ICLR 2026 Papers

Understanding generalization in overparameterized neural networks hinges on the interplay between the data geometry, neural architecture, and training dynamics. In this paper, we theoretically explore how data geometry controls this implicit bias. This paper presents theoretical results for overparametrized two-layer ReLU networks trained *below the edge of stability*. First, for data distributions supported on a mixture of low-dimensional balls, we derive generalization bounds that provably adapt to the intrinsic dimension. Second, for a family of isotropic distributions that vary in how strongly probability mass concentrates toward the unit sphere, we derive a spectrum of bounds showing that rates deteriorate as the mass concentrates toward the sphere. These results instantiate a unifying principle: When the data is harder to “shatter” with respect to the activation thresholds of the ReLU neurons, gradient descent tends to learn representations that capture shared patterns and thus finds solutions that generalize well. On the other hand, for data that is easily shattered (e.g., data supported on the sphere) gradient descent favors memorization. Our theoretical results consolidate disparate empirical findings that have appeared in the literature.

The merit of Conformal Prediction (CP), as a distribution-free framework for uncertainty quantification, depends on generating prediction sets that are efficient, reflected in small average set sizes, while adaptive, meaning they signal uncertainty by varying in size according to input difficulty. A central limitation for deep conformal classifiers is that the nonconformity scores are derived from softmax outputs, which can be unreliable indicators of how certain the model truly is about a given input, sometimes leading to overconfident misclassifications or undue hesitation. In this work, we argue that this unreliability can be inherited by the prediction sets generated by CP, limiting their capacity for adaptiveness. We propose a new approach that leverages information from the pre-softmax logit space, using the Helmholtz Free Energy as a measure of model uncertainty and sample difficulty. By reweighting nonconformity scores with a monotonic transformation of the energy score of each sample, we improve their sensitivity to input difficulty. Our experiments with four state-of-the-art score functions on multiple datasets and deep architectures show that this energy-based enhancement improves the adaptiveness of the prediction sets, leading to a notable increase in both efficiency and adaptiveness compared to baseline nonconformity scores, without introducing any post-hoc complexity.

Radiance fields have been successful in reconstructing 3D assets for scenes presented in Virtual Reality and Augmented Reality (VR/AR). The general workflow of scanning objects with radiance field representation involves a heavy workload of capturing images depicting the object empirically by the user, and lacks feedback for the image collection stage. This would lead to potential repeated or deficient gathering of information, affecting the efficiency of the reconstruction workflow. In this paper, we therefore present an active learning algorithm for 3D Gaussian Splatting that guides the image capturing by estimating the pose of the most informative image. Specifically, our method first partitions the consistent regions in the model by analyzing the Gaussian attributes and visibility features. Then, we determine the informative region to explore by estimating the semantic feature variance of each Gaussian, which evaluates the quality of the Gaussian cloud from the semantic level features. Furthermore, we tackle the practical problem of noise in the pose of the collected image via a robust pose optimization method. Extensive experimental results on both synthetic and real-world scenes demonstrate the remarkable performance of our algorithm in active learning of the radiance field under both accurate and noisy pose conditions.

Achieving generalization in robotic manipulation remains a critical challenge, particularly for unseen scenarios and novel tasks. Current Vision-Language-Action (VLA) models, while building on top of general Vision-Language Models (VLMs), still fall short of achieving robust zero-shot performance due to the scarcity and heterogeneity prevalent in embodied datasets. To address these limitations, we propose FSD (From Seeing to Doing), a novel vision-language model that generates intermediate representations through spatial relationship reasoning, providing fine-grained guidance for robotic manipulation. Our approach combines a hierarchical data construction pipeline for training with a self-consistency mechanism that aligns spatial coordinates with visual signals. Through extensive experiments, we comprehensively validated FSD’s capabilities in both “seeing” and “doing”, achieving outstanding performance across 8 benchmarks for general spatial reasoning and embodied reference abilities, as well as on our proposed more challenging benchmark VABench. We also verified zero-shot capabilities in robot manipulation, demonstrating significant performance improvements over baseline methods in both SimplerEnv and real robot settings. Experimental results show that FSD achieves 40.6% success rate in SimplerEnv and 72% success rate across 8 real-world tasks, outperforming the strongest baseline by 30%.

