ICML 2026 论文列表

Identifying the drivers of causal mechanism shifts, distinguishing functional changes from noise alterations, termed *dissection*, is a critical yet under-explored problem in data science (e.g., biomedical science and manufacturing). This paper introduces a more general and unified framework, the *function and noise separation* (FANS) framework, that detects and dissects shifts in non-additive, non-linear Structural Causal Models (SCMs) beyond existing additive noise models. Our approach is grounded in a theoretical independence criterion, where function shifts induce a statistical dependence between a node's parents and residual noise. Building on this foundation, we develop a practical two-stage algorithm to efficiently detect and dissect these shifts without retraining. Furthermore, we address the complex challenge of simultaneous function and noise shifts, introducing a formal assumption to resolve their inherent non-identifiability. Our results are corroborated by simulations. Our code is available at https://github.com/MLAI-Yonsei/FANS/.

Graph Contrastive Learning (GCL) has significantly advanced self-supervised representation learning on graphs, yet its practical efficacy remains hindered by random augmentations that induce semantic distortion and rigid one-to-one sampling strategy that amplifies inter-class entanglement and intra-class dispersion. To address these limitations, we develop CL-GCL, a Comprehensive and Lightweight Graph Contrastive Learning framework. Specifically, we exploit graph coarsening‌ to preserve structural semantics through community-level representations and manifold learning‌ to capture local geometric relations without costly pairwise distance computations. This design naturally aligns with the neighborhood aggregation principle of Graph Convolutional Networks, enhancing structural consistency while eliminating negative sampling bias. We theoretically prove that CL-GCL approximates node-level contrastive loss under mild conditions. Extensive experiments demonstrate consistent superiority in both accuracy and efficiency over state-of-the-art GCL methods.

Auto-regressive models have emerged as powerful tools for sequential data, from language to video. Understanding how and why these models learn latent representations remains an open theoretical question. In this work, we demonstrate that when trained by empirical risk minimization on data from partially observed linear dynamical systems, two-layer linear auto-regressive models naturally learn to approximate Kalman filtering. In particular, we show that the learned hidden representation coincides, up to a similarity transformation, with the state estimates produced by the optimal (Kalman) filter, even though the model has no explicit knowledge of the underlying dynamics or state. The result follows from three main insights. First, we establish that the Kalman filter is well approximated by an auto-regressive model with bounded truncation error. Second, we show that despite non-convexity, the two-layer optimization landscape is benign, i.e., all stationary points are either strict saddles or global minima. Finally, as our main contributions, we provide finite-sample guarantees on prediction error, parameter estimation error, and latent state recovery. Numerical simulations support the theoretical results and demonstrate that the latent representations of auto-regressive models recover state estimates.

Semi‑supervised statistical inference plays a key role in biomedical research, where labeled data often have higher quality but are limited due to costly clinical annotation. Yet, existing semi‑supervised statistical inference methods rely heavily on structured variables and strictly matched covariates between labeled and unlabeled datasets -- limitations ill‑suited for the heterogeneity and unstructured nature of real-world biomedical data. Modern biomedical studies increasingly collect unstructured data (clinical notes, patient audio and video recordings), with inconsistent protocols across datasets causing covariate misalignment (for instance, detailed medication histories may be recorded in one study but not another). Recent advances in pre‑trained multimodal large language models (LLMs), which excel at handling unstructured data, present an attractive potential solution. To transform this potential into rigorous semi-supervised statistical inference methods for biomedical research, two key challenges must be addressed: (1) How can we reliably integrate LLMs to enhance semi-supervised inference efficiency without compromising statistical validity? (2) How can those efficiency gains persist despite mismatched covariates between labeled and unlabeled datasets? In this paper, we tackle these challenges by systematically *calibrating pseudo-labels* provided LLMs with a novel *prediction-invariance identification* strategy. Our resulting semi‑supervised inference framework improves parameter estimation efficiency while maintaining full statistical validity, as demonstrated through our theoretical results and illustrated in a case study for identifying key biomarkers in Alzheimer’s disease detection with speech data.

Modern large-scale neural networks are often trained and released in multiple sizes to accommodate diverse inference budgets. To improve efficiency, recent work has explored *model upscaling*: initializing larger models from trained smaller ones to accelerate convergence. However, this method can be sensitive to hyperparameters that need to be tuned at the target upscaled model size, which is prohibitively costly to do directly. It remains unclear whether tuning hyperparameters on smaller models and extrapolating via scaling laws is sound in this setting. We address this with principled approaches to width-based upscaling and efficient hyperparameter tuning in this setting. Motivated by $\mu$P and any-dimensional architectures, we introduce a general upscaling method that, like Net2Net, copies and perturbs weights, but uses theoretically grounded, width-dependent scalings for the perturbation noise and optimizer hyperparameters. First, we prove that under zero perturbation, the upscaled model is functionally equivalent to the base model throughout training. Second, we extend the $\mu$P theory to enable infinite-width limit analysis and establish hyperparameter transfer for upscaled models, greatly reducing the tuning cost. We empirically demonstrate that this method is effective on realistic datasets and architectures.

