ICLR 2026 Papers

Accurate prediction of extreme wind velocities has substantial significance in industry, particularly for the operation management of wind power plants. Although the state-of-the-art data-driven models perform well for general meteorological forecasting, they may exhibit large errors for extreme weather—for example, systematically underestimating the magnitudes and short-term variation of extreme winds. To address this issue, we conduct a theoretical analysis of how the data frequency spectrum influences errors in extreme wind prediction. Based on these insights, we propose a novel loss function that incorporates a gradient penalty to mitigate the magnitude shrinkage of extreme weather, and we theoretically justify its effectiveness via a PDE-based energy–enstrophy analysis. To capture more precise short-term wind velocity variations, we design a novel structure of physics-embedded machine learning models with frequency reweighting. Experiments demonstrate that, compared to the baseline models, our approach achieves significant improvements in predicting extreme wind velocities while maintaining robust overall performance.

Reinforcement learning has been central to recent advances in large language model reasoning, but most algorithms rely on on-policy training that demands fresh rollouts at every update, limiting efficiency and scalability. Asynchronous RL systems alleviate this by decoupling rollout generation from training, yet their effectiveness hinges on tolerating large staleness in rollout data, a setting where existing methods either degrade in performance or collapse. We revisit this challenge and uncover a \emph{prosperity-before-collapse} phenomenon: stale data can be as informative as on-policy data if exploited properly. Building on this insight, we introduce M2PO (Second-Moment Trust Proxy Optimization), which constrains the second moment of importance weights to suppress only extreme outliers while preserving informative updates. Notably, M2PO sharply reduces the fraction of clipped tokens under high staleness (from 1.22% to 0.006% over training), precisely masking high-variance tokens while maintaining stable optimization. Extensive evaluation across six model scales (1.7B–32B) and eight reasoning benchmarks shows that M2PO delivers stable off-policy training even with data stale by *at least 256 model updates* and matches on-policy performance.

We construct VisualPRM400K, a dataset comprising about 400K multimodal process supervision data. Building upon this dataset, we develop VisualPRM, an advanced multimodal Process Reward Model (PRM) capable of estimating the value score of each step during the reasoning process. Under the Best-of-N evaluation setting, our model improves the reasoning performance of three types of MLLMs and four different model scales. Even when applied to the highly capable InternVL2.5-78B, it achieves a 5.9-point improvement across seven multimodal reasoning benchmarks. Experimental results show that the PRM model trained on our VisualPRM400K exhibits superior performance compared to Outcome Reward Models and Self-Consistency during BoN evaluation. To further facilitate the development of multimodal PRMs, we construct VisualProcessBench, a benchmark designed to measure the abilities of PRMs and MLLMs to detect incorrect steps in multimodal reasoning tasks. We hope that our work can inspire more future research and contribute to the development of MLLMs. Our model, data, and benchmark will be released.

Neural networks implicitly learn class-specific functional modules. In this work, we ask: Can such modules be isolated and recombined? We introduce a method for training sparse networks that accurately classify only a designated subset of classes while remaining deliberately uncertain on all others, functioning as class-specific subnetworks. A novel KL-divergence-based loss trains only the functional module for the assigned set, and an iterative magnitude pruning procedure removes irrelevant weights. Across multiple datasets (MNIST, FMNIST, tabular data, CIFAR-10) and architectures (MLPs, CNNs, ResNet, VGG), we show that these subnetworks achieve high accuracy on their target classes with minimal leakage to others. When combined via weight summation or logit averaging, these specialized subnetworks act as functional modules of a composite model that often recovers generalist performance. For simpler models and datasets, we experimentally confirm that the resulting modules are mode-connected, which justifies summing their weights. Our approach offers a new pathway toward building modular, composable deep networks with interpretable functional structure.

We introduce DRBench, a benchmark for evaluating AI agents on complex, open-ended deep research tasks in enterprise settings. Unlike prior benchmarks that focus on simple questions or web-only queries, DRBench evaluates agents on multi-step queries (for example, "What changes should we make to our product roadmap to ensure compliance with this standard?") that require identifying supporting facts from both the public web and private company knowledge base. Each task is grounded in realistic user personas and enterprise context, spanning a heterogeneous search space that includes productivity software, cloud file systems, emails, chat conversations, and the open web. Tasks are generated through a carefully designed synthesis pipeline with human-in-the-loop verification, and agents are evaluated on their ability to recall relevant insights, maintain factual accuracy, and produce coherent, well-structured reports. We release 100 deep research tasks across 10 domains, such as Sales, Cybersecurity, and Compliance. We demonstrate the effectiveness of DRBench by evaluating diverse DR agents across open- and closed-source models (such as GPT, Llama, and Qwen) and DR strategies, highlighting their strengths, weaknesses, and the critical path for advancing enterprise deep research.