Multi-view clustering seeks to exploit complementary information across different views to enhance clustering performance, where both semantic and structural information are crucial. However, existing approaches often bias toward one type of information while treating the other as auxiliary, overlooking that the reliability of these signals may vary across datasets and that semantic and structural cues can provide complementary and parallel guidance. As a result, such methods may face limitations in generalization and suboptimal clustering performance. To address these issues, we propose a novel method, Dual-branch Representations with dynamic gatEd fusion and triple-grAnularity alignMent (DREAM), for deep multi-view clustering. Specifically, DREAM disentangles semantic information via a Variational Autoencoder (VAE) branch, while simultaneously captures structure-aware features through a Graph Convolutional Network (GCN) branch. The resulting representations are dynamically integrated using a gated fusion module that leverages structural cues as complementary guidance, adaptively balancing semantic and structural contributions to produce clustering-oriented latent embeddings. To further improve robustness and discriminability, we introduce a triple-granularity feature alignment mechanism that enforces consistency across views, within individual samples, and intra-cluster, thereby preserving semantic-structural coherence while enhancing inter-cluster separability. Extensive experiments on benchmark datasets demonstrate that DREAM significantly outperforms SOTA approaches, highlighting the effectiveness of disentangled dual-branch encoding, adaptive gated fusion, and triple-granularity feature alignment.

Tensor-based incomplete multi-view clustering has attracted significant research attention due to its capability to exploit high-order correlations across different views for revealing underlying cluster structures from partially observed multi-view data. However, most existing approaches construct tensors from adjacency matrices, which necessitate post-processing operations (e.g., singular value decomposition, SVD) and thereby introduce additional computational overhead and potential errors. Some approaches instead employ latent embedding tensors to avoid post-processing, but they often fail to capture the geometric structure of the underlying graph. To address these limitations, we propose **C**onst**A**nt degree **M**trix-driv**E**n incomp**L**ete multi-view clustering via connectivity-structure and embedding tensor learning (**CAMEL**). Specifically, CAMEL jointly learns view-specific latent embeddings under structured constraints and organizes them into a tensor with an ${\ell_{\delta}}$ low-rank constraint, thereby enabling coordinated optimization of graph connectivity and high-order correlations. To further mitigate the $\mathcal{O}(n^2)$ or ever higher complexity complexity associated with conventional connectivity constraints, CAMEL approximates the variable Laplacian degree matrix with a constant-degree matrix, reducing the computational cost to $\mathcal{O}(1)$. Clustering assignments are subsequently derived via $k$-means on the concatenated embeddings, eliminating the need for post-processing operations on adjacency matrices such as SVD. Extensive experiments on nine benchmark datasets demonstrate the superior effectiveness and efficiency of CAMEL.

Implicit neural representations (INRs) have recently emerged as a powerful paradigm for modeling data, offering a continuous alternative to traditional discrete signal representations. Their ability to compactly encode complex signals has led to strong performance across a wide range of computer vision tasks. In previous studies, it has been repeatedly shown that INR performance has a strong correlation with the activation functions used in its multilayer perceptrons. Although numerous competitive activation functions for INRs have been proposed, the theoretical foundations underlying their effectiveness remain poorly understood. Moreover, key challenges persist, including spectral bias (the reduced sensitivity to high-frequency signal content), limited robustness to noise, and difficulties in jointly capturing both local and global features. In this paper, we explore the underlying mechanism of INR signal representation, leveraging harmonic analysis and Chebyshev Polynomials. Through a rigorous mathematical proof, we show that modulating activation functions using a complex sinusoidal term yields better and complete spectral support throughout the INR network. To support our theoretical framework, we present empirical results over a wide range of experiments using Chebyshev analysis. We further develop a new activation function, leveraging the new theoretical findings to highlight its feasibility in INRs. We also incorporate a regularized deep prior, extracted from the signal via a task-specific model, to adjust the activation functions. This integration further improves convergence speed and stability across tasks. Through a series of experiments which include image reconstruction (with an average PSNR improvement of +5.67 dB over the nearest counterpart across a diverse image dataset), denoising (with a +0.46 dB increase in PSNR), super-resolution (with a +0.64 dB improvement over the nearest State-Of-The-Art (SOTA) method for 6X super-resolution), inpainting, and 3D shape reconstruction we demonstrate the novel proposed activation over existing state of the art activation functions.