Modern imaging techniques heavily rely on Bayesian statistical models to address difficult image reconstruction and restoration tasks. This paper addresses the objective evaluation of such models in settings where ground truth is unavailable, with a focus on model selection and misspecification diagnosis. Existing unsupervised model evaluation methods are often unsuitable for computational imaging due to their high computational cost and incompatibility with modern image priors defined implicitly via machine learning models. We herein propose a general methodology for unsupervised model selection and misspecification detection in Bayesian imaging sciences, based on a novel combination of Bayesian cross-validation and data fission, a randomized measurement splitting technique. The approach is compatible with any Bayesian imaging sampler, including diffusion and plug-and-play samplers. We demonstrate the methodology through experiments involving various scoring rules and types of model misspecification, where we achieve excellent selection and detection accuracy with a low computational cost.

Recent research has established that the impact of context in a vanilla transformer can be represented implicitly by forming a token-dependent, rank-1 patch to its MLP weights. This work extends that foundational theory to the diverse architectures of modern Large Language Models. We first demonstrate a precise, analytical solution for a Gemma-style transformer block, proving that the entire effect of a context can be perfectly mapped to rank-1 patches on its MLP weight matrices and a patch to the RMSNorm scale. We then generalize this result, providing a constructive proof and algorithm for multi-layer models. To unify these findings, we introduce a general framework centered on two core properties: input controllability and output controllability. We prove that a perfect implicit weight patch is possible for any MLP block where the inner function is input-controllable and the outer function is output-controllable. This provides a simpler and more powerful lens for understanding how transformer models transmute prompts into effective weights. This setup generalizes to a wide range of modern LLM architectures including gating, pre-/post-norm, mixture of experts and sequential/parallel transformer blocks.

Continual learning with large pre-trained models offers significant potential for cross-task knowledge accumulation, but faces critical challenges such as catastrophic forgetting and parameter interference, especially when historical data is unavailable. Existing approaches typically rely on sequential fine-tuning or model merging strategies, yet often overlook the impact of loss landscape sharpness and dominant singular value directions, which leads to subspace misalignment and severe knowledge forgetting. In this paper, we propose the Sharpness-Aware Isotropic Merging (SAIM) framework, which introduces targeted optimizations in both the fine-tuning and merging stages to address these issues. Specifically, SAIM consists of two synergistic modules: (1) a Sharpness-Aware Block Coordinate Descent (SA-BCD) optimizer that guides the model toward flatter minima and selectively updates the most task-sensitive parameters, thereby mitigating parameter interference and enhancing robustness; (2) an adaptive isotropic merging algorithm that dynamically balances the singular value spectrum across tasks, effectively preventing the model from overemphasizing any single task direction, maintaining balanced knowledge representation, and improving subspace alignment. Extensive experiments on vision and language benchmarks demonstrate that SAIM achieves 5-10\% higher accuracy than existing methods and maintains robust performance as the number of tasks increases. Our code are available at \url{https://github.com/Yangqun123456/SAIM}.

This paper studies a fundamental yet often overlooked premise in evolutionary multi-view classification (EMVC): the impact of label noise on EMVC, such as distorting fitness landscapes shaped by individual fitness values (e.g., test accuracy). Traditional EMVC assumes training labels are noise-free, yet this often fails in practice. As a result, label noise introduces harmful supervision during the training phase, resulting in distorted fitness landscapes and the emergence of fitness evaluation bias (FEB). This bias misguides the evolutionary trajectory, causing the search process to stagnate in local optima. Given that label noise largely stems from the mislabeling of samples near their decision boundaries by human annotators, we thus compared the decision boundaries of human annotators and models, and found discrepancies between the two. Based on this observation, we propose a simple yet effective ``detect-then-calibrate" data purification framework that leverages outlier analysis in the gradient space (i.e., treating outliers as noisy samples) and prototype calibration in the feature space (i.e., utilizing feature prototypes of noise-free samples to correct the labels of noisy samples). Experimental results demonstrate that this strategy can effectively purify the data and alleviate FEB; moreover, it can improve the performance of various multi-view learning paradigms in label noise scenarios. (https://github.com/LiShuailzn/ICML-2026-GFD-EMVC)

Symmetry is everywhere in nature and society. Geometric deep learning exploits symmetries in data to improve the performance and efficiency of deep learning systems. In this paper, we extend geometric deep learning to utilize richer symmetry structures. Specifically, we develop order-equivariant neural networks (OENN), which generalize standard graph message passing and sheaf neural networks via the theory of equivariant bundles over face posets (face categories). We (i) characterize all linear order-equivariant maps, (ii) build OENN layers, and (iii) prove universal approximation theorems (UATs) for continuous order-equivariant maps, which are new results even when restricted to sheaf neural networks (for which no UAT was known before). We illustrate the framework on graph and sheaf models. Our results can also be seen as extending the known UAT for graph neural networks to a more general setting that subsumes sheaf neural networks as well. In addition, we show that OENN can be extended further to CENN, Category-Equivariant Neural Network, which gives the general form of equivariant neural networks as well as of equivariant universal approximation theorems, allowing us to leverage categorical symmetry in data (e.g., non-invertible symmetries on multiple objects with compositional relations on those symmetries).

Recent class-incremental learning (CIL) methods built on large pre-trained vision models have shown that strong performance can be retained even under strict data access constraints. This raises a fundamental question: which properties of pre-trained representations make such recovery possible in the class-incremental setting? In this work, we show that class-level feature statistics play a central role in enabling effective CIL under strong pre-training. When the visual backbone is frozen, maintaining simple class-wise statistical estimators of features can recover a substantial fraction of the performance achieved by static joint training across diverse benchmarks. We make this observation explicit through deliberately minimal reference points built on frozen CLIP representations. In particular, we demonstrate that competitive performance can be achieved without continual parameter updates, by performing class-incremental inference based solely on class-level statistical estimators instantiated from frozen features. Our findings suggest that class-level statistics constitute an important and previously underemphasized component of recent PTM-based CIL approaches, offering a complementary perspective for understanding their strong empirical performance. Our code is available at https://github.com/HdTgon/baseCIL.

Large language models (LLMs) commonly boost reasoning via sample-evaluate-ensemble decoders (e.g., majority voting), achieving label free gains without ground truth. However, prevailing strategies score candidates using only external outputs such as token probabilities, entropies, or self evaluations, and these signals can be poorly calibrated after post training. We instead analyze internal behavior based on neuron activations and uncover three findings: (1) external signals are low dimensional projections of richer internal dynamics; (2) correct responses activate substantially fewer unique neurons than incorrect ones throughout generation; and (3) activations from correct responses exhibit stronger cross sample agreement, whereas incorrect ones diverge. Motivated by these observations, we propose Neuron Agreement Decoding (NAD), an unsupervised best of N method that selects candidates using activation sparsity and cross sample neuron agreement, operating solely on internal signals and without requiring comparable textual outputs. NAD enables early correctness prediction within the first 32 generated tokens and supports aggressive early stopping. Across math and science benchmarks with verifiable answers, NAD matches majority voting; on open ended coding benchmarks where majority voting is inapplicable, NAD consistently outperforms Avg@64. By pruning unpromising trajectories early, NAD reduces token usage by 99% with minimal loss in generation quality, showing that internal signals provide reliable, scalable, and efficient guidance for label free ensemble decoding.

We propose Bayesian Forest Thompson Sampling (BFTS), which performs Thompson sampling using arm-wise Bayesian Additive Regression Trees (BART) to model each action's mean reward and generate MCMC-based posterior draws for decision-making. We derive an information-theoretic Bayesian regret bound of order $\widetilde{\mathcal O}(K\sqrt{T})$ for ideal posterior sampling under a correctly specified Bayesian design. Empirically, BFTS achieves competitive regret on nonlinear synthetic benchmarks with near-nominal uncertainty calibration, attains the best average rank across nine OpenML contextual bandit benchmarks, and yields higher estimated policy values than linear, neural, and tree-ensemble baselines in a Drink Less micro-randomized trial case study. Across OpenML benchmarks, BFTS is robust to hyperparameter choices.

Diffusion models are widely used for high-quality generation, but their performance is sensitive to the accuracy of the estimated score. We first derive a stepwise Wasserstein error bound in a Gaussian-mixture setting, where the score admits a closed-form structure, and the score Hessian can be controlled explicitly, leading to sharp Wasserstein estimates. We then extend the analysis to general data distributions, which yields a more general but typically looser upper bound. This general bound can be sharpened under mild regularity: when the initial distribution has a globally Lipschitz score, the curvature contribution at small times is uniformly bounded, avoiding the worst-case blow-up. The results hold for both variance-preserving (VP) and variance-exploding (VE) diffusions, and apply to both the reverse-time SDE and the associated probability-flow ODE.

Rotary Position Embedding (RoPE) is widely adopted in Transformer models, yet its extension to high-dimensional domains lacks a unified theoretical formulation. Most existing approaches either apply rotations independently along each axis or empirically mix frequencies, which limits cross-dimensional interactions and yields direction-dependent representations. To address these limitations, we propose *nD-RoPE*, a decomposition-free generalization of RoPE to arbitrary dimensions. From a translation-invariant formulation in continuous Hilbert space, we derive a spectral condition for isotropy that requires treating positions and frequencies as coupled $n$-dimensional vectors. We instantiate this formulation with a multi-scale regular-simplex wave-vector design, which provides non-degenerate spatial coverage and a symmetric, directionally balanced second-order response. Experiments across images, videos, and point clouds demonstrate consistent performance gains and improved generalization in high-dimensional settings.

