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Nov 3

How explainable are adversarially-robust CNNs?

Three important criteria of existing convolutional neural networks (CNNs) are (1) test-set accuracy; (2) out-of-distribution accuracy; and (3) explainability. While these criteria have been studied independently, their relationship is unknown. For example, do CNNs that have a stronger out-of-distribution performance have also stronger explainability? Furthermore, most prior feature-importance studies only evaluate methods on 2-3 common vanilla ImageNet-trained CNNs, leaving it unknown how these methods generalize to CNNs of other architectures and training algorithms. Here, we perform the first, large-scale evaluation of the relations of the three criteria using 9 feature-importance methods and 12 ImageNet-trained CNNs that are of 3 training algorithms and 5 CNN architectures. We find several important insights and recommendations for ML practitioners. First, adversarially robust CNNs have a higher explainability score on gradient-based attribution methods (but not CAM-based or perturbation-based methods). Second, AdvProp models, despite being highly accurate more than both vanilla and robust models alone, are not superior in explainability. Third, among 9 feature attribution methods tested, GradCAM and RISE are consistently the best methods. Fourth, Insertion and Deletion are biased towards vanilla and robust models respectively, due to their strong correlation with the confidence score distributions of a CNN. Fifth, we did not find a single CNN to be the best in all three criteria, which interestingly suggests that CNNs are harder to interpret as they become more accurate.

  • 4 authors
·
May 25, 2022

Interpreting Object-level Foundation Models via Visual Precision Search

Advances in multimodal pre-training have propelled object-level foundation models, such as Grounding DINO and Florence-2, in tasks like visual grounding and object detection. However, interpreting these models\' decisions has grown increasingly challenging. Existing interpretable attribution methods for object-level task interpretation have notable limitations: (1) gradient-based methods lack precise localization due to visual-textual fusion in foundation models, and (2) perturbation-based methods produce noisy saliency maps, limiting fine-grained interpretability. To address these, we propose a Visual Precision Search method that generates accurate attribution maps with fewer regions. Our method bypasses internal model parameters to overcome attribution issues from multimodal fusion, dividing inputs into sparse sub-regions and using consistency and collaboration scores to accurately identify critical decision-making regions. We also conducted a theoretical analysis of the boundary guarantees and scope of applicability of our method. Experiments on RefCOCO, MS COCO, and LVIS show our approach enhances object-level task interpretability over SOTA for Grounding DINO and Florence-2 across various evaluation metrics, with faithfulness gains of 23.7\%, 31.6\%, and 20.1\% on MS COCO, LVIS, and RefCOCO for Grounding DINO, and 102.9\% and 66.9\% on MS COCO and RefCOCO for Florence-2. Additionally, our method can interpret failures in visual grounding and object detection tasks, surpassing existing methods across multiple evaluation metrics. The code will be released at https://github.com/RuoyuChen10/VPS.

  • 8 authors
·
Nov 25, 2024

Less is More: Efficient Black-box Attribution via Minimal Interpretable Subset Selection

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.

  • 7 authors
·
Apr 1

Causal Analysis for Robust Interpretability of Neural Networks

Interpreting the inner function of neural networks is crucial for the trustworthy development and deployment of these black-box models. Prior interpretability methods focus on correlation-based measures to attribute model decisions to individual examples. However, these measures are susceptible to noise and spurious correlations encoded in the model during the training phase (e.g., biased inputs, model overfitting, or misspecification). Moreover, this process has proven to result in noisy and unstable attributions that prevent any transparent understanding of the model's behavior. In this paper, we develop a robust interventional-based method grounded by causal analysis to capture cause-effect mechanisms in pre-trained neural networks and their relation to the prediction. Our novel approach relies on path interventions to infer the causal mechanisms within hidden layers and isolate relevant and necessary information (to model prediction), avoiding noisy ones. The result is task-specific causal explanatory graphs that can audit model behavior and express the actual causes underlying its performance. We apply our method to vision models trained on classification tasks. On image classification tasks, we provide extensive quantitative experiments to show that our approach can capture more stable and faithful explanations than standard attribution-based methods. Furthermore, the underlying causal graphs reveal the neural interactions in the model, making it a valuable tool in other applications (e.g., model repair).

  • 5 authors
·
May 15, 2023

Better Understanding Differences in Attribution Methods via Systematic Evaluations

Deep neural networks are very successful on many vision tasks, but hard to interpret due to their black box nature. To overcome this, various post-hoc attribution methods have been proposed to identify image regions most influential to the models' decisions. Evaluating such methods is challenging since no ground truth attributions exist. We thus propose three novel evaluation schemes to more reliably measure the faithfulness of those methods, to make comparisons between them more fair, and to make visual inspection more systematic. To address faithfulness, we propose a novel evaluation setting (DiFull) in which we carefully control which parts of the input can influence the output in order to distinguish possible from impossible attributions. To address fairness, we note that different methods are applied at different layers, which skews any comparison, and so evaluate all methods on the same layers (ML-Att) and discuss how this impacts their performance on quantitative metrics. For more systematic visualizations, we propose a scheme (AggAtt) to qualitatively evaluate the methods on complete datasets. We use these evaluation schemes to study strengths and shortcomings of some widely used attribution methods over a wide range of models. Finally, we propose a post-processing smoothing step that significantly improves the performance of some attribution methods, and discuss its applicability.