Vision Transformers have emerged as powerful, scalable and versatile representation learners. To capture both global and local features, a learnable [CLS] class token is typically prepended to the input sequence of patch tokens. Despite their distinct nature, both token types are processed identically throughout the model. In this work, we investigate the friction between global and local feature learning under different pre-training strategies by analyzing the interactions between class and patch tokens. Our analysis reveals that standard normalization layers introduce an implicit differentiation between these token types. Building on this insight, we propose specialized processing paths that selectively disentangle the computational flow of class and patch tokens, particularly within normalization layers and early query-key-value projections. This targeted specialization leads to significantly improved patch representation quality for dense prediction tasks. Our experiments demonstrate segmentation performance gains of over 2 mIoU points on standard benchmarks, while maintaining strong classification accuracy. The proposed modifications introduce only an 8\% increase in parameters, with no additional computational overhead. Through comprehensive ablations, we provide insights into which architectural components benefit most from specialization and how our approach generalizes across model scales and learning frameworks.

We examine gradient descent in matrix factorization and show that under large step sizes the parameter space develops a fractal structure. We derive the exact critical step size for convergence in scalar-vector factorization and show that near criticality the selected minimizer depends sensitively on the initialization. Moreover, we show that adding regularization amplifies this sensitivity, generating a fractal boundary between initializations that converge and those that diverge. The analysis extends to general matrix factorization with orthogonal initialization. Our findings reveal that near-critical step sizes induce a chaotic regime of gradient descent where the training outcome is unpredictable and there are no simple implicit biases, such as towards balancedness, minimum norm, or flatness.

Graph Neural Networks (GNNs) have demonstrated both empirical efficiency and universal expressivity for solving constrained optimization problems such as linear and quadratic programming. However, extending this paradigm to more general convex problems with universality guarantees, particularly Second-Order Cone Programs (SOCPs), remains largely unexplored. We address this challenge by proposing a novel graph representation that captures the inherent structure of conic constraints. We then establish a key universality theorem: *there exist GNNs that can provably approximate essential SOCP properties, including instance feasibility and optimal solutions*. We further derive the sample complexity for GNN generalization based on Rademacher complexity, filling an important gap for Weisfeiler-Lehman-based GNNs in learning-to-optimize paradigms. Our results provide a rigorous foundation linking GNN expressivity and generalization power to conic optimization structure, opening new avenues for scalable, data-driven SOCP solvers. The approach extends naturally to $p$-order cone programming for any $p \geq 1$ while preserving universal expressivity and requiring no structural modifications to the GNN architecture. Numerical experiments on randomly generated SOCPs and real-world power grid problems demonstrate the effectiveness of our approach, achieving superior prediction accuracy with significantly fewer parameters than fully connected neural networks.

Generative models, particularly diffusion and flow-matching approaches, have achieved remarkable success across diverse domains, including image synthesis and robotic planning. However, a fundamental challenge persists: ensuring generated samples strictly satisfy problem-specific constraints — a crucial requirement for physics-informed problems, safety-critical applications, watermark embedding, etc. Existing approaches, such as mirror maps and reflection methods, either have limited applicable constraint sets or introduce significant computational overhead. In this paper, we develop gauge flow matching (GFM), a simple yet efficient framework for constrained generative modeling. Our GFM approach introduces a generalized bijective gauge mapping to transform generation over arbitrary compact convex sets into an equivalent process over the unit ball, which allows low-complexity feasibility-ensuring operations such as reflection. The generated samples are then mapped back to the original domain for output. We prove that our GFM framework guarantees strict constraint satisfaction, with low generation complexity and bounded distribution approximation errors. We further extend our GFM framework to two popular non-convex settings, namely, star-convex and geodesic-convex sets. Extensive experiments show that GFM outperforms existing methods in generation speed and quality across multiple benchmarks.

When training large-scale models, the performance typically scales with the number of parameters and the dataset size according to a slow power law. A fundamental theoretical and practical question is whether comparable performance can be achieved with significantly smaller models and substantially less data. In this work, we provide a positive and constructive answer. We prove that a generic permutation-invariant function of $d$ objects can be asymptotically compressed into a function of $\operatorname{polylog} d$ objects with vanishing error. This theorem yields two key implications: (Ia) a large neural network can be compressed to polylogarithmic width while preserving its learning dynamics; (Ib) a large dataset can be compressed to polylogarithmic size while leaving the loss landscape of the corresponding model unchanged. (Ia) directly establishes a proof of the \textit{dynamical} lottery ticket hypothesis, which states that any ordinary network can be strongly compressed such that the learning dynamics and result remain unchanged. (Ib) shows that a neural scaling law of the form $L\sim d^{-\alpha}$ can be boosted to an arbitrarily fast power law decay, and ultimately to $\exp(-\alpha' \sqrt[m]{d})$.

The open set recognition (OSR) problem aims to identify test samples from novel semantic classes that are not part of the training classes, a task that is crucial in many practical scenarios. However, the existing OSR methods use a constant scaling factor (the temperature) to the logits before applying a loss function, which hinders the model from exploring both ends of the spectrum in representation learning -- from instance-level to clas-specific features. In this paper, we address this problem by enabling temperature-modulated representation learning using a set of proposed temperature schedules, including our novel negative cosine schedule. Our temperature schedules allow the model to form a coarse decision boundary at the beginning of training by focusing on fewer neighbors, and gradually prioritizes more neighbors to smooth out the rough edges. This gradual task switching leads to a richer and more generalizable representation space. While other OSR methods benefit by including regularization or auxiliary negative samples, such as with mix-up, thereby adding a significant computational overhead, our schedules can be folded into any existing OSR loss function with no overhead. We implement the novel schedule on top of a number of baselines, using cross-entropy, contrastive and the ARPL loss functions and find that it boosts both the OSR and the closed set performance in most cases, especially on the tougher semantic shift benchmarks.

Score-based methods are powerful across machine learning, but they face a paradox: theoretically path-independent, yet practically path-dependent. We resolve this by proving that practical training objectives differ from the ideal, ground-truth objective by a crucial, overlooked term: the path variance of the score function. We propose the MinPV (**Min**imum **P**ath **V**ariance) Principle to minimize this path variance. Our key contribution is deriving a closed-form expression for the variance, making optimization tractable. By parameterizing the path with a flexible Kumaraswamy Mixture Model, our method learns data-adaptive, low-variance paths without heuristic manual selection. This principled optimization of the complete objective yields more accurate and stable estimators, establishing new state-of-the-art results on challenging benchmarks and providing a general framework for optimizing score-based interpolation.

Spiking Neural Networks (SNNs) have emerged as an efficient neuromorphic computing paradigm, offering low energy consumption and strong representational capacity through binary spike-based information processing. However, their performance is heavily shaped by the input encoding method. While direct encoding has gained traction for its efficiency and accuracy, it proves less robust than traditional rate encoding. To illuminate this issue, we introduce Gradient Temporal Collinearity (GTC), a principled measure that quantifies the directional alignment of gradient components across time steps, and we show—both empirically and theoretically—that elevated GTC in direct encoding undermines robustness. Guided by this insight, we propose Structured Temporal Orthogonal Decorrelation (STOD), which integrates parametric orthogonal kernels with structured constraints into the input layer of direct encoding to diversify temporal features and effectively reduce GTC. Extensive experiments on visual classification benchmarks, show that STOD consistently outperforms state-of-the-art methods in robustness, highlighting its potential to drive SNNs toward safer and more reliable deployment.

We investigate the label noise problem in supervised binary classification settings and resurface the underutilized instance-_only_ dependent noise model through loss correction. On the one hand, based on risk equivalence, the instance-aware loss correction scheme completes the bridge from _empirical noisy risk minimization_ to _true clean risk minimization_ provided the base loss is classification calibrated (e.g., cross-entropy). On the other hand, the instance-only dependent modeling of the label noise at the core of the correction enables us to estimate a single value per instance instead of a matrix. Furthermore, the estimation of the transition rates becomes a very flexible process, for which we offer several computationally efficient ways. Empirical findings over different dataset domains (image, audio, tabular) with different learners (neural networks, gradient-boosted machines) validate the promised generalization ability of the method.

Unsupervised representation learning, particularly sequential disentanglement, aims to separate static and dynamic factors of variation in data without relying on labels. This remains a challenging problem, as existing approaches based on variational autoencoders and generative adversarial networks often rely on multiple loss terms, complicating the optimization process. Furthermore, sequential disentanglement methods face challenges when applied to real-world data, and there is currently no established evaluation protocol for assessing their performance in such settings. Recently, diffusion models have emerged as state-of-the-art generative models, but no theoretical formalization exists for their application to sequential disentanglement. In this work, we introduce the Diffusion Sequential Disentanglement Autoencoder (DiffSDA), a novel, modal-agnostic framework effective across diverse real-world data modalities, including time series, video, and audio. DiffSDA leverages a new probabilistic modeling, latent diffusion, and efficient samplers, while incorporating a challenging evaluation protocol for rigorous testing. Our experiments on diverse real-world benchmarks demonstrate that DiffSDA outperforms recent state-of-the-art methods in sequential disentanglement.

Brain tumor segmentation in multi-modal MRIs poses significant challenges when one or more modalities are missing. Recent approaches commonly employ parallel fusion strategies; however, these methods often risk losing crucial shared information across modalities, which can degrade segmentation performance. In this paper, we advocate leveraging sequential information bottleneck fusion to effectively preserve shared information across modalities. From an information-theoretic perspective, sequential fusion not only produces more robust fused representations in missing-data scenarios but also achieves a tighter generalization upper bound compared to parallel fusion approaches. Building on this principle, we propose the Sequential Multi-modal Segmentation Network (SMSN), which integrates an Information-Bottleneck Fusion Module (IBFM). The IBFM sequentially extracts modality-common features while reconstructing modality-specific features through a dedicated feature extraction module. Extensive experiments on the BRATS18 and BRATS20 glioma datasets demonstrate that SMSN consistently outperforms traditional parallel fusion-based baselines, achieving exceptional robustness in diverse missing-modality settings. Furthermore, SMSN exhibits superior cross-domain generalization, as evidenced by its ability to transfer a trained model from BRATS20 to a brain metastasis dataset without fine-tuning. To ensure reproducibility, the code of the SMSN is provided in the supplementary file.

Positive-Unlabeled (PU) learning, a challenging paradigm for training binary classifiers from only positive and unlabeled samples, is fundamental to many applications. While numerous PU learning methods have been proposed, the research is systematically hindered by the lack of a standardized and comprehensive benchmark for rigorous evaluation. Inconsistent data generation, disparate experimental settings, and divergent metrics have led to irreproducible findings and unsubstantiated performance claims. To address this foundational challenge, we introduce **PU-Bench**, the first unified open-source benchmark for PU learning. PU-Bench provides: 1) a unified data generation pipeline to ensure consistent input across configurable sampling schemes, label ratios and labeling mechanisms; 2) an integrated framework of 18 state-of-the-art PU methods; and 3) standardized protocols for reproducible assessment. Through a large-scale empirical study on 8 diverse datasets (**2880** evaluations in total), PU-Bench reveals a complex yet intuitive performance landscape, uncovering critical trade-offs between effectiveness and efficiency, and systematically mapping method robustness against variations in label frequency and selection bias. It is anticipated to serve as a foundational resource to catalyze reproducible, rigorous, and impactful research in the PU learning community. The source code is publicly available at <https://github.com/XiXiphus/PU-Bench>.