Automating the formalization of mathematical statements for theorem proving remains a major challenge for Large Language Models (LLMs). LLMs struggle to identify and utilize the prerequisite mathematical knowledge and its corresponding formal representation in languages like Lean. Current retrieval-augmented autoformalization methods query external libraries using the informal statement directly, but overlook a fundamental limitation: informal mathematical statements are often complex and offer limited context on the underlying math concepts. To address this, we introduce DRIFT, a novel framework that enables LLMs to decompose informal mathematical statements into smaller, more tractable ``sub-components''. This facilitates targeted retrieval of premises from mathematical libraries such as Mathlib. Additionally, DRIFT retrieves illustrative theorems to help models use premises more effectively in formalization tasks. We evaluate DRIFT across diverse benchmarks (ProofNet, ConNF, and MiniF2F-test) and find that it consistently improves premise retrieval, nearly doubling the F1 score compared to the DPR baseline on ProofNet. Notably, DRIFT demonstrates strong performance on the out-of-distribution ConNF benchmark, with BEq+@10 improvements of 42.25\% and 37.14\% using GPT-4.1 and DeepSeek-V3.1, respectively. Our analysis shows that retrieval effectiveness in mathematical autoformalization depends heavily on model-specific knowledge boundaries, highlighting the need for adaptive retrieval strategies aligned with each model’s capabilities.

Decoding visual representations from brain signals has attracted significant attention in both neuroscience and artificial intelligence. However, the degree to which brain signals truly encode visual information remains unclear. Current visual decoding approaches explore various brain–image alignment strategies, yet most emphasize high-level semantic features while neglecting pixel-level details, thereby limiting our understanding of the human visual system. In this paper, we propose a brain–image alignment strategy that leverages multiple pre-trained visual encoders with distinct inductive biases to capture hierarchical and multiscale visual representations, while employing a contrastive learning objective to achieve effective alignment between brain signals and visual embeddings. Furthermore, we introduce a Fusion Prior, which learns a stable mapping on large-scale visual data and subsequently matches brain features to this pre-trained prior, thereby enhancing distributional consistency across modalities. Extensive quantitative and qualitative experiments demonstrate that our method achieves a favorable balance between retrieval accuracy and reconstruction fidelity.

Model-based methods for offline Reinforcement Learning transfer extensive policy exploration and evaluation to data-driven dynamics models, effectively saving real-world samples in the offline setting. We expect the dynamics model to allow the policy to roll out full-horizon episodes, which is crucial for ensuring sufficient exploration and reliable evaluation. However, many previous dynamics models exhibit limited capability in long-horizon prediction. This work follows the paradigm of the Any-step Dynamics Model (ADM) that improves future predictions by reducing bootstrapping prediction to direct prediction. We structurally decouple each recurrent forward of the RNN cell from the backtracked state and propose the second version of ADM (ADM-v2), making the direct prediction more flexible. ADM-v2 not only enhances the accuracy of direct predictions for making full-horizon roll-outs but also supports parallel estimation of the any-step prediction uncertainty to improve efficiency. The results on DOPE validate the reliability of ADM-v2 for policy evaluation. Moreover, via full-horizon roll-out, ADM-v2 for policy optimization enables substantial advancements, whereas other dynamics models degrade due to long-horizon error accumulation. We are the first to achieve SOTA under the full-horizon roll-out setting on both D4RL and NeoRL.

All-in-one image restoration (IR) aims to recover high-quality images from diverse degradations, which in real-world settings are often mixed and unknown. Unlike single-task IR, this problem requires a model to approximate a family of heterogeneous inverse functions, making it fundamentally more challenging and practically important. Although recent focus has shifted toward large multimodal models, their robustness still depends on faithful low-level inputs, and the principles that govern effective restoration remain underexplored. We revisit attention mechanisms through the lens of all-in-one IR and identify two overlooked bottlenecks in widely adopted Restormer-style backbones: \textit{(i) the value path remains purely linear}, restricting outputs to the span of inputs and weakening expressivity, and \textit{(ii) the absence of an explicit global slot} prevents attention from encoding degradation context. To address these issues, we propose two minimal, backbone-agnostic primitives: a nonlinear value transform that upgