ICML 2026 Papers

International Conference on Machine Learning

Decision breakdown

6,341papers

Counted from the official paper list; may differ slightly from the number the conference announced.

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Topic: Social aspects · accountability transparency and interpretability · 541 papers · Reset filters

Orthogonal Concept Erasure for Diffusion Models

Yuhao Sun, Lingyun Yu, Hao-Xiang Xu, Fengyuan Miao, Zhuoer Xu, Hongtao Xie

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Concept erasure has emerged as a promising approach to mitigate undesired or unsafe content in diffusion models, yet existing methods still face significant limitations. While training-based methods are effective, their high computational cost limits scalability. Editing-based methods are more efficient and deployment-friendly, yet they struggle to simultaneously achieve precise concept erasure and preserve overall generative capacity. We identify this core limitation of the editing-based methods as reliance on additive parameter updates. Our empirical analysis reveals that concept semantics primarily depend on *neuron direction* rather than *neuron magnitude*, while overall generative capacity relies on the *angular geometry* of neurons. As additive updates inherently entangle direction, magnitude, and angular geometry, they inevitably introduce unintended interference between concept erasure and overall generation performance. To address this, we propose **Orthogonal Concept Erasure (OCE)**, which reformulates editing-based erasure as multiplicative parameter updates from a geometric perspective. Specifically, OCE applies layer-wise orthogonal transformations derived from a closed-form solution to the parameters, enabling precise concept erasure while preserving the neuron magnitude and angular geometry. Furthermore, to address conflicting constraints in multi-concept erasure, OCE introduces a subspace-level objective with structured subspace manipulation, yielding a more effective and scalable erasure. Extensive experiments on single- and multi-concept erasure demonstrate that OCE outperforms existing methods in concept erasure and non-target preservation, erasing up to 100 concepts in 4.3 s. Code: https://github.com/HansSunY/OCE.

Spotlight
Learning to Watermark in the Latent Space of Generative Models

Sylvestre-Alvise Rebuffi, Tuan A. Tran, Valeriu Lacatusu, Pierre Fernandez, Tomáš Souček, Nikola Jovanović, Tom Sander, Hady Elsahar, Alexandre Mourachko

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Existing approaches for watermarking AI-generated images often rely on post-hoc methods applied in pixel space, introducing computational overhead and potential visual artifacts. In this work, we explore latent space watermarking and introduce DistSeal, a unified approach for latent watermarking that works across both diffusion and autoregressive models. Our approach works by training post-hoc watermarking models in the latent space of generative models. We demonstrate that these latent watermarkers can be effectively distilled either into the generative model itself or into the latent decoder, enabling in-model watermarking. The resulting latent watermarks achieve competitive robustness while offering similar imperceptibility and up to 20x speedup compared to pixel-space baselines. Our experiments further reveal that distilling latent watermarkers outperforms distilling pixel-space ones, providing a solution that is both more efficient and more robust.

Poster
From Associations to Activations: Comparing Behavioral and Hidden-State Semantic Geometry in LLMs

Louis Schiekiera, Max Zimmer, Christophe Roux, Sebastian Pokutta, Fritz Günther

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We investigate the extent to which an LLM’s hidden-state geometry can be recovered from its behavior in psycholinguistic experiments. Across eight instruction-tuned transformer models, we run two experimental paradigms---similarity-based forced choice and free association---over a shared 5,000-word vocabulary, collecting 17.5M+ trials to build behavior-based similarity matrices. Using representational similarity analysis, we compare behavioral geometries to layerwise hidden-state similarity and benchmark against FastText, BERT, and cross-model consensus. We find that forced-choice behavior aligns substantially more with hidden-state geometry than free association. In a held-out-words regression, behavioral similarity (especially forced choice) predicts unseen hidden-state similarities beyond lexical baselines and cross-model consensus, indicating that behavior-only measurements retain recoverable information about internal semantic geometry. Finally, we discuss implications for the ability of behavioral tasks to uncover hidden cognitive states.

