ICML 2026 Papers

With the rapid emergence of multi-behavior learning in recommender systems, leveraging auxiliary user behaviors has proven effective for mitigating target-behavior data sparsity. Yet auxiliary behavior graphs frequently contain noisy or irrelevant interactions that do not align with the target task, impeding the learning of accurate user and item embeddings. Moreover, the scarcity of direct supervised from the target behavior complicates the extraction of informative collaborative signals. In this paper, we introduce GCIB Graph Contrastive Information Bottleneck, a novel framework that denoises auxiliary behavior information and enriches target behavior representations at both the structural and feature levels. At the structural level, GCIB employs a Graph Information Bottleneck (GIB) objective to maximize mutual information between the denoised auxiliary graph and the target-behavior graph while minimizing mutual information with the original auxiliary graph. This formulation preserves task-relevant structural patterns and suppresses spurious interactions. At the feature level, we propose a cross-behavior Graph Contrastive Learning (GCL) scheme in which denoised auxiliary features and target-behavior features serve as complementary views for both users and items. By contrasting these views, GCIB enriches sparse target-behavior representations with semantics distilled from auxiliary behaviors. Extensive experiments on multiple real-world datasets demonstrate that GCIB outperforms state-of-the-art baselines, highlighting its ability to learn noise-resilient and target-aware representations for multi-behavior recommendation.

Identifying molecular structures from spectral data is essential for early-stage chemical analysis, yet it remains a difficult task due to severe functional group imbalance and complex inter-group dependencies, which often cause existing methods to overfit frequent groups while underperforming on rare ones. To address these issues, we present **SymSpectra**, a **Sym**metric Conditional Information Bottleneck (SCIB) framework designed to seamlessly integrate multi-modal **Spectra** features. Our model employs the SCIB framework to fuse multi-modal spectroscopic data into a unified representation, effectively preserving discriminative signals while mitigating redundancy. To enhance robustness against data imbalance, we incorporate conditional mutual information into the training objective, increasing the model’s sensitivity to rare functional groups and challenging molecular cases. Additionally, a specialized module captures the dependencies among functional groups, improving both prediction accuracy and chemically meaningful interpretability. Experiments on multimodal spectral datasets show that SymSpectra outperforms state-of-the-art methods, achieving an F1-score of 0.970 in substructure classification and demonstrating strong robustness under various imbalance settings.

Large Language Models (LLMs) can be seen as compressed knowledge bases, but it remains unclear what knowledge they truly contain and how far their knowledge boundary extends. Existing benchmarks are mostly static and provide limited support for systematic knowledge probing. In this paper, we propose an interactive agentic framework to systematically extract and quantify the knowledge of LLMs. Our method includes four adaptive exploration policies to probe knowledge at different granularity. To ensure the quality of extracted knowledge, we introduce a three-stage knowledge processing pipeline that combines vector-based filtering to remove strict duplicates, LLM-based adjudication to resolve ambiguous semantic overlap, and domain relevance auditing to retain valid knowledge units. Through extensive experiments, we find that Recursive Taxonomy is the most effective exploration strategy. We also observe a clear knowledge scaling law, where larger models consistently recover more knowledge. In addition, we identify a Pass@1 versus Pass@k trade-off: domain-specialized models achieve higher initial accuracy but experience rapid degradation, while general-purpose models maintain stable performance over extended extraction. Finally, our results show that differences in training data composition lead to distinct and measurable knowledge profiles across model families, reflecting how pretraining shapes each model's parametric knowledge.

We study the problem of learning Transformer-based sequence models with black-box access to their outputs. In this setting, a learner may adaptively query the oracle with any sequence of vectors and observe the output of the target function. We begin with studying the learnability of the simplest formulation, that is, learning a single-head attention-based regressor with queries. We show that for a model with width $d$, there is an elementary algorithm to learn the parameters of single-head attention with $O(d^2)$ queries. Further, we show that if there exists an algorithm to learn ReLU feedforward networks (FFNs), then the single-head algorithm can be easily adapted to learn one-layer Transformers with single-head attention. Next, we show that, in the common regime where the head dimension $r \ll d$, single-head attention-based models can be learned with $O(rd)$ queries via compressed sensing arguments. We also study robustness to noisy oracle access, proving that under mild norm and margin conditions, the parameters can be estimated to $\varepsilon$ accuracy with a polynomial number of queries even when outputs are only provided up to additive tolerance. Finally, we consider the learnability of multi-head attention and show that they are not identifiable from queries, and hence, learnability in the same sense is not feasible without additional assumptions. We discuss potential approaches to learn multi-head attention-based models under certain structural assumptions.

This paper considers the problem of converting a given dense linear layer to low precision. The tradeoff between compressed length and output discrepancy is analyzed information theoretically (IT). It is shown that a popular GPTQ algorithm may have an arbitrarily large gap to the IT limit. To alleviate this problem, a novel algorithm, termed "WaterSIC", is proposed and is shown to be within a rate gap of 0.255 bits to the IT limit, uniformly over all possible covariance matrices of input activations. The key innovation of WaterSIC's is to allocate different quantization rates to different columns (in-features) of the weight matrix, mimicking the classical IT solution known as ``waterfilling''. Applying WaterSIC to the Llama and Qwen family of LLMs establishes new state-of-the-art performance for all quantization rates from 1 to 4 bits. Our code is available at https://github.com/egorlifar/watersic.

Kullback-Leibler (KL) divergence regularization is widely used in reinforcement learning, but it becomes infinite under support mismatch and can degenerate in low-noise regimes. Using a unified information-geometric framework, we introduce KL analogs by replacing the Fisher–Rao geometry in the dynamical formulation of the KL with transport-based geometries, and derive closed-form expressions for common distribution families. Between elliptic distributions, these divergences remain finite for degenerating equal covariances and yield a geometric interpretation of regularization heuristics used in Kalman ensemble methods. We demonstrate the utility of these divergences in KL-regularized optimal control. In the fully tractable setting of linear time-invariant systems with Gaussian process noise, the classical KL reduces to a quadratic control penalty that becomes singular as process noise vanishes. Our variants remove this singularity and yield well-posed problems. On a double integrator and a cart-pole example, the resulting controls preserve nontrivial feedback and achieve better closed-loop performance.

We present a general theoretical framework for analyzing how information about past inputs is encoded in recurrent networks into evolving dynamics rather than being represented as convergence to static attractors. Using dynamic mean-field theory and diffusion from physics, we derive a Fisher information diffusion operator that links network connectivity structure to the time-resolved propagation of information across interacting subpopulations. The analysis reveals that operating near criticality (spectral radius near one) is necessary but not sufficient for reliable memory in structured or non-normal recurrent networks; effective information retention requires alignment between input–output structure and stable dynamical subspaces. The theory yields principled initialization rules that balance stability and sensitivity, mitigating vanishing and exploding gradients. Experiments on the copy task and sequential MNIST show faster convergence and higher accuracy than standard random initialization. Together, these results provide both principled design guidelines for recurrent networks and new theoretical insight into how information can be preserved over time in their dynamics.

Incomplete multi-view multi-label classification addresses scenarios where views and labels are partially missing. While existing methods treat labels solely as supervision signals, they overlook the semantic structure inherent in partial annotations. We propose Label-Guided Representation Learning (LGRL) that systematically exploits label semantics as structural priors throughout learning. Our framework constructs a semantic-informed mixture prior via learnable category prototypes to guide representation extraction, and introduces category-specific conditional posteriors where prototypes act as Bayesian experts for multi-view fusion. We further derive a principled label-driven information bottleneck objective balancing reconstruction sufficiency with cross-view consistency, enabling category-conditional reasoning. Extensive experimental results demonstrate the effectiveness of LGRL across benchmark datasets as well as real-world applications in sports analytics and medical imaging.

Reinforcement learning from verifiable rewards (RLVR) has become an important paradigm for enhancing the reasoning capabilities of large language models, while it also involves a persistent tradeoff between optimization stability and learning efficiency. Token-level importance weighting supports fine-grained credit assignment, but it often introduces high variance and unstable parameter updates, whereas sequence-level optimization provides more stable learning dynamics while failing to fully exploit informative local signals. We introduce **T**rust-**G**ated **P**olicy **O**ptimization (TGPO), an efficient policy optimization framework that integrates two complementary mechanisms, namely *sequence anchors* and *information gates*. TGPO aligns token-wise updates with a stable sequence-level reference, which reduces the influence of extreme local likelihood fluctuations on the gradient, and a trust-based information gate adaptively modulates the contribution of token-level signals. By retaining and reweighting gradients from imperfect trajectories rather than excluding them, TGPO improves gradient utilization and sample efficiency while maintaining stable optimization behavior. Empirical results across seven mathematical reasoning datasets and multiple model scales show that TGPO consistently enhances learning efficiency and overall performance in outcome-supervised reinforcement learning settings.

Diffusion models have become the foundation of modern generative systems, with most research focusing primarily on improving generation efficiency and output quality. The timestep embedding component is a crucial part of the diffusion pipeline, which provides a temporal conditioning signal to the denoising network, enabling it to adapt its predictions across different noise levels throughout the process. Despite their potential to contain substantial information, timestep embeddings remain underexplored in current research, especially for security risks and reliable provenance. To fill this gap, we introduce **Shadow Timestep Embedding (STE)**, a novel mechanism that investigates the underutilized temporal space for malicious information injection into diffusion models. In particular, when zooming in on the timestep embedding space, we find that different timesteps exhibit distinct representational capabilities that can encode side-channel information. Moreover, such encoded information can be utilized for attack and defense purposes through the scheduler interface. We present a theoretical analysis of timestep embeddings as position-encoding mappings and derive a mutual coherence evaluation that explains the separability of disjoint timestep intervals. Our findings reveal the diffusion model's timestep as a powerful side channel for carrying dedicated information, motivating new directions for adversarial generative modeling by understanding the temporal dimension.

Multi-modal clustering, which integrates information from diverse sources and feature modalities, has shown great potential in data mining and computer vision. However, existing methods relying on single-granularity relationships often struggle with complex data distributions, leading to limited performance, as fine-grained features are prone to local heterogeneity and redundant perturbations while coarse-grained representations tend to lose local structural information. To address these limitations, we introduce granular-balls (GBs), adaptive multi-granularity hyperspheres that enclose similar samples, and propose the Structure-aware Granular-Ball based Information Bottleneck (SGB-IB) algorithm. This method initializes the dataset as a single GB and recursively splits GBs based on a purity metric, which quantifies the average mutual information between sample features and K-means-derived pseudo-labels across all modalities. It also balances local structure preservation and global redundancy suppression through a structure-aware objective function. Extensive experiments on benchmark datasets demonstrate that our method outperforms state-of-the-art approaches, validating the effectiveness of fusing GB structures with information-theoretic principles.

High-resolution visual encoders in multimodal large language models (MLLMs) substantially improve fine-grained perception, yet incur prohibitive computational costs.Existing token pruning methods are effective on natural images but struggle with spatially sparse structured inputs (e.g., charts), where critical high-frequency information is sparse, localized, and structurally essential. To address this challenge, we propose Adaptive Dual-Branch Token Sparsification (AD-BTS), a density-aware framework that dynamically allocates computation according to input signal characteristics. Specifically, AD-BTS introduces a Gradient-based Routing Gate (GRG) that uses lightweight pixel-level gradient statistics to estimate structural flatness and guide routing. Then, AD-BTS activates either a Redundancy Selection Branch (RSB) for aggressive token pruning with a frozen encoder, or a Structural Fusion Branch (SFB) with conditional LoRA and context fusion to preserve sparse structural information.Extensive experiments on Qwen2.5-VL demonstrate that AD-BTS establishes a new Pareto frontier between efficiency and accuracy. Under extreme compression (20% token retention), AD-BTS outperforms the strongest baseline by 12.1% on ChartQA while achieving a 1.8× prefill speedup, effectively reconciling computational efficiency with structural robustness.

While iTransformer pioneered general inter-variate dependency (IVD) modeling in Transformers for multivariate time series forecasting (MTSF), subsequent research on such universal paradigms has been surprisingly scarce. Through comprehensive analysis, we identify a critical structural inconsistency in Variate Transformers: typically capturing inter-variate dependencies via shallow self-attention layers while neglecting the critical requirement for deep-layer IVD modeling, which causes spurious correlations modeling and difficulties in model optimization. To address these limitations, we propose CGTFra, as a general framework for consistent IVD modeling. Specifically, we reconsider existing timestamp-based modeling and introduce a frequency-domain masking and resampling method for periodicity preservation, which serves as a general strategy for input feature enhancement. Additionally, CGTFra promotes consistent IVD modeling from two perspectives. Initially, a dynamic graph learning framework is integrated into Transformers to explicitly model IVD in deep network layer. Furthermore, grounded in the Information Bottleneck principle, we further propose a consistency-constrained alignment to learn more robust IVD and temporal feature representations. These three core design philosophies of CGTFra can be integrated into any existing Variate Transformer-based framework, and CGTFra achieves superior predictive performance across 13 long- and short-term datasets with high computational efficiency and desirable interpretability. Code is available at https://github.com/05Pikachu24/Consistent-CGTFra.

Large language models (LLMs) can struggle to memorize factual knowledge in their parameters, often leading to hallucinations and poor performance on knowledge-intensive tasks. In this paper, we formalize fact memorization from an information-theoretic perspective and study how training data distributions affect fact accuracy. We show that fact accuracy is suboptimal (below the capacity limit) whenever the amount of information contained in the training data facts exceeds model capacity. This is further exacerbated when the fact frequency distribution is skewed (e.g. a power law). We propose data selection schemes based on the training loss alone that aim to limit the number of facts in the training data and flatten their frequency distribution. On semi-synthetic datasets containing high-entropy facts, our selection method effectively boosts fact accuracy to the capacity limit. When pretraining language models from scratch on an annotated Wikipedia corpus, our selection method enables a GPT2-Small model (110m parameters) to memorize 1.3X more entity facts compared to standard training, matching the performance of a 10X larger model (1.3B parameters) pretrained on the full dataset.

Vision-Language Models (VLMs) frequently suffer from visual perception errors and hallucinations that compromise answer accuracy in complex reasoning tasks. Reinforcement Learning with Verifiable Rewards (RLVR) offers a promising solution by optimizing policies using answer correctness signals. Despite their effectiveness, prevailing RLVR methods face two critical limitations. First, much of the sampling budget is wasted on trajectories doomed to fail due to early visual description errors. Second, sparse rewards cannot distinguish whether failures stem from visual perception or reasoning stages. We introduce MIRL, a decoupled framework that addresses both limitations by leveraging mutual information (MI) between generated descriptions and visual inputs as a cheap pre-screening signal. This enables intelligent budget allocation toward high-potential trajectories via forking, while decoupled training provides independent MI-based rewards for visual perception optimization, resolving reward blindness. Experiments on six vision-language reasoning benchmarks demonstrate that MIRL achieves 70.22\% average accuracy and successfully surpasses the performance of sampling 16 complete trajectories using only 10 pre-samples with top-6 selection (25\% fewer complete trajectories). Our code is available at: https://github.com/youwyouw/mirl-main.

Standard diffusion models for graph generation typically rely on uniform time-stepping, an approach that overlooks the non-homogeneous dynamics of distributional evolution on complex manifolds. In this paper, we present an information-geometric framework that reinterprets the diffusion sampling trajectory as a parametric curve on a Riemannian manifold. Our key observation is that the Fisher-Rao metric provides a principled measure of the intrinsic distance. By analyzing this metric, we derive the Drift Variation Score (DVS), a geometry-aware indicator that quantifies the instantaneous rate of distributional change. Unlike prior heuristic-based adaptive samplers, our DVS solver enforces a constant informational speed on the statistical manifold, automatically maintaining a uniform rate of distributional change along the sampling trajectory. This equal arc-length strategy ensures that each discretization step contributes equally to the information speed. Theoretical analysis verifies that DVS characterizes the local stiffness of the sampling dynamics in the Fisher-Rao sense. Experimental results on molecule and social network generation show that DVS significantly improves structural fidelity and sampling efficiency.

In many prediction problems, we have extra information during training (for example, measurements that are expensive or slow to collect) that will not be available when the model is deployed. A common strategy is to first train a model that uses all training information, then use its predictions on unlabeled examples to train a second model that only uses the inputs available at test time. However, when the extra training-only information is weak or noisy, this two-step approach can mislead the deployable model and even hurt accuracy. We propose a joint training method that learns the two models together, so the deployable model can benefit from the extra information only when it actually helps, instead of inheriting its mistakes. We provide guarantees that describe when joint training improves prediction accuracy and analyze a simple alternating training algorithm for large, high-dimensional models. Experiments on synthetic data and medical prediction tasks show that our approach avoids these failures and consistently outperforms standard two-step baselines.

A fundamental bottleneck in human-AI collaboration is the ``intention expression gap", the difficulty for humans to effectively convey complex, high-dimensional thoughts to AI. This challenge often traps users in inefficient trial-and-error loops and is exacerbated by the diverse expertise levels of users. We reframe this problem from passive instruction following to a Socratic collaboration paradigm, proposing an agent that actively probes for information to resolve its uncertainty about user intent. We name the proposed agent Nous, trained to acquire proficiency in this inquiry policy. The core mechanism of Nous is a training framework grounded in the first principles of information theory. Within this framework, we define the information gain from dialogue as an intrinsic reward signal, which is fundamentally equivalent to the reduction of Shannon entropy over a structured task space. This reward design enables us to avoid reliance on costly human preference annotations or external reward models. To validate our framework, we develop an automated simulation pipeline to generate a large-scale, preference-based dataset for the challenging task of scientific diagram generation. Comprehensive experiments, including ablations, subjective and objective evaluations, and tests across user expertise levels, demonstrate the effectiveness of our proposed framework. Nous achieves leading efficiency and output quality, while remaining robust to varying user expertise. Our research provides a systematic methodology and a new perspective for addressing ambiguous intentions in complex human-machine collaboration.

We study contextual bandits with paid observations, where the learner actively chooses which actions to observe at a given cost in each round, with the goal of minimizing total regret that jointly accounts for learning loss and observation expenditure. We develop a near-optimal algorithm for adversarial environments and show that even small observation costs fundamentally raise the minimax regret order. We further uncover a novel phase transition under a free observation budget: below a critical threshold, free observations only reduce total cost without improving the regret rate; above it, asymptotic improvements become possible. To exploit this phenomenon, we design a meta-controller that adaptively switches between strategies to achieve near-optimal performance across all budget regimes. To handle large or infinite policy spaces, we also propose an oracle-efficient algorithm under a function approximation framework that maintains rigorous guarantees with computational efficiency. Our analysis also connects to related problems including switching costs, budgeted constraints, model misspecification, and knapsack bandits. Numerical experiments validate our theoretical findings.