ICLR 2026 论文列表

Vector quantization is common in deep models, yet its hard assignments block gradients and hinder end-to-end training. We propose DiVeQ, which treats quantization as adding an error vector that mimics the quantization distortion, keeping the forward pass hard while letting gradients flow. We also present a space-filling variant (SF-DiVeQ) that assigns to a curve constructed by the lines connecting codewords, resulting in less quantization error and full codebook usage. Both methods train end-to-end without requiring auxiliary losses or temperature schedules. On VQ-VAE compression and VQGAN generation across various data sets, they improve reconstruction and sample quality over alternative quantization approaches.

Multi-view clustering aims to segment the view-specific data into the corresponding clusters. There have been a large number of works for multi-view clustering in recent years. As representive methods in multi-view clustering, works built on the graph make use of a view-consistent and discriminative graph while utilizing graph partitioning for the final clustering results. Despite the achieved significant success, these methods usually construct full graphs and the efficiency is not well guaranteed for the multi-view datasets with large scales. To handle the large-scale data, multi-view clustering methods based on anchor have been developed by learning the anchor graph with smaller size. However, the existing works neglect the interpretability of multi-view clustering based on anchor from the probabilistic perspective. These methods also ignore analyzing the relationship between the input data and the final clustering results based on the assigned meaningful probability associations in a unified manner. In this work, we propose a novel method termed Unified and Efficient Multi-view Clustering from Probabilistic perspective(UEMCP). It aims to improve the explanation ability of multi-view clustering based on anchor from the probabilistic perspective in an end-to-end manner. It ensures the consistent inherent structures among these views by learning the common transition probability from data points to categories in one step. With the guidance of the common transition probability matrix from data points to categories, the soft label of data points can be achieved based on the common transition probability matrix from anchor points to categories in the learning framework. Experiments on different challenging multi-view datasets confirm the superiority of UEMCP compared with the representative ones.

The InfoNCE objective, originally introduced for contrastive representation learning, has become a popular choice for mutual information (MI) estimation, despite its indirect connection to MI. In this paper, we demonstrate why InfoNCE should not be regarded as a valid MI estimator, and we introduce a simple modification, which we refer to as *InfoNCE-anchor*, for accurate MI estimation. Our modification introduces an auxiliary \emph{anchor} class, enabling consistent density ratio estimation and yielding a plug-in MI estimator with significantly reduced bias. Beyond this, we generalize our framework using proper scoring rules, which recover InfoNCE-anchor as a special case when the log score is employed. This formulation unifies a broad spectrum of contrastive objectives, including NCE, InfoNCE, and $f$-divergence variants, under a single principled framework. Empirically, we find that InfoNCE-anchor with the log score achieves the most accurate MI estimates; however, in self-supervised representation learning experiments, we find that the anchor does not improve the downstream task performance. These findings corroborate that contrastive representation learning benefits not from accurate MI estimation per se, but from the learning of structured density ratios.

Self-supervised contrastive learning (CL) has achieved remarkable empirical success, often producing representations that rival supervised pre-training on downstream tasks. Recent theory explains this by showing that the CL loss closely approximates a supervised surrogate, Negatives-Only Supervised Contrastive Learning (NSCL), as the number of classes grows. Yet this loss-level similarity leaves an open question: {\em Do CL and NSCL also remain aligned at the representation level throughout training, not just in their objectives?} We address this by analyzing the representation alignment of CL and NSCL models trained under shared randomness (same initialization, batches, and augmentations). First, we show that their induced representations remain similar: specifically, we prove that the similarity matrices of CL and NSCL stay close under realistic conditions. Our bounds provide high-probability guarantees on alignment metrics such as centered kernel alignment (CKA) and representational similarity analysis (RSA), and they clarify how alignment improves with more classes, higher temperatures, and its dependence on batch size. In contrast, we demonstrate that parameter-space coupling is inherently unstable: divergence between CL and NSCL weights can grow exponentially with training time. Finally, we validate these predictions empirically, showing that CL–NSCL alignment strengthens with scale and temperature, and that NSCL tracks CL more closely than other supervised objectives. This positions NSCL as a principled bridge between self-supervised and supervised learning.

Learning from Label Proportions~(LLP) aims to use bags of instances associated with the proportions of each label within the bag to learn an instance-level classifier. Proportion matching is a widely used strategy that aligns the average model outputs of all instances in a bag with the label proportions in order to induce the classifier. However, simply fitting the label proportions does not encourage discriminative instance-level predictions and may cause over-smoothing problems, resulting in poor classification performance. In this paper, we propose a novel LLP approach that can mitigate the over-smoothing problems with theoretical guarantees. Rather than fitting the label proportions directly, we treat them as targets for an auxiliary proportional value classification task to induce the target classifier. Our approach only requires the incorporation of an aggregation function after the classification layer. We also introduce an efficient computational approach with a divide-and-conquer strategy. Extensive experiments on various benchmark datasets and under different bag-generation strategies demonstrate that our approach achieves superior performance compared with state-of-the-art LLP methods. The code is publicly available at https://github.com/TianhaoMa5/ICLR2026_LLP-PVC.

Sets represent a fundamental abstraction across many types of data. To handle the unordered nature of set-structured data, models such as DeepSets and PointNet rely on fixed, non-learnable pooling operations (e.g., sum or max) -- a design choice that can hinder the transferability of learned embeddings and limits model expressivity. More recently, learnable aggregation functions have been proposed as more expressive alternatives. In this work, we advance this line of research by introducing the Neuralized Kolmogorov Mean (NKM) -- a novel, trainable framework for learning a generalized measure of central tendency through an invertible neural function. We further propose quasi-arithmetic neural networks (QUANNs), which incorporate the NKM as a learnable aggregation function. We provide a theoretical analysis showing that, QUANNs are universal approximators for a broad class of common set-function decompositions and, thanks to their invertible neural components, learn more structured latent representations. Empirically, QUANNs outperform state-of-the-art baselines across diverse benchmarks, while learning embeddings that transfer effectively even to tasks that do not involve sets.

Unsupervised Skill Discovery (USD) aims to autonomously learn a diverse set of skills without relying on extrinsic rewards. One of the most common USD approaches is to maximize the Mutual Information (MI) between skill latent variables and states. However, MI-based methods tend to favor simple, static skills due to their invariance properties, limiting the discovery of dynamic, task-relevant behaviors. Distance-Maximizing Skill Discovery (DSD) promotes more dynamic skills by leveraging state-space distances, yet still fall short in encouraging comprehensive skill sets that engage all controllable factors or entities in the environment. In this work, we introduce SUSD, a novel framework that harnesses the compositional structure of environments by factorizing the state space into independent components (e.g., objects or controllable entities). SUSD allocates distinct skill variables to different factors, enabling more fine-grained control on the skill discovery process. A dynamic model also tracks learning across factors, adaptively steering the agent’s focus toward underexplored factors. This structured approach not only promotes the discovery of richer and more diverse skills, but also yields a factorized skill representation that enables fine-grained and disentangled control over individual entities which facilitates efficient training of compositional downstream tasks via Hierarchical Reinforcement Learning (HRL). Our experimental results across three environments, with factors ranging from 1 to 10, demonstrate that our method can discover diverse and complex skills without supervision, significantly outperforming existing unsupervised skill discovery methods in factorized and complex environments. Code is available at the anonymous repository: [https://anonymous.4open.science/r/SUSD](https://anonymous.4open.science/r/SUSD).

Partial multi-label learning and complementary multi-label learning are two popular weakly supervised multi-label classification paradigms that aim to alleviate the high annotation costs of collecting precisely annotated multi-label data. In partial multi-label learning, each instance is annotated with a candidate label set, among which only some labels are relevant; in complementary multi-label learning, each instance is annotated with complementary labels indicating the classes to which the instance does not belong. Existing consistent approaches for the two paradigms either require accurate estimation of the generation process of candidate or complementary labels or assume a uniform distribution to eliminate the estimation problem. However, both conditions are usually difficult to satisfy in real-world scenarios. In this paper, we propose consistent approaches that do not rely on the aforementioned conditions to handle both problems in a unified way. Specifically, we propose two risk estimators based on first- and second-order strategies. Theoretically, we prove consistency w.r.t. two widely used multi-label classification evaluation metrics and derive convergence rates for the estimation errors of the proposed risk estimators. Empirically, extensive experimental results validate the effectiveness of our proposed approaches against state-of-the-art methods.

Symmetry-based disentangled representation learning leverages the group structure of environment transformations to uncover the latent factors of variation. Prior approaches to symmetry-based disentanglement have required strong prior knowledge of the symmetry group's structure, or restrictive assumptions about the subgroup properties. In this work, we remove these constraints by proposing a method whereby an embodied agent autonomously discovers the group structure of its action space through unsupervised interaction with the environment. We prove the identifiability of the true action group decomposition under minimal assumptions, and derive two algorithms: one for discovering the group decomposition from interaction data, and another for learning Linear Symmetry-Based Disentangled (LSBD) representations without assuming specific subgroup properties. Our method is validated on three environments exhibiting different group decompositions, where it outperforms existing LSBD approaches.

Vision-language models have achieved remarkable success in multi-modal representation learning from large-scale pairs of visual scenes and linguistic descriptions. However, they still struggle to simultaneously express two distinct types of semantic structures: the hierarchy within a concept family (e.g., *dog* $\preceq$ *mammal* $\preceq$ *animal*) and the compositionality across different concept families (e.g., "a dog in a car" $\preceq$ *dog*, *car*). Recent works have addressed this challenge by employing hyperbolic space, which efficiently captures tree-like hierarchy, yet its suitability for representing compositionality remains unclear. To resolve this dilemma, we propose *PHyCLIP*, which employs an $\ell_1$-*P*roduct metric on a Cartesian product of *Hy*perbolic factors. With our design, intra-family hierarchies emerge within individual hyperbolic factors, and cross-family composition is captured by the $\ell_1$-product metric, analogous to a Boolean algebra. Experiments on zero-shot classification, retrieval, hierarchical classification, and compositional understanding tasks demonstrate that PHyCLIP outperforms existing single-space approaches and offers more interpretable structures in the embedding space.

Dataset-level heterogeneity introduces significant domain biases that fundamentally degrade generalization on general Time Series Foundation Models (TSFMs), yet this challenge remains underexplored. This paper rethinks the from-scratch training of TSFMs using the paradigm of federated learning. We propose a novel Federated Dataset Learning (FeDaL) approach to tackle heterogeneous time series by learning dataset-agnostic temporal representations. Specifically, the distributed architecture of federated learning is a nature solution to decompose heterogeneous TS datasets into shared generalized knowledge and preserved personalized knowledge. Moreover, based on the TSFM architecture, FeDaL explicitly mitigates both local and global biases by adding two complementary mechanisms: Domain Bias Elimination (DBE) and Global Bias Elimination (GBE). FeDaL`s cross-dataset generalization has been extensively evaluated in real-world datasets spanning eight tasks (including various regression and classification), against 54 baselines. We further analyze federated scaling behavior, showing how data volume, client count, and join rate affect model performance under decentralization.

Cross-modal retrieval is a significant task that aims to learn the semantic correspondence between visual and textual modalities. Unsupervised hashing methods can efficiently manage large-scale data and can be effectively applied to cross-modal retrieval studies. However, existing methods typically fail to fully exploit the hierarchical structure between text and image data. Moreover, the commonly used direct modal alignment cannot effectively bridge the semantic gap between these two modalities. To address these issues, we introduce a novel Hierarchical Encoding Tree with Modality Mixup (HINT) method, which achieves effective cross-modal retrieval by extracting hierarchical cross-modal relations. HINT constructs a cross-modal encoding tree guided by hierarchical structural entropy and generates proxy samples of text and image modalities for each instance from the encoding tree. Through the curriculum-based mixup of proxy samples, HINT achieves progressive modal alignment and effective cross-modal retrieval. Furthermore, we conduct cross-modal consistency learning to achieve global-view semantic alignment between text and image representations. Extensive experiments on a range of cross-modal retrieval datasets demonstrate the superiority of HINT over state-of-the-art methods.

Neural synchrony is hypothesized to help the brain organize visual scenes into structured multi-object representations. In machine learning, synchrony-based models analogously learn object-centric representations by storing binding in the phase of complex-valued features. Rotating Features (RF) instantiate this idea with vector-valued activations, encoding object presence in magnitudes and affiliation in orientations. We propose Orthogonal Rotating Features (OrthoRF), which enforces orthogonality in RF’s orientation space via an inner-product loss and architectural modifications. This yields sharper phase alignment and more reliable grouping. In evaluations of unsupervised object discovery, including settings with overlapping objects, noise, and out-of-distribution tests, OrthoRF matches or outperforms current models while producing more interpretable representations, and it eliminates the post-hoc clustering required by many synchrony-based approaches. Unlike current models, OrthoRF also recovers occluded object parts, indicating stronger grouping under occlusion. Overall, orthogonality emerges as a simple, effective inductive bias for synchrony-based object-centric learning.

Disentangled representation learning aims to identify and organize the underlying sources of variation in observed data. However, learning disentangled representations without any additional supervision necessitates inductive biases to solve the fundamental identifiability problem of uniquely recovering the true latent structure and parameters of the data-generating process from observational data alone. Existing methods address this by imposing heuristic inductive biases that typically lack theoretical identifiability guarantees. They also rely on strong regularization to impose these inductive biases, creating an inherent trade-off in which stronger regularization improves disentanglement but limits the latent capacity to represent underlying variations. To address both challenges, we propose a principled generative model with a Bayesian nonparametric hierarchical mixture prior that embeds inductive biases within a provably identifiable framework for unsupervised disentanglement. Specifically, the hierarchical mixture prior imposes the structural constraints necessary for identifiability guarantees, while the nonparametric formulation enables inference of sufficient latent capacity to represent the underlying variations without violating these constraints. To enable tractable inference under this nonparametric hierarchical prior, we develop a structured variational inference framework with a nested variational family that both preserves the hierarchical structure of the identifiable generative model and approximates the expressiveness of the nonparametric prior. We evaluate our proposed probabilistic model on standard disentanglement benchmarks, 3DShapes and MPI3D datasets characterized by diverse source variation distributions, to demonstrate that our method consistently outperforms strong baseline models through structural biases and a unified objective function, obviating the need for auxiliary regularization constraints or careful hyperparameter tuning.

Traditional decision-based black-box adversarial attacks on image classifiers aim to generate adversarial examples by slightly modifying input images while keeping the number of queries low, where each query involves sending an input to the model and observing its output. Most existing methods assume that all queries have equal cost. However, in practice, queries may incur *asymmetric costs*; for example, in content moderation systems, certain output classes may trigger additional review, enforcement, or penalties, making them more costly than others. While prior work has considered such asymmetric cost settings, effective algorithms for this scenario remain underdeveloped. In this paper, we introduce asymmetric black-box attacks, a new family of decision-based attacks that generalize to the asymmetric query-cost setup. We develop new methods for boundary search and gradient estimation when crafting adversarial examples. Specifically, we propose *Asymmetric Search (AS)*, a more conservative alternative to binary search that reduces reliance on high-cost queries, and *Asymmetric Gradient Estimation (AGREST)*, which shifts the sampling distribution in Monte Carlo style gradient estimation to favor low-cost queries. We design efficient algorithms that reduce total attack cost by balancing different query types, in contrast to earlier methods such as *stealthy attacks* that focus only on limiting expensive (high-cost) queries. We perform both theoretical analysis and empirical evaluation on standard image classification benchmarks. Across various cost regimes, our method consistently achieves lower total query cost and smaller perturbations than existing approaches, reducing the perturbation norm by up to 40\% in some settings.

Federated Graph-level Clustering (FGC) offers a promising framework for analyzing distributed graph data while ensuring privacy protection. However, existing methods fail to simultaneously consider knowledge heterogeneity across intra- and inter-client, and still attempt to share as much knowledge as possible, resulting in consensus failure in the server. To solve these issues, we propose a novel **F**ederated **G**raph-level **C**lustering **N**etwork with **D**ual **K**nowledge **S**eparation (FGCN-DKS). The core idea is to decouple differentiated subgraph patterns and optimize them separately on the client, and then leverage cluster-oriented patterns to guide personalized knowledge aggregation on the server. Specifically, on the client, we separate personalized variant subgraphs and cluster-oriented invariant subgraphs for each graph. Then the former are retained locally for further refinement of the clustering process, while pattern digests are extracted from the latter for uploading to the server. On the server, we calculate the relation of inter-cluster patterns to adaptively aggregate cluster-oriented prototypes and parameters. Finally, the server generates personalized guidance signals for each cluster of clients, which are then fed back to local clients to enhance overall clustering performance. Extensive experiments on multiple graph benchmark datasets have proven the superiority of the proposed FGCN-DKS over the SOTA methods.

Separable neural networks (SepNNs) are emerging neural architectures that significantly reduce computational costs by factorizing a multivariate function into linear combinations of univariate functions, benefiting downstream applications such as implicit neural representations (INRs) and physics-informed neural networks (PINNs). However, fundamental theoretical analysis for SepNN, including detailed representation capacity and spectral bias characterization \& alleviation, remains unexplored. This work makes three key contributions to theoretically understanding and improving SepNN. First, using Weierstrass-based approximation and universal approximation theory, we prove that SepNN can approximate any multivariate function with arbitrary precision, confirming its representation completeness. Second, we derive the neural tangent kernel (NTK) regimes for SepNN, showing that the NTK of infinite-width SepNN converges to a deterministic (or random) kernel under infinite (or fixed) decomposition rank, with corresponding convergence and spectral bias characterization. Third, we propose an efficient separable preconditioned gradient descent (SepPGD) for optimizing SepNN, which alleviates the spectral bias of SepNN by provably adjusting its NTK spectrum. The SepPGD enjoys an efficient $\mathcal{O}(nD)$ complexity for $n^D$ training samples, which is much more efficient than previous neural network PGD methods. Extensive experiments for kernel ridge regression, image and surface representation using INRs, and numerical PDEs using PINNs validate the efficiency of SepNN and the effectiveness of SepPGD for alleviating spectral bias.

Token-level attention tuning -- a class of training-free methods including Post-hoc Attention Steering (PASTA) and Attention Calibration (ACT) -- has emerged as a promising approach for improving frozen LLMs via interpretable interventions. However, these methods rely on auxiliary heuristics to identify important task-specific tokens, which can introduce bias and limit applicability when token importance is ambiguous or when optimized kernels make attention maps inaccessible. We propose a simpler alternative: intervening only on the initial token (e.g., <BOS> in LLaMA). We theoretically show that adding lightweight biases to this token’s attention logits systematically shifts and reshapes downstream attention patterns -- an effect amplified by its natural role as an attention sink. Empirically, we find that this tuning can improve LLM performance and better elicit pretrained knowledge, with stronger effects in early layers and distinct scaling preferences across attention heads. Building on these findings, we introduce ZeroTuning, a training-free method that improves LLM performance by applying head-specific attention adjustments to the initial token, requiring no parameter updates. We present two variants: a supervised mode that calibrates on validation examples, and an unsupervised mode that directly minimizes output entropy. ZeroTuning requires no KV-cache or decoding changes and is kernel-agnostic (works with SDPA and FlashAttention). It requires only four lines of modification to standard \texttt{LlamaAttention} code, achieves gains across 15 datasets, and outperforms prior, more complex methods. For example, on Llama-3.1-8B, it yields relative improvements of 19.9% on classification, 4.5% on question answering, and 2.1% on dialogue. ZeroTuning also works out of the box with quantized inference and maintains its improvements as context length increases. Our work provides a lightweight tool for inference-time improvement, advancing both optimization and interpretability. Our code and runnable demo are available at https://anonymous.4open.science/r/ZeroTuning.

Regret matching (RM)---and its modern variants---is a foundational online algorithm that has been at the heart of many AI breakthrough results in solving benchmark zero-sum games, such as poker. Yet, surprisingly little is known so far in theory about its convergence beyond two-player zero-sum games. For example, whether regret matching converges to Nash equilibria in potential games has been an open problem for two decades. Even beyond games, one could try to use RM variants for general constrained optimization problems. Recent empirical evidence suggests that they---particularly regret matching$^+$ (RM$^+$)---attain strong performance on benchmark constrained optimization problems, outperforming traditional gradient descent-type algorithms. We show that alternating RM$^+$ converges to an $\epsilon$-KKT point after $O_\epsilon(1/\epsilon^4)$ iterations, establishing for the first time that it is a sound and fast first-order optimizer. Our argument relates the KKT gap to the accumulated regret, two quantities that are entirely disparate in general but interact in an intriguing way in our setting, so much so that when regrets are bounded, our complexity bound improves all the way to $O_\epsilon(1/\epsilon^2)$. From a technical standpoint, while RM$^+$ does not have the usual one-step improvement property in general, we show that it does in a certain region that the algorithm will quickly reach and remain in thereafter. In sharp contrast, our second main result establishes a lower bound: RM, with or without alternation, can take an exponential number of iterations to reach a crude approximate solution even in two-player potential games. This represents the first worst-case separation between RM and RM$^+$. Our lower bound shows that convergence to coarse correlated equilibria in potential games is exponentially faster than convergence to Nash equilibria.