Poster
Quantifying LLM Attention-Head Stability: Implications for Circuit Universality

Karan Bali, Jack Stanley, Praneet Suresh, Danilo Bzdok

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In mechanistic interpretability, recent work scrutinizes transformer “circuits”—sparse, mono or multi layer sub computations, that may reflect human understandable functions. Yet, these network circuits are rarely acid-tested for their stability across different instances of the same deep learning architecture. Without this, it remains unclear whether reported circuits emerge universally across labs or turn out to be idiosyncratic to a particular estimation instance, potentially limiting confidence in safety-critical settings. Here, we systematically study stability across-refits in increasingly complex transformer language models of various sizes. We quantify, layer by layer, how similarly attention heads learn representations across independently initialized training runs. Our rigorous experiments show that (1) middle-layer heads are the least stable yet the most representationally distinct; (2) deeper models exhibit stronger mid-depth divergence; (3) unstable heads in deeper layers become more functionally important than their peers from the same layer; (4) applying weight decay optimization substantially improves attention-head stability across random model initializations; and (5) the residual stream is comparatively stable. Our findings establish the cross-instance robustness of circuits as an essential yet underappreciated prerequisite for scalable oversight, drawing contours around possible white-box monitorability of AI systems.

Poster
FakeWorld 1.0: An Omni-modal Benchmark for Fake Media and Content

Yifeng Gao, Yifan Ding, LI Wang, Feida Huang, Ye Sun, Yixu Wang, Xin Wang, Yutao Wu, Hanxun Huang, Yunhao Feng, Yingshui Tan, Xingjun Ma, Yu-Gang Jiang

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The rapidly increasing realism of AI-generated media has intensified the spread of deceptive content and undermined public trust. Existing research largely treats this challenge along two separate axes: media authenticity, which assesses whether content is real or machine-generated, and content veracity, which evaluates semantic consistency and factual correctness. This separation overlooks how real-world deception jointly exploits both dimensions. In this work, we present FakeWorld 1.0, an omni-modal benchmark that unifies media authenticity and content veracity within a single evaluation framework. Along the media axis, FakeWorld spans text, audio, image, and video synthesis. Along the content axis, it systematically instantiates cross-modal semantic inconsistencies and factual errors. These two axes are jointly embedded in realistic web-based and streaming-style presentation scenarios, reflecting how multimodal deception is composed, contextualized, and delivered in practice. FakeWorld further provides explainable annotations in the form of per-instance rationales, enabling transparent and evidence-based analysis. Under a unified evaluation protocol, experiments on both open- and closed-source multimodal large language models (MLLMs) reveal fundamental capability limits and demonstrate FakeWorld’s effectiveness in exposing high-fidelity, mixed-source deception. Beyond the benchmark, we introduce OmniChecker, an agentic framwork that performs joint, explainable detection across both axes and produces evidence-backed diagnostic reports. We position FakeWorld 1.0 as a realistic stress test and a practical foundation for advancing scalable, explainable detection of fake multimodal content.

Poster
A Game-Theoretic Framework for Measuring and Explaining Metric Compatibility in Fair Machine Learning

Lingfeng Zhang, Jingran Yang, Zhaohui Wang, Min Zhang, Zhang Qing

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Machine learning fairness research documents trade-offs but lacks quantitative frameworks to measure intrinsic metric compatibility without requiring causal graphs. We introduce a game-theoretic framework that decomposes metrics into interaction vectors, enabling compatibility measurement between metrics via cosine similarity and mechanistic attribution to attribute coalitions. Through analysis of 6 datasets, 7 models, and 6 debiasing methods, we reveal that fairness and utility are often structurally orthogonal (median compatibility $\approx 0$) rather than diametrically opposed, with conflicts driven by sparse, low-order interactions. We further show that debiasing improves fairness by compressing the compatibility space—reducing compatibility of both synergistic and conflicting relationships—rather than eliminating conflicts, providing a mechanistic basis for understanding metric alignment.

Poster
Falling Trees: A Model Class for Interpretable Risk Prioritization

Varun Babbar, Zachery Boner, Margo Seltzer, Cynthia Rudin

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Many real-world decisions require prioritizing high-risk cases, such as clinicians prioritizing high-risk patients before lower-risk ones. Falling rule lists (FRLs), which are ordered if--then rules with monotonically decreasing risks, provide an interpretable framework for such tasks; however, their single-path structure yields a highly restricted model class. We introduce falling trees, a new family of interpretable models that enforces the same monotonic risk constraint while permitting tree-structured branching. We present GraviTree, a novel dynamic-programming-with-bounds algorithm for learning the Rashomon set of falling trees under depth and branching constraints. Our formulation can interpolate between rule lists and full decision trees, enabling user-desired model expressivity. In a new clinical dataset and in many public classification benchmarks, falling trees match or outperform FRLs and other interpretable baselines, often producing more sparse decisions for high-risk instances. Our results show that falling trees strike a practical balance between interpretability, expressiveness, and risk prioritization for high-stakes settings.

Spotlight
Revisiting Neural Processes via Fourier Transform and Volterra Series

Peiman Mohseni, Nick Duffield, Raymond K. W. Wong

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Modeling unknown latent functions from finite, irregularly sampled measurements is a recurring challenge across science and engineering. Neural processes (NPs), a family of probabilistic functional models, are promising solutions---especially when endowed with domain-specific symmetries like translation equivariance, which improve sample efficiency and generalization. Yet existing translation-equivariant NPs face two limitations: (i) they stack generic components with non-linearities, obscuring the induced function class and limiting interpretability; and (ii) convolutional designs rely on kernels with local receptive fields and require dense uniform input grids, while attention-based methods avoid these issues but scale quadratically with the number of observations. We address both with two contributions. First, using the Volterra expansion, we characterize continuous translation-equivariant operators as sums of higher-order convolutions, yielding analytical transparency while admitting efficient approximation by first-order convolutions. Second, we introduce set Fourier convolutions (SFConvs), a frequency-domain parameterization that operates directly on irregularly sampled points, achieves approximately global receptive fields, and scales linearly in the number of observations. Building on these ideas, we propose two conditional NPs (CNPs): SFConvCNPs, which stack SFConv blocks with non-linearities, and SFVConvCNPs, which integrate the Volterra formulation. Experiments on synthetic and real-world datasets demonstrate our methods' efficacy against state-of-the-art baselines.

Poster
Eliminating Solution Bias in Differentially Private Optimization

DONGRUN LI, YUN ZENG, Zibo Wei, Jiacheng Wei, Qinnan Zhang, Faguo Wu, Xiao Zhang, Zhiming Zheng

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Differentially private (DP) stochastic optimization algorithms are widely used in privacy-preserving deep learning, where per-sample gradient clipping and noise injection protect sensitive information. However, these operations limit existing DP algorithms to converge within a constant-radius neighborhood of the first-order stationary point, leading to solution bias and the well-known privacy-utility trade-off. To enhance model utility, we propose a novel algorithmic framework called DP-C4, which is designed to be error-Consistently-vanishing, Coupledly-clipped, solution-Calibrated, and Convergence-guaranteed. Specifically, it incorporates a carefully designed coupled clipping scheme with shifted threshold strategy, ensuring that both clipping bias and noise variance asymptotically vanish, thereby eliminating the DP-induced solution bias. Moreover, we extend existing sensitivity analysis techniques and develop a tailored privacy budget allocation to guarantee the privacy of DP-C4. Compared with the well-recognized DP-SGD, our framework injects significantly less noise under the same privacy level. In addition, we prove that our framework converges to the optimum in strongly-convex case and to a diminishing neighborhood of the first-order stationary point in non-convex case. Experiments show that DP-C4 achieves superior privacy-utility trade-off over existing baselines across various tasks and datasets.

Poster
OmniVL-Guard: Towards Unified Vision-Language Forgery Detection and Grounding via Balanced RL

Jinjie Shen, Jing Wu, Yaxiong Wang, Lechao Cheng, Shengeng Tang, Tianrui Hui, Nan Pu, Zhun Zhong

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Existing forgery detection methods are often limited to uni-modal or bi-modal settings, failing to handle the interleaved text, images, and videos prevalent in real-world misinformation. To bridge this gap, we propose **OmniVL-Guard**, a unified framework for omni vision-language forgery detection and grounding. In this unified setting, the interplay between diverse modalities and the dual requirements of simultaneous detection and localization pose significant optimization challenges. Through extensive investigations, we identify a critical difficulty bias in this multi-task optimization: the simpler veracity classification task tends to dominate the gradients, leading to suboptimal performance in fine-grained grounding. To address this imbalance, we first develop a Self-Evolving CoT Generation pipeline to synthesize high-quality reasoning paths, effectively overcoming the cold-start challenge. Building upon this, we propose **A**daptive **R**eward **S**caling **P**olicy **O**ptimization (**ARSPO**). By dynamically modulating reward scales and task weights, ARSPO ensures a balanced joint optimization that prioritizes challenging grounding objectives. Extensive experiments demonstrate that OmniVL-Guard significantly outperforms state-of-the-art methods and exhibits robust zero-shot generalization across out-of-domain scenarios.

Poster
Sparse Relaxed-Lasso Steering: Automatic Sparse Autoencoder Feature Selection for Precise Image Editing

Zongxin Liu, Xiaoyong Xue, Sun Weidi, Shengchao Qin, Lijun Zhang

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Precise, training-free image editing with text-to-image diffusion models requires balancing alignment (faithful realization of the target attribute), consistency (preserving non-target content), and quality (maintaining sharp, artifact-free textures). Sparse autoencoder (SAE) steering offers interpretable, smooth ``slider-like'' control by manipulating SAE feature activations derived from the text encoder; however, existing approaches rely on heuristic feature selection and manual steering-strength tuning, leading to suboptimal trade-offs among the three objectives. We propose Sparse Relaxed-Lasso Steering (SRLS), which casts steering-vector discovery as a convex sparse recovery problem. Exploiting the affine structure of the SAE decoder, SRLS automatically identifies sparse, generalizable support sets via a Lasso objective and then debiases the coefficients using support-restricted ridge refitting. We further replace manual strength tuning with a fixed-budget Bayesian optimization procedure. Across diverse attributes and subjects, SRLS improves the alignment--consistency--quality trade-off over competing methods.

Poster
From Directions to Regions: Decomposing Activations in Language Models via Local Geometry

Or David Shafran, Shaked Ronen, Omri Fahn, Shauli Ravfogel, Atticus Geiger, Mor Geva

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Activation decomposition methods in language models are tightly coupled to geometric assumptions on how concepts are realized in activation space. Existing approaches search for individual global directions, implicitly assuming linear separability, which overlooks concepts with nonlinear or multi-dimensional structure. In this work, we leverage Mixture of Factor Analyzers (MFA) as a scalable, unsupervised alternative that models the activation space as a collection of Gaussian regions with their *local* covariance structure. MFA decomposes activations into two compositional geometric objects: the region's centroid in activation space, and the local variation from the centroid. We train large-scale MFAs for Llama-3.1-8B and Gemma-2-2B, and show they capture complex, nonlinear structures in activation space. Moreover, evaluations on localization and steering benchmarks show that MFA outperforms unsupervised baselines, is competitive with supervised localization methods, and often achieves stronger steering performance than sparse autoencoders. Together, our findings position local geometry, expressed through subspaces, as a promising unit of analysis for scalable concept discovery and model control, accounting for complex structures that isolated directions fail to capture.

Poster
Social Hippocampus Memory Learning

Liping Yi, Zhiming Zhao, Kewen Zhu, Xiang Li, Zhiwei Shang, Qinghua Hu

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Social learning highlights that learning agents improve not in isolation, but through interaction and structured knowledge exchange with others. When introduced into machine learning, this principle gives rise to social machine learning (SML), where multiple agents collaboratively learn by sharing abstracted knowledge. Federated learning (FL) provides a natural collaboration substrate for this paradigm, yet existing heterogeneous FL approaches often rely on sharing model parameters or intermediate representations, which may expose sensitive information and incur additional overhead. In this work, we propose **SoHip** (**So**cial **Hip**pocampus Memory Learning), a memory-centric social machine learning framework that enables collaboration among heterogeneous agents via memory sharing rather than model sharing. SoHip abstracts each agent’s individual short-term memory from local representations, consolidates it into individual long-term memory through a hippocampus-inspired mechanism, and fuses it with collectively aggregated long-term memory to enhance local prediction. Throughout the process, raw data and local models remain on-device, while only lightweight memory are exchanged. We provide theoretical analysis on convergence and privacy preservation properties. Experiments on two benchmark datasets with seven baselines demonstrate that SoHip consistently outperforms existing methods, achieving up to 8.78% accuracy improvements. The code of SoHip is available at https://github.com/LipingYi/SoHip.

Poster
Localize and Neutralize: Gradient-Guided Token Suppression Against Visual Prompt Injection Attack

Dongpeng Zhang, Ke Ma, Yangbangyan Jiang, Gaozheng Pei, Longtao Huang, Qianqian Xu, Qingming Huang

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Adversarial images pose a severe security threat to multimodal large language models through prompt injection. Existing defenses largely lack a principled understanding of the underlying mechanisms and struggle to balance efficiency and fidelity. In this work, we show that successful adversarial attacks do not rely on the entire image uniformly but instead depend on a small subset of critical image tokens. Based on this insight, we propose a defense that first localizes these critical tokens via gradient analysis and then neutralizes them through masking. We show that attribution based on output probabilities fails when adversarial attacks preserve the predicted token. To overcome this limitation, we introduce the Hidden-State Gradient Norm score for adversarial behavior attribution and prove that its ranking is consistent with that of the full adversarial loss gradient, providing a theoretical guarantee for accurate localization. GTM requires only a single forward–backward pass to identify and zero out a small number of high-scoring tokens, effectively disrupting the adversarial attack path. Extensive experiments on prompt injection and multimodal jailbreak attacks demonstrate that our approach reduces attack success rates (ASR) to near zero while preserving model utility with negligible computational overhead. The code is available at: https://github.com/fish883/GTM-Defense.

Poster
Belief Dynamics Reveal the Dual Nature of In-Context Learning and Activation Steering

Eric Bigelow, Daniel Wurgaft, YingQiao Wang, Noah Goodman, Tomer Ullman, Hidenori Tanaka, Ekdeep Singh Lubana

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Large language models (LLMs) can be controlled at inference time through prompts (in-context learning) and internal activations (activation steering). Different accounts have been proposed to explain these methods, yet their common goal of controlling model behavior raises the question of whether these seemingly disparate methodologies can be seen as specific instances of a broader framework. Motivated by this, we develop a unifying, predictive account of LLM control from a Bayesian perspective. Specifically, we posit that both context- and activation-based interventions impact model behavior by altering its belief in latent concepts: steering operates by changing concept priors, while in-context learning leads to an accumulation of evidence. This results in a closed-form Bayesian model that is highly predictive of LLM behavior across context- and activation-based interventions in a set of domains inspired by prior work on many-shot in-context learning. This model helps us explain prior empirical phenomena - e.g., sigmoidal learning curves as in-context evidence accumulates--while predicting novel ones--e.g., additivity of both interventions in log-belief space, which results in distinct phases such that sudden and dramatic behavioral shifts can be induced by slightly changing intervention controls. Taken together, this work offers a unified account of prompt-based and activation-based control of LLM behavior, and a methodology for empirically predicting the effects of these interventions.

Poster
Neural Concept Verifier: Scaling Prover-Verifier Games via Concept Encodings

Berkant Turan, Suhrab Asadulla, David Steinmann, Kristian Kersting, Wolfgang Stammer, Sebastian Pokutta

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While *Prover-Verifier Games* (PVGs) offer a promising path toward verifiability in nonlinear classification models, they have not yet been applied to complex inputs such as high-dimensional images. Conversely, expressive *concept encodings* effectively allow to translate such data into interpretable concepts but are often utilised in the context of low-capacity linear predictors. In this work, we push towards real-world verifiability by combining the strengths of both approaches. We introduce *Neural Concept Verifier (NCV)*, a unified framework combining PVGs for formal verifiability with concept encodings to handle complex, high-dimensional inputs in an interpretable way. NCV achieves this by utilizing recent minimally supervised concept discovery models to extract structured concept encodings from raw inputs. A *prover* then selects a subset of these encodings, which a *verifier*, implemented as a nonlinear predictor, uses exclusively for decision-making. Our evaluations show that NCV outperforms classic concept-based models and pixel-based PVG classifier baselines on high-dimensional, logically complex datasets and helps mitigate shortcut behavior. Overall, we demonstrate NCV as a promising step toward concept-level, verifiable AI.

Spotlight
Benchmarking LLM-Assisted Blue Teaming via Standardized Threat Hunting

Yuqiao Meng, Luoxi Tang, Feiyang Yu, Xi Li, Guanhua Yan, Ping Yang, Zhaohan Xi

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As cyber threats continue to grow in scale and sophistication, blue team defenders increasingly require advanced tools to proactively detect and mitigate risks. Large Language Models (LLMs) offer promising capabilities for enhancing threat analysis. However, their effectiveness in real-world blue team threat-hunting scenarios remains insufficiently explored. This paper presents CYBERTEAM, a benchmark designed to guide LLMs in blue teaming practice. CYBERTEAM constructs a standardized workflow in two stages. First, it models realistic threat-hunting workflows by capturing the dependencies among analytical tasks from threat attribution to incident response. Next, each task is addressed through a set of operational modules tailored to its specific analytical requirements. This transforms threat hunting into a structured sequence of reasoning steps, with each step grounded in a discrete operation and ordered according to task-specific dependencies. Guided by this framework, LLMs are directed to perform threat-hunting tasks through modularized steps. Overall, CYBERTEAM integrates 30 tasks and 9 operational modules to guide LLMs through standardized threat analysis. We evaluate both leading LLMs and state-of-the-art cybersecurity agents, comparing CYBERTEAM against open-ended reasoning strategies. Our results highlight the improvements enabled by standardized design, while also revealing the limitations of open-ended reasoning in real-world threat hunting.

Poster
Towards Disentangled Preference Optimization Dynamics: Suppress the Loser, Preserve the Winner

Wei Chen, Yubing Wu, Junmei Yang, Delu Zeng, Qibin Zhao, John Paisley, Min Chen, Zhou Wang

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Preference optimization is widely used to align large language models (LLMs) with human preferences. However, many margin-based methods also suppress the chosen response when they try to suppress the rejected one, and there is no general way to prevent this across different objectives. We address this issue with a unified **incentive-score decomposition** of preference optimization, revealing that different objectives share the same local update directions and differ only in their scalar weights. This decomposition provides a common framework for analyzing objectives that were previously studied in separate settings. Building on this decomposition, by analyzing the dynamics of the chosen/rejected likelihoods, we identify the **disentanglement band** (DB), a simple, testable condition that tells us when training can follow the desired path: suppress the loser while preserving the winner, possibly after an early stage. Using the DB, we propose **reward calibration** (RC), a plug‑and‑play method that adaptively rebalances the updates for chosen and rejected likelihoods to satisfy the DB, without redesigning the base objective. Empirical results show that RC leads to more disentangled dynamics, with better downstream performance observed across several settings. Our code is available at https://github.com/IceyWuu/DisentangledPreferenceOptimization.

Poster
A Distributional View for Visual Mechanistic Interpretability: KL-Minimal Soft-Constraint Principle

Guancheng Zhou, Yisi Luo, Zhengfu He, Zhenyu Jin, Xuyang Ge, Wentao Shu, Deyu Meng, Xipeng Qiu

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Most current paradigms in visual mechanistic interpretability (MI) remain confined to interpreting internal units of the vision model via heuristic methods (e.g., top-$K$ activation retrieval or optimization with regularization). In this work, we establish a theoretical distributional view for visual MI, which models the influence of a feature activation on the natural image distribution, thereby formulating a Kullback-Leibler (KL)-minimal optimization problem to model the MI task. Under this framework, statistical biases are identified within previous MI paradigms, which reveal that they may either be perceptually uninterpretable to humans (i.e., deviate from the natural image distribution), or mechanistically unfaithful to the vision models (i.e., unable to activate model features). To resolve the biases under the distributional view, we propose a model with a KL-minimal soft-constraint principle for visual MI that theoretically balances interpretability and faithfulness. We realize this principle via energy-guided diffusion posterior sampling. Extensive experiments validate the theoretical soundness of the proposed distributional view and demonstrate the practical effectiveness of our paradigm on the DINOv3 vision model. The code is available at https://github.com/SII-ZhouGC/EnergyDPS.

Spotlight
Ambiguous Strategic Classification

Ivri Hikri, Nir Rosenfeld

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A common assumption in strategic classification is that the classifier is public knowledge. However, it remains unclear whether, and why, a system would choose to commit to full disclosure. We study a setting in which regulation requires the system to disclose some, but not all, of the information. This induces a learning task in which the learner must jointly optimize the classifier and the uncertainty surrounding it. To this end, we adopt from robust mechanism design the notion of *ambiguity*, which in our setting allows the learner to reveal a set or range of possible classifiers, while privately choosing which of them to ultimately realize. We investigate how ambiguity affects the learning task, develop efficient algorithms for computing best-responses and training, and empirically explore strategic learning and its outcomes in this novel setting and using our approach.

Poster