Continual Model Merging (CMM) enables rapid customization of foundation models by sequentially incorporating task-adapted models without repeated retraining. However, existing merging rules usually update the deployed model through fixed algebraic or projection-based operations, providing limited control over how much previously accumulated knowledge should be retained relative to the incoming task model. This limitation leads to unstable retention and performance degradation in long task streams, and becomes more pronounced when tasks have heterogeneous utilities. We propose ODE-driven Merging (ODE-M), a controllable framework that formulates each continual merge as a trajectory in parameter space rather than a one-step endpoint update. Motivated by mode connectivity, ODE-M constructs a barrier-aware trajectory using a rectified time-dependent velocity field, where lightweight first-order feedback from a small calibration set suppresses loss-increasing motion while preserving progress toward the incoming model. The next merged model is then obtained by selecting an operating point along this trajectory through a utility-aware time schedule, providing an explicit mechanism for balancing retained historical knowledge and incoming task expertise. Extensive experiments on standard CMM benchmarks show that ODE-M consistently improves over strong continual merging baselines across CLIP ViT backbones, stream lengths, and heterogeneous task-utility settings.

Recent progress in large-scale flow and diffusion models raised two fundamental algorithmic challenges: $(i)$ control-based reward adaptation of pre-trained flows, and $(ii)$ integration of multiple models, i.e., flow merging. While current approaches address them separately, we introduce a unifying probability-space framework that subsumes both as limit cases, and enables *reward-guided flow merging*, allowing principled, task-aware combination of multiple pre-trained flows (e.g., merging priors while maximizing drug-discovery utilities). Our formulation renders possible to express a rich family of *operators over generative models densities*, including intersection (e.g., to enforce safety), union (e.g., to compose diverse models), interpolation (e.g., for discovery), their reward-guided counterparts, as well as complex logical expressions via *generative circuits*. Next, we introduce Reward-Guided Flow Merging (RFM), a mirror-descent scheme that reduces reward-guided flow merging to a sequence of standard fine-tuning problems. Then, we provide first-of-their-kind theoretical guarantees for reward-guided and *pure* flow merging via RFM. Ultimately, we showcase the capabilities of the proposed method on illustrative settings providing visually interpretable insights, and apply our method to high-dimensional de-novo molecular design and low-energy conformer generation.

A range of methods aim to enhance the performance of vision-language models (VLMs) at test time. Among them, transduction has emerged as a promising paradigm due to its strong compatibility and efficiency. However, realistic evaluations often involve highly imbalanced class distributions, which cause performance degradation or even collapse. In this work, we systematically revisit transduction from the perspective of penalized likelihood estimation (PLE), showing that PLE with a KL-divergence anchor term naturally yields an adaptive shrinkage behavior between prior anchors and empirical estimates. From this viewpoint, the brittleness of transductive methods can be attributed to the absence of anchoring mechanism and static modeling of the shrinkage strength. Therefore, we propose Mixture of Von Mises-Fisher Models with Dynamic Shrinkage (MOON). MOON is built upon a mixture of von Mises-Fisher distributions to model feature representations on the unit hypersphere. To handle imbalance, MOON dynamically adjusts the shrinkage strength using zero-shot priors at both instance and class levels. Thus, it suppresses unreliable assignments and prevents harmful updates from outlier classes, thereby mitigating negative transfer. MOON is model-agnostic, training-free, and requires no task-specific hyperparameter tuning. Extensive experiments further validate the advantage of MOON in both performance and efficiency.

Deep multi-view graph clustering (DMGC) typically leverages graph neural networks for representation learning, but most existing methods excessively depend on local and static graph structures and only utilize simplistic cross-view fusion strategies. To this end, this paper proposes **A**ttribute-aware Bidirectional Structural Refinement (ABSR) and **P**seudo-label Guided Multi-level Fusion (PGMF) for DM**GC**, termed **APGC**. Specifically, ABSR selectively strengthens high-quality connections and suppresses semantically conflicting relationships, achieving bidirectional refinement of the graph structure based on attribute similarity. It incorporates global attribute semantics into the graph structure, thereby promoting the homophilic connections for discriminative graph representation learning. Guided by reliable pseudo-labels, PGMF achieves adaptive weighted fusion at both the node-level and the view-level, effectively balancing the differentiated contributions of multi-view information. Experiments on six homophilic and heterophilic datasets demonstrate the superior clustering performance of the proposed APGC method. The code of APGC could be available at https://github.com/TianxiangZhao0474/APGC.git.