y) from an unknown distribution on R^n times { pm 1}, whose marginal distribution on x is the standard Gaussian and the labels y can be arbitrary, the goal is to output a hypothesis with 0-1 loss OPT+epsilon, where OPT is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

Dual encoders perform retrieval by encoding documents and queries into dense lowdimensional vectors, scoring each document by its inner product with the query. We investigate the capacity of this architecture relative to sparse bag-of-words models and attentional neural networks. Using both theoretical and empirical analysis, we establish connections between the encoding dimension, the margin between gold and lower-ranked documents, and the document length, suggesting limitations in the capacity of fixed-length encodings to support precise retrieval of long documents. Building on these insights, we propose a simple neural model that combines the efficiency of dual encoders with some of the expressiveness of more costly attentional architectures, and explore sparse-dense hybrids to capitalize on the precision of sparse retrieval. These models outperform strong alternatives in large-scale retrieval.

We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a local region around the query variable in the target model so that the marginal distribution of the query variable can be accurately approximated. We introduce two approximation error bounds based on the Dobrushin's comparison theorem and apply our bounds to derive a greedy expansion algorithm that efficiently guides the selection of neighbor nodes for localized inference. We verify our theoretical bounds on various datasets and demonstrate that our localized inference algorithm can provide fast and accurate approximation for large graphical models.

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.

Semantic word embeddings represent the meaning of a word via a vector, and are created by diverse methods. Many use nonlinear operations on co-occurrence statistics, and have hand-tuned hyperparameters and reweighting methods. This paper proposes a new generative model, a dynamic version of the log-linear topic model of~mnih2007three. The methodological novelty is to use the prior to compute closed form expressions for word statistics. This provides a theoretical justification for nonlinear models like PMI, word2vec, and GloVe, as well as some hyperparameter choices. It also helps explain why low-dimensional semantic embeddings contain linear algebraic structure that allows solution of word analogies, as shown by~mikolov2013efficient and many subsequent papers. Experimental support is provided for the generative model assumptions, the most important of which is that latent word vectors are fairly uniformly dispersed in space.

Stochastic optimization is one of the central problems in Machine Learning and Theoretical Computer Science. In the standard model, the algorithm is given a fixed distribution known in advance. In practice though, one may acquire at a cost extra information to make better decisions. In this paper, we study how to buy information for stochastic optimization and formulate this question as an online learning problem. Assuming the learner has an oracle for the original optimization problem, we design a 2-competitive deterministic algorithm and a e/(e-1)-competitive randomized algorithm for buying information. We show that this ratio is tight as the problem is equivalent to a robust generalization of the ski-rental problem, which we call super-martingale stopping. We also consider an adaptive setting where the learner can choose to buy information after taking some actions for the underlying optimization problem. We focus on the classic optimization problem, Min-Sum Set Cover, where the goal is to quickly find an action that covers a given request drawn from a known distribution. We provide an 8-competitive algorithm running in polynomial time that chooses actions and decides when to buy information about the underlying request.

With the recent surge in interest surrounding generative paradigms, generative recommendation has increasingly attracted the attention of researchers in the recommendation community. This paradigm generally consists of two stages. In the first stage, pretrained semantic embeddings or collaborative ID embeddings are quantized to create item codes, aiming to capture and preserve rich semantic or collaborative knowledge within these codes. The second stage involves utilizing these discrete codes to perform an autoregressive sequence generation task. Existing methods often either overlook collaborative or semantic knowledge, or combine the two roughly. In this paper, we observe that naively concatenating representations from semantic and collaborative modality leads to a semantic domination issue, where the resulting representation is overly influenced by semantic information, effectively overshadowing the collaborative representation. Consequently, downstream recommendation tasks fail to fully exploit the knowledge from both modalities, resulting in suboptimal performance. To address this, we propose a progressive collaborative and semantic knowledge fusion model for generative recommendation, named PRORec, which integrates semantic and collaborative knowledge with a unified code through a two-stage framework. Specifically, in the first stage, we propose a cross-modality knowledge alignment task, which integrates semantic knowledge into collaborative embeddings, enhancing their representational capability. In the second stage, we propose an in-modality knowledge distillation task, designed to effectively capture and integrate knowledge from both semantic and collaborative modalities. Extensive experiments on three widely used benchmarks validate the effectiveness of our approach, demonstrating its superiority compared to existing methods.

We propose Meta-Prod2vec, a novel method to compute item similarities for recommendation that leverages existing item metadata. Such scenarios are frequently encountered in applications such as content recommendation, ad targeting and web search. Our method leverages past user interactions with items and their attributes to compute low-dimensional embeddings of items. Specifically, the item metadata is in- jected into the model as side information to regularize the item embeddings. We show that the new item representa- tions lead to better performance on recommendation tasks on an open music dataset.