  • 3 authors
·
Mar 21, 2023

Less is More: Fewer Interpretable Region via Submodular Subset Selection

Image attribution algorithms aim to identify important regions that are highly relevant to model decisions. Although existing attribution solutions can effectively assign importance to target elements, they still face the following challenges: 1) existing attribution methods generate inaccurate small regions thus misleading the direction of correct attribution, and 2) the model cannot produce good attribution results for samples with wrong predictions. To address the above challenges, this paper re-models the above image attribution problem as a submodular subset selection problem, aiming to enhance model interpretability using fewer regions. To address the lack of attention to local regions, we construct a novel submodular function to discover more accurate small interpretation regions. To enhance the attribution effect for all samples, we also impose four different constraints on the selection of sub-regions, i.e., confidence, effectiveness, consistency, and collaboration scores, to assess the importance of various subsets. Moreover, our theoretical analysis substantiates that the proposed function is in fact submodular. Extensive experiments show that the proposed method outperforms SOTA methods on two face datasets (Celeb-A and VGG-Face2) and one fine-grained dataset (CUB-200-2011). For correctly predicted samples, the proposed method improves the Deletion and Insertion scores with an average of 4.9% and 2.5% gain relative to HSIC-Attribution. For incorrectly predicted samples, our method achieves gains of 81.0% and 18.4% compared to the HSIC-Attribution algorithm in the average highest confidence and Insertion score respectively. The code is released at https://github.com/RuoyuChen10/SMDL-Attribution.

  • 5 authors
·
Feb 14, 2024

A likelihood approach to nonparametric estimation of a singular distribution using deep generative models

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

  • 4 authors
·
May 9, 2021

RelP: Faithful and Efficient Circuit Discovery via Relevance Patching

Activation patching is a standard method in mechanistic interpretability for localizing the components of a model responsible for specific behaviors, but it is computationally expensive to apply at scale. Attribution patching offers a faster, gradient-based approximation, yet suffers from noise and reduced reliability in deep, highly non-linear networks. In this work, we introduce Relevance Patching (RelP), which replaces the local gradients in attribution patching with propagation coefficients derived from Layer-wise Relevance Propagation (LRP). LRP propagates the network's output backward through the layers, redistributing relevance to lower-level components according to local propagation rules that ensure properties such as relevance conservation or improved signal-to-noise ratio. Like attribution patching, RelP requires only two forward passes and one backward pass, maintaining computational efficiency while improving faithfulness. We validate RelP across a range of models and tasks, showing that it more accurately approximates activation patching than standard attribution patching, particularly when analyzing residual stream and MLP outputs in the Indirect Object Identification (IOI) task. For instance, for MLP outputs in GPT-2 Large, attribution patching achieves a Pearson correlation of 0.006, whereas RelP reaches 0.956, highlighting the improvement offered by RelP. Additionally, we compare the faithfulness of sparse feature circuits identified by RelP and Integrated Gradients (IG), showing that RelP achieves comparable faithfulness without the extra computational cost associated with IG.

  • 4 authors
·
Aug 28

CRAFT: Concept Recursive Activation FacTorization for Explainability

Attribution methods, which employ heatmaps to identify the most influential regions of an image that impact model decisions, have gained widespread popularity as a type of explainability method. However, recent research has exposed the limited practical value of these methods, attributed in part to their narrow focus on the most prominent regions of an image -- revealing "where" the model looks, but failing to elucidate "what" the model sees in those areas. In this work, we try to fill in this gap with CRAFT -- a novel approach to identify both "what" and "where" by generating concept-based explanations. We introduce 3 new ingredients to the automatic concept extraction literature: (i) a recursive strategy to detect and decompose concepts across layers, (ii) a novel method for a more faithful estimation of concept importance using Sobol indices, and (iii) the use of implicit differentiation to unlock Concept Attribution Maps. We conduct both human and computer vision experiments to demonstrate the benefits of the proposed approach. We show that the proposed concept importance estimation technique is more faithful to the model than previous methods. When evaluating the usefulness of the method for human experimenters on a human-centered utility benchmark, we find that our approach significantly improves on two of the three test scenarios. Our code is freely available at github.com/deel-ai/Craft.

  • 8 authors
·
Nov 17, 2022

Fine-Grained Perturbation Guidance via Attention Head Selection

Recent guidance methods in diffusion models steer reverse sampling by perturbing the model to construct an implicit weak model and guide generation away from it. Among these approaches, attention perturbation has demonstrated strong empirical performance in unconditional scenarios where classifier-free guidance is not applicable. However, existing attention perturbation methods lack principled approaches for determining where perturbations should be applied, particularly in Diffusion Transformer (DiT) architectures where quality-relevant computations are distributed across layers. In this paper, we investigate the granularity of attention perturbations, ranging from the layer level down to individual attention heads, and discover that specific heads govern distinct visual concepts such as structure, style, and texture quality. Building on this insight, we propose "HeadHunter", a systematic framework for iteratively selecting attention heads that align with user-centric objectives, enabling fine-grained control over generation quality and visual attributes. In addition, we introduce SoftPAG, which linearly interpolates each selected head's attention map toward an identity matrix, providing a continuous knob to tune perturbation strength and suppress artifacts. Our approach not only mitigates the oversmoothing issues of existing layer-level perturbation but also enables targeted manipulation of specific visual styles through compositional head selection. We validate our method on modern large-scale DiT-based text-to-image models including Stable Diffusion 3 and FLUX.1, demonstrating superior performance in both general quality enhancement and style-specific guidance. Our work provides the first head-level analysis of attention perturbation in diffusion models, uncovering interpretable specialization within attention layers and enabling practical design of effective perturbation strategies.

Adversarial Style Augmentation for Domain Generalization

It is well-known that the performance of well-trained deep neural networks may degrade significantly when they are applied to data with even slightly shifted distributions. Recent studies have shown that introducing certain perturbation on feature statistics (\eg, mean and standard deviation) during training can enhance the cross-domain generalization ability. Existing methods typically conduct such perturbation by utilizing the feature statistics within a mini-batch, limiting their representation capability. Inspired by the domain generalization objective, we introduce a novel Adversarial Style Augmentation (ASA) method, which explores broader style spaces by generating more effective statistics perturbation via adversarial training. Specifically, we first search for the most sensitive direction and intensity for statistics perturbation by maximizing the task loss. By updating the model against the adversarial statistics perturbation during training, we allow the model to explore the worst-case domain and hence improve its generalization performance. To facilitate the application of ASA, we design a simple yet effective module, namely AdvStyle, which instantiates the ASA method in a plug-and-play manner. We justify the efficacy of AdvStyle on tasks of cross-domain classification and instance retrieval. It achieves higher mean accuracy and lower performance fluctuation. Especially, our method significantly outperforms its competitors on the PACS dataset under the single source generalization setting, \eg, boosting the classification accuracy from 61.2\% to 67.1\% with a ResNet50 backbone. Our code will be available at https://github.com/YBZh/AdvStyle.

  • 5 authors
·
Jan 29, 2023

Comprehensive Attribution: Inherently Explainable Vision Model with Feature Detector

As deep vision models' popularity rapidly increases, there is a growing emphasis on explanations for model predictions. The inherently explainable attribution method aims to enhance the understanding of model behavior by identifying the important regions in images that significantly contribute to predictions. It is achieved by cooperatively training a selector (generating an attribution map to identify important features) and a predictor (making predictions using the identified features). Despite many advancements, existing methods suffer from the incompleteness problem, where discriminative features are masked out, and the interlocking problem, where the non-optimized selector initially selects noise, causing the predictor to fit on this noise and perpetuate the cycle. To address these problems, we introduce a new objective that discourages the presence of discriminative features in the masked-out regions thus enhancing the comprehensiveness of feature selection. A pre-trained detector is introduced to detect discriminative features in the masked-out region. If the selector selects noise instead of discriminative features, the detector can observe and break the interlocking situation by penalizing the selector. Extensive experiments show that our model makes accurate predictions with higher accuracy than the regular black-box model, and produces attribution maps with high feature coverage, localization ability, fidelity and robustness. Our code will be available at https://github.com/Zood123/COMET{https://github.com/Zood123/COMET}.

  • 3 authors
·
Jul 27, 2024

Experts Don't Cheat: Learning What You Don't Know By Predicting Pairs

Identifying how much a model {p}_{theta}(Y|X) knows about the stochastic real-world process p(Y|X) it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate p(Y|X) and also estimate the remaining gaps between {p}_{theta}(Y|X) and p(Y|X): train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for p(Y|X) and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don't know across ambiguous image classification, (synthetic) language modeling, and partially-observable navigation tasks, outperforming existing techniques.

  • 4 authors
·
Feb 13, 2024

Identifying Representations for Intervention Extrapolation

The premise of identifiable and causal representation learning is to improve the current representation learning paradigm in terms of generalizability or robustness. Despite recent progress in questions of identifiability, more theoretical results demonstrating concrete advantages of these methods for downstream tasks are needed. In this paper, we consider the task of intervention extrapolation: predicting how interventions affect an outcome, even when those interventions are not observed at training time, and show that identifiable representations can provide an effective solution to this task even if the interventions affect the outcome non-linearly. Our setup includes an outcome Y, observed features X, which are generated as a non-linear transformation of latent features Z, and exogenous action variables A, which influence Z. The objective of intervention extrapolation is to predict how interventions on A that lie outside the training support of A affect Y. Here, extrapolation becomes possible if the effect of A on Z is linear and the residual when regressing Z on A has full support. As Z is latent, we combine the task of intervention extrapolation with identifiable representation learning, which we call Rep4Ex: we aim to map the observed features X into a subspace that allows for non-linear extrapolation in A. We show that the hidden representation is identifiable up to an affine transformation in Z-space, which is sufficient for intervention extrapolation. The identifiability is characterized by a novel constraint describing the linearity assumption of A on Z. Based on this insight, we propose a method that enforces the linear invariance constraint and can be combined with any type of autoencoder. We validate our theoretical findings through synthetic experiments and show that our approach succeeds in predicting the effects of unseen interventions.

  • 5 authors
·
Oct 6, 2023

Generalizable Data-free Objective for Crafting Universal Adversarial Perturbations

Machine learning models are susceptible to adversarial perturbations: small changes to input that can cause large changes in output. It is also demonstrated that there exist input-agnostic perturbations, called universal adversarial perturbations, which can change the inference of target model on most of the data samples. However, existing methods to craft universal perturbations are (i) task specific, (ii) require samples from the training data distribution, and (iii) perform complex optimizations. Additionally, because of the data dependence, fooling ability of the crafted perturbations is proportional to the available training data. In this paper, we present a novel, generalizable and data-free approaches for crafting universal adversarial perturbations. Independent of the underlying task, our objective achieves fooling via corrupting the extracted features at multiple layers. Therefore, the proposed objective is generalizable to craft image-agnostic perturbations across multiple vision tasks such as object recognition, semantic segmentation, and depth estimation. In the practical setting of black-box attack scenario (when the attacker does not have access to the target model and it's training data), we show that our objective outperforms the data dependent objectives to fool the learned models. Further, via exploiting simple priors related to the data distribution, our objective remarkably boosts the fooling ability of the crafted perturbations. Significant fooling rates achieved by our objective emphasize that the current deep learning models are now at an increased risk, since our objective generalizes across multiple tasks without the requirement of training data for crafting the perturbations. To encourage reproducible research, we have released the codes for our proposed algorithm.

  • 3 authors
·
Jan 24, 2018

WOUAF: Weight Modulation for User Attribution and Fingerprinting in Text-to-Image Diffusion Models

The rapid advancement of generative models, facilitating the creation of hyper-realistic images from textual descriptions, has concurrently escalated critical societal concerns such as misinformation. Traditional fake detection mechanisms, although providing some mitigation, fall short in attributing responsibility for the malicious use of synthetic images. This paper introduces a novel approach to model fingerprinting that assigns responsibility for the generated images, thereby serving as a potential countermeasure to model misuse. Our method modifies generative models based on each user's unique digital fingerprint, imprinting a unique identifier onto the resultant content that can be traced back to the user. This approach, incorporating fine-tuning into Text-to-Image (T2I) tasks using the Stable Diffusion Model, demonstrates near-perfect attribution accuracy with a minimal impact on output quality. We rigorously scrutinize our method's secrecy under two distinct scenarios: one where a malicious user attempts to detect the fingerprint, and another where a user possesses a comprehensive understanding of our method. We also evaluate the robustness of our approach against various image post-processing manipulations typically executed by end-users. Through extensive evaluation of the Stable Diffusion models, our method presents a promising and novel avenue for accountable model distribution and responsible use.

  • 5 authors
·
Jun 7, 2023 1

Spectral Bottleneck in Deep Neural Networks: Noise is All You Need

Deep neural networks are known to exhibit a spectral learning bias, wherein low-frequency components are learned early in training, while high-frequency modes emerge more gradually in later epochs. However, when the target signal lacks low-frequency components and is dominated by broadband high frequencies, training suffers from a 'spectral bottleneck', and the model fails to reconstruct the entire signal, including the frequency components that lie within the network's representational capacity. We examine such a scenario in the context of implicit neural representations (INRs) with sinusoidal representation networks (SIRENs), focusing on the challenge of fitting high-frequency-dominant signals that are susceptible to spectral bottleneck. To effectively fit any target signal irrespective of it's frequency content, we propose a generalized target-aware 'weight perturbation scheme' (WINNER - weight initialization with noise for neural representations) for network initialization. The scheme perturbs uniformly initialized weights with Gaussian noise, where the noise scales are adaptively determined by the spectral centroid of the target signal. We show that the noise scales can provide control over the spectra of network activations and the eigenbasis of the empirical neural tangent kernel. This method not only addresses the spectral bottleneck but also yields faster convergence and with improved representation accuracy, outperforming state-of-the-art approaches in audio fitting and achieving notable gains in image fitting and denoising tasks. Beyond signal reconstruction, our approach opens new directions for adaptive weight initialization strategies in computer vision and scientific machine learning.

  • 5 authors
·
Sep 9

A Song of (Dis)agreement: Evaluating the Evaluation of Explainable Artificial Intelligence in Natural Language Processing

There has been significant debate in the NLP community about whether or not attention weights can be used as an explanation - a mechanism for interpreting how important each input token is for a particular prediction. The validity of "attention as explanation" has so far been evaluated by computing the rank correlation between attention-based explanations and existing feature attribution explanations using LSTM-based models. In our work, we (i) compare the rank correlation between five more recent feature attribution methods and two attention-based methods, on two types of NLP tasks, and (ii) extend this analysis to also include transformer-based models. We find that attention-based explanations do not correlate strongly with any recent feature attribution methods, regardless of the model or task. Furthermore, we find that none of the tested explanations correlate strongly with one another for the transformer-based model, leading us to question the underlying assumption that we should measure the validity of attention-based explanations based on how well they correlate with existing feature attribution explanation methods. After conducting experiments on five datasets using two different models, we argue that the community should stop using rank correlation as an evaluation metric for attention-based explanations. We suggest that researchers and practitioners should instead test various explanation methods and employ a human-in-the-loop process to determine if the explanations align with human intuition for the particular use case at hand.

  • 4 authors
·
May 9, 2022

A Frustratingly Simple Yet Highly Effective Attack Baseline: Over 90% Success Rate Against the Strong Black-box Models of GPT-4.5/4o/o1

Despite promising performance on open-source large vision-language models (LVLMs), transfer-based targeted attacks often fail against black-box commercial LVLMs. Analyzing failed adversarial perturbations reveals that the learned perturbations typically originate from a uniform distribution and lack clear semantic details, resulting in unintended responses. This critical absence of semantic information leads commercial LVLMs to either ignore the perturbation entirely or misinterpret its embedded semantics, thereby causing the attack to fail. To overcome these issues, we notice that identifying core semantic objects is a key objective for models trained with various datasets and methodologies. This insight motivates our approach that refines semantic clarity by encoding explicit semantic details within local regions, thus ensuring interoperability and capturing finer-grained features, and by concentrating modifications on semantically rich areas rather than applying them uniformly. To achieve this, we propose a simple yet highly effective solution: at each optimization step, the adversarial image is cropped randomly by a controlled aspect ratio and scale, resized, and then aligned with the target image in the embedding space. Experimental results confirm our hypothesis. Our adversarial examples crafted with local-aggregated perturbations focused on crucial regions exhibit surprisingly good transferability to commercial LVLMs, including GPT-4.5, GPT-4o, Gemini-2.0-flash, Claude-3.5-sonnet, Claude-3.7-sonnet, and even reasoning models like o1, Claude-3.7-thinking and Gemini-2.0-flash-thinking. Our approach achieves success rates exceeding 90% on GPT-4.5, 4o, and o1, significantly outperforming all prior state-of-the-art attack methods. Our optimized adversarial examples under different configurations and training code are available at https://github.com/VILA-Lab/M-Attack.

  • 5 authors
·
Mar 13 2

PAC Generalization via Invariant Representations

One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find invariant representations of the data. These are representations of the covariates such that the best model on top of the representation is invariant across training environments. In the context of linear Structural Equation Models (SEMs), invariant representations might allow us to learn models with out-of-distribution guarantees, i.e., models that are robust to interventions in the SEM. To address the invariant representation problem in a {\em finite sample} setting, we consider the notion of epsilon-approximate invariance. We study the following question: If a representation is approximately invariant with respect to a given number of training interventions, will it continue to be approximately invariant on a larger collection of unseen SEMs? This larger collection of SEMs is generated through a parameterized family of interventions. Inspired by PAC learning, we obtain finite-sample out-of-distribution generalization guarantees for approximate invariance that holds probabilistically over a family of linear SEMs without faithfulness assumptions. Our results show bounds that do not scale in ambient dimension when intervention sites are restricted to lie in a constant size subset of in-degree bounded nodes. We also show how to extend our results to a linear indirect observation model that incorporates latent variables.

  • 3 authors
·
May 30, 2022

Debiasing Multimodal Models via Causal Information Minimization

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

  • 3 authors
·
Nov 28, 2023

ClaimVer: Explainable Claim-Level Verification and Evidence Attribution of Text Through Knowledge Graphs

In the midst of widespread misinformation and disinformation through social media and the proliferation of AI-generated texts, it has become increasingly difficult for people to validate and trust information they encounter. Many fact-checking approaches and tools have been developed, but they often lack appropriate explainability or granularity to be useful in various contexts. A text validation method that is easy to use, accessible, and can perform fine-grained evidence attribution has become crucial. More importantly, building user trust in such a method requires presenting the rationale behind each prediction, as research shows this significantly influences people's belief in automated systems. It is also paramount to localize and bring users' attention to the specific problematic content, instead of providing simple blanket labels. In this paper, we present ClaimVer, a human-centric framework tailored to meet users' informational and verification needs by generating rich annotations and thereby reducing cognitive load. Designed to deliver comprehensive evaluations of texts, it highlights each claim, verifies it against a trusted knowledge graph (KG), presents the evidence, and provides succinct, clear explanations for each claim prediction. Finally, our framework introduces an attribution score, enhancing applicability across a wide range of downstream tasks.

  • 7 authors
·
Mar 12, 2024

CausaLM: Causal Model Explanation Through Counterfactual Language Models

Understanding predictions made by deep neural networks is notoriously difficult, but also crucial to their dissemination. As all machine learning based methods, they are as good as their training data, and can also capture unwanted biases. While there are tools that can help understand whether such biases exist, they do not distinguish between correlation and causation, and might be ill-suited for text-based models and for reasoning about high level language concepts. A key problem of estimating the causal effect of a concept of interest on a given model is that this estimation requires the generation of counterfactual examples, which is challenging with existing generation technology. To bridge that gap, we propose CausaLM, a framework for producing causal model explanations using counterfactual language representation models. Our approach is based on fine-tuning of deep contextualized embedding models with auxiliary adversarial tasks derived from the causal graph of the problem. Concretely, we show that by carefully choosing auxiliary adversarial pre-training tasks, language representation models such as BERT can effectively learn a counterfactual representation for a given concept of interest, and be used to estimate its true causal effect on model performance. A byproduct of our method is a language representation model that is unaffected by the tested concept, which can be useful in mitigating unwanted bias ingrained in the data.

  • 4 authors
·
May 27, 2020

Unifying Self-Supervised Clustering and Energy-Based Models

Self-supervised learning excels at learning representations from large amounts of data. At the same time, generative models offer the complementary property of learning information about the underlying data generation process. In this study, we aim at establishing a principled connection between these two paradigms and highlight the benefits of their complementarity. In particular, we perform an analysis of self-supervised learning objectives, elucidating the underlying probabilistic graphical models and presenting a standardized methodology for their derivation from first principles. The analysis suggests a natural means of integrating self-supervised learning with likelihood-based generative models. We instantiate this concept within the realm of cluster-based self-supervised learning and energy models, introducing a lower bound proven to reliably penalize the most important failure modes and unlocking full unification. Our theoretical findings are substantiated through experiments on synthetic and real-world data, including SVHN, CIFAR10, and CIFAR100, demonstrating that our objective function allows to jointly train a backbone network in a discriminative and generative fashion, consequently outperforming existing self-supervised learning strategies in terms of clustering, generation and out-of-distribution detection performance by a wide margin. We also demonstrate that the solution can be integrated into a neuro-symbolic framework to tackle a simple yet non-trivial instantiation of the symbol grounding problem. The code is publicly available at https://github.com/emsansone/GEDI.

  • 2 authors
·
Dec 29, 2023

Do Input Gradients Highlight Discriminative Features?

Post-hoc gradient-based interpretability methods [Simonyan et al., 2013, Smilkov et al., 2017] that provide instance-specific explanations of model predictions are often based on assumption (A): magnitude of input gradients -- gradients of logits with respect to input -- noisily highlight discriminative task-relevant features. In this work, we test the validity of assumption (A) using a three-pronged approach. First, we develop an evaluation framework, DiffROAR, to test assumption (A) on four image classification benchmarks. Our results suggest that (i) input gradients of standard models (i.e., trained on original data) may grossly violate (A), whereas (ii) input gradients of adversarially robust models satisfy (A). Second, we introduce BlockMNIST, an MNIST-based semi-real dataset, that by design encodes a priori knowledge of discriminative features. Our analysis on BlockMNIST leverages this information to validate as well as characterize differences between input gradient attributions of standard and robust models. Finally, we theoretically prove that our empirical findings hold on a simplified version of the BlockMNIST dataset. Specifically, we prove that input gradients of standard one-hidden-layer MLPs trained on this dataset do not highlight instance-specific signal coordinates, thus grossly violating assumption (A). Our findings motivate the need to formalize and test common assumptions in interpretability in a falsifiable manner [Leavitt and Morcos, 2020]. We believe that the DiffROAR evaluation framework and BlockMNIST-based datasets can serve as sanity checks to audit instance-specific interpretability methods; code and data available at https://github.com/harshays/inputgradients.

  • 3 authors
·
Feb 25, 2021

When Noisy Labels Meet Long Tail Dilemmas: A Representation Calibration Method

Real-world large-scale datasets are both noisily labeled and class-imbalanced. The issues seriously hurt the generalization of trained models. It is hence significant to address the simultaneous incorrect labeling and class-imbalance, i.e., the problem of learning with noisy labels on long-tailed data. Previous works develop several methods for the problem. However, they always rely on strong assumptions that are invalid or hard to be checked in practice. In this paper, to handle the problem and address the limitations of prior works, we propose a representation calibration method RCAL. Specifically, RCAL works with the representations extracted by unsupervised contrastive learning. We assume that without incorrect labeling and class imbalance, the representations of instances in each class conform to a multivariate Gaussian distribution, which is much milder and easier to be checked. Based on the assumption, we recover underlying representation distributions from polluted ones resulting from mislabeled and class-imbalanced data. Additional data points are then sampled from the recovered distributions to help generalization. Moreover, during classifier training, representation learning takes advantage of representation robustness brought by contrastive learning, which further improves the classifier performance. We derive theoretical results to discuss the effectiveness of our representation calibration. Experiments on multiple benchmarks justify our claims and confirm the superiority of the proposed method.

  • 5 authors
·
Nov 20, 2022

PFGM++: Unlocking the Potential of Physics-Inspired Generative Models

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

  • 6 authors
·
Feb 8, 2023

Detecting Adversarial Data by Probing Multiple Perturbations Using Expected Perturbation Score

Adversarial detection aims to determine whether a given sample is an adversarial one based on the discrepancy between natural and adversarial distributions. Unfortunately, estimating or comparing two data distributions is extremely difficult, especially in high-dimension spaces. Recently, the gradient of log probability density (a.k.a., score) w.r.t. the sample is used as an alternative statistic to compute. However, we find that the score is sensitive in identifying adversarial samples due to insufficient information with one sample only. In this paper, we propose a new statistic called expected perturbation score (EPS), which is essentially the expected score of a sample after various perturbations. Specifically, to obtain adequate information regarding one sample, we perturb it by adding various noises to capture its multi-view observations. We theoretically prove that EPS is a proper statistic to compute the discrepancy between two samples under mild conditions. In practice, we can use a pre-trained diffusion model to estimate EPS for each sample. Last, we propose an EPS-based adversarial detection (EPS-AD) method, in which we develop EPS-based maximum mean discrepancy (MMD) as a metric to measure the discrepancy between the test sample and natural samples. We also prove that the EPS-based MMD between natural and adversarial samples is larger than that among natural samples. Extensive experiments show the superior adversarial detection performance of our EPS-AD.

  • 7 authors
·
May 25, 2023

Robust Representation Consistency Model via Contrastive Denoising

Robustness is essential for deep neural networks, especially in security-sensitive applications. To this end, randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations. Recently, diffusion models have been successfully employed for randomized smoothing to purify noise-perturbed samples before making predictions with a standard classifier. While these methods excel at small perturbation radii, they struggle with larger perturbations and incur a significant computational overhead during inference compared to classical methods. To address this, we reformulate the generative modeling task along the diffusion trajectories in pixel space as a discriminative task in the latent space. Specifically, we use instance discrimination to achieve consistent representations along the trajectories by aligning temporally adjacent points. After fine-tuning based on the learned representations, our model enables implicit denoising-then-classification via a single prediction, substantially reducing inference costs. We conduct extensive experiments on various datasets and achieve state-of-the-art performance with minimal computation budget during inference. For example, our method outperforms the certified accuracy of diffusion-based methods on ImageNet across all perturbation radii by 5.3% on average, with up to 11.6% at larger radii, while reducing inference costs by 85times on average. Codes are available at: https://github.com/jiachenlei/rRCM.

  • 8 authors
·
Jan 22

Exploring Geometry of Blind Spots in Vision Models

Despite the remarkable success of deep neural networks in a myriad of settings, several works have demonstrated their overwhelming sensitivity to near-imperceptible perturbations, known as adversarial attacks. On the other hand, prior works have also observed that deep networks can be under-sensitive, wherein large-magnitude perturbations in input space do not induce appreciable changes to network activations. In this work, we study in detail the phenomenon of under-sensitivity in vision models such as CNNs and Transformers, and present techniques to study the geometry and extent of "equi-confidence" level sets of such networks. We propose a Level Set Traversal algorithm that iteratively explores regions of high confidence with respect to the input space using orthogonal components of the local gradients. Given a source image, we use this algorithm to identify inputs that lie in the same equi-confidence level set as the source image despite being perceptually similar to arbitrary images from other classes. We further observe that the source image is linearly connected by a high-confidence path to these inputs, uncovering a star-like structure for level sets of deep networks. Furthermore, we attempt to identify and estimate the extent of these connected higher-dimensional regions over which the model maintains a high degree of confidence. The code for this project is publicly available at https://github.com/SriramB-98/blindspots-neurips-sub

  • 4 authors
·
Oct 30, 2023

Quantifying Bias in Text-to-Image Generative Models

Bias in text-to-image (T2I) models can propagate unfair social representations and may be used to aggressively market ideas or push controversial agendas. Existing T2I model bias evaluation methods only focus on social biases. We look beyond that and instead propose an evaluation methodology to quantify general biases in T2I generative models, without any preconceived notions. We assess four state-of-the-art T2I models and compare their baseline bias characteristics to their respective variants (two for each), where certain biases have been intentionally induced. We propose three evaluation metrics to assess model biases including: (i) Distribution bias, (ii) Jaccard hallucination and (iii) Generative miss-rate. We conduct two evaluation studies, modelling biases under general, and task-oriented conditions, using a marketing scenario as the domain for the latter. We also quantify social biases to compare our findings to related works. Finally, our methodology is transferred to evaluate captioned-image datasets and measure their bias. Our approach is objective, domain-agnostic and consistently measures different forms of T2I model biases. We have developed a web application and practical implementation of what has been proposed in this work, which is at https://huggingface.co/spaces/JVice/try-before-you-bias. A video series with demonstrations is available at https://www.youtube.com/channel/UCk-0xyUyT0MSd_hkp4jQt1Q

  • 4 authors
·
Dec 20, 2023

Towards Exact Computation of Inductive Bias

Much research in machine learning involves finding appropriate inductive biases (e.g. convolutional neural networks, momentum-based optimizers, transformers) to promote generalization on tasks. However, quantification of the amount of inductive bias associated with these architectures and hyperparameters has been limited. We propose a novel method for efficiently computing the inductive bias required for generalization on a task with a fixed training data budget; formally, this corresponds to the amount of information required to specify well-generalizing models within a specific hypothesis space of models. Our approach involves modeling the loss distribution of random hypotheses drawn from a hypothesis space to estimate the required inductive bias for a task relative to these hypotheses. Unlike prior work, our method provides a direct estimate of inductive bias without using bounds and is applicable to diverse hypothesis spaces. Moreover, we derive approximation error bounds for our estimation approach in terms of the number of sampled hypotheses. Consistent with prior results, our empirical results demonstrate that higher dimensional tasks require greater inductive bias. We show that relative to other expressive model classes, neural networks as a model class encode large amounts of inductive bias. Furthermore, our measure quantifies the relative difference in inductive bias between different neural network architectures. Our proposed inductive bias metric provides an information-theoretic interpretation of the benefits of specific model architectures for certain tasks and provides a quantitative guide to developing tasks requiring greater inductive bias, thereby encouraging the development of more powerful inductive biases.

  • 5 authors
·
Jun 22, 2024

Fighting Fire with Fire: Contrastive Debiasing without Bias-free Data via Generative Bias-transformation

Despite their remarkable ability to generalize with over-capacity networks, deep neural networks often learn to abuse spurious biases in the data instead of using the actual task-related information. Since such shortcuts are only effective within the collected dataset, the resulting biased model underperforms on real-world inputs, or cause unintended social repercussions such as gender discrimination. To counteract the influence of bias, existing methods either exploit auxiliary information which is rarely obtainable in practice, or sift for bias-free samples in the training data, hoping for the sufficient existence of clean samples. However, such presumptions about the data are not always guaranteed. In this paper, we propose Contrastive Debiasing via Generative Bias-transformation~(CDvG) which is capable of operating in more general environments where existing methods break down due to unmet presumptions such as insufficient bias-free samples. Motivated by our observation that not only discriminative models, as previously known, but also generative models tend to focus on the bias when possible, CDvG uses a translation model to transform the bias in the sample to another mode of bias while preserving task-relevant information. Through contrastive learning, we set transformed biased views against another, learning bias-invariant representations. Experimental results on synthetic and real-world datasets demonstrate that our framework outperforms the current state-of-the-arts, and effectively prevents the models from being biased even when bias-free samples are extremely scarce.

  • 4 authors
·
Dec 2, 2021

On the Provable Advantage of Unsupervised Pretraining

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.

  • 4 authors
·
Mar 2, 2023

All Patches Matter, More Patches Better: Enhance AI-Generated Image Detection via Panoptic Patch Learning

The exponential growth of AI-generated images (AIGIs) underscores the urgent need for robust and generalizable detection methods. In this paper, we establish two key principles for AIGI detection through systematic analysis: (1) All Patches Matter: Unlike conventional image classification where discriminative features concentrate on object-centric regions, each patch in AIGIs inherently contains synthetic artifacts due to the uniform generation process, suggesting that every patch serves as an important artifact source for detection. (2) More Patches Better: Leveraging distributed artifacts across more patches improves detection robustness by capturing complementary forensic evidence and reducing over-reliance on specific patches, thereby enhancing robustness and generalization. However, our counterfactual analysis reveals an undesirable phenomenon: naively trained detectors often exhibit a Few-Patch Bias, discriminating between real and synthetic images based on minority patches. We identify Lazy Learner as the root cause: detectors preferentially learn conspicuous artifacts in limited patches while neglecting broader artifact distributions. To address this bias, we propose the Panoptic Patch Learning (PPL) framework, involving: (1) Random Patch Replacement that randomly substitutes synthetic patches with real counterparts to compel models to identify artifacts in underutilized regions, encouraging the broader use of more patches; (2) Patch-wise Contrastive Learning that enforces consistent discriminative capability across all patches, ensuring uniform utilization of all patches. Extensive experiments across two different settings on several benchmarks verify the effectiveness of our approach.

  • 11 authors
·
Apr 2

Key-Locked Rank One Editing for Text-to-Image Personalization

Text-to-image models (T2I) offer a new level of flexibility by allowing users to guide the creative process through natural language. However, personalizing these models to align with user-provided visual concepts remains a challenging problem. The task of T2I personalization poses multiple hard challenges, such as maintaining high visual fidelity while allowing creative control, combining multiple personalized concepts in a single image, and keeping a small model size. We present Perfusion, a T2I personalization method that addresses these challenges using dynamic rank-1 updates to the underlying T2I model. Perfusion avoids overfitting by introducing a new mechanism that "locks" new concepts' cross-attention Keys to their superordinate category. Additionally, we develop a gated rank-1 approach that enables us to control the influence of a learned concept during inference time and to combine multiple concepts. This allows runtime-efficient balancing of visual-fidelity and textual-alignment with a single 100KB trained model, which is five orders of magnitude smaller than the current state of the art. Moreover, it can span different operating points across the Pareto front without additional training. Finally, we show that Perfusion outperforms strong baselines in both qualitative and quantitative terms. Importantly, key-locking leads to novel results compared to traditional approaches, allowing to portray personalized object interactions in unprecedented ways, even in one-shot settings.

  • 4 authors
·
May 2, 2023 1

WILD: a new in-the-Wild Image Linkage Dataset for synthetic image attribution

Synthetic image source attribution is an open challenge, with an increasing number of image generators being released yearly. The complexity and the sheer number of available generative techniques, as well as the scarcity of high-quality open source datasets of diverse nature for this task, make training and benchmarking synthetic image source attribution models very challenging. WILD is a new in-the-Wild Image Linkage Dataset designed to provide a powerful training and benchmarking tool for synthetic image attribution models. The dataset is built out of a closed set of 10 popular commercial generators, which constitutes the training base of attribution models, and an open set of 10 additional generators, simulating a real-world in-the-wild scenario. Each generator is represented by 1,000 images, for a total of 10,000 images in the closed set and 10,000 images in the open set. Half of the images are post-processed with a wide range of operators. WILD allows benchmarking attribution models in a wide range of tasks, including closed and open set identification and verification, and robust attribution with respect to post-processing and adversarial attacks. Models trained on WILD are expected to benefit from the challenging scenario represented by the dataset itself. Moreover, an assessment of seven baseline methodologies on closed and open set attribution is presented, including robustness tests with respect to post-processing.

  • 17 authors
·
Apr 28

Using Degeneracy in the Loss Landscape for Mechanistic Interpretability

Mechanistic Interpretability aims to reverse engineer the algorithms implemented by neural networks by studying their weights and activations. An obstacle to reverse engineering neural networks is that many of the parameters inside a network are not involved in the computation being implemented by the network. These degenerate parameters may obfuscate internal structure. Singular learning theory teaches us that neural network parameterizations are biased towards being more degenerate, and parameterizations with more degeneracy are likely to generalize further. We identify 3 ways that network parameters can be degenerate: linear dependence between activations in a layer; linear dependence between gradients passed back to a layer; ReLUs which fire on the same subset of datapoints. We also present a heuristic argument that modular networks are likely to be more degenerate, and we develop a metric for identifying modules in a network that is based on this argument. We propose that if we can represent a neural network in a way that is invariant to reparameterizations that exploit the degeneracies, then this representation is likely to be more interpretable, and we provide some evidence that such a representation is likely to have sparser interactions. We introduce the Interaction Basis, a tractable technique to obtain a representation that is invariant to degeneracies from linear dependence of activations or Jacobians.

  • 8 authors
·
May 17, 2024

Can We Generate Images with CoT? Let's Verify and Reinforce Image Generation Step by Step

Chain-of-Thought (CoT) reasoning has been extensively explored in large models to tackle complex understanding tasks. However, it still remains an open question whether such strategies can be applied to verifying and reinforcing image generation scenarios. In this paper, we provide the first comprehensive investigation of the potential of CoT reasoning to enhance autoregressive image generation. We focus on three techniques: scaling test-time computation for verification, aligning model preferences with Direct Preference Optimization (DPO), and integrating these techniques for complementary effects. Our results demonstrate that these approaches can be effectively adapted and combined to significantly improve image generation performance. Furthermore, given the pivotal role of reward models in our findings, we propose the Potential Assessment Reward Model (PARM) and PARM++, specialized for autoregressive image generation. PARM adaptively assesses each generation step through a potential assessment approach, merging the strengths of existing reward models, and PARM++ further introduces a reflection mechanism to self-correct the generated unsatisfactory image. Using our investigated reasoning strategies, we enhance a baseline model, Show-o, to achieve superior results, with a significant +24% improvement on the GenEval benchmark, surpassing Stable Diffusion 3 by +15%. We hope our study provides unique insights and paves a new path for integrating CoT reasoning with autoregressive image generation. Code and models are released at https://github.com/ZiyuGuo99/Image-Generation-CoT

  • 7 authors
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Jan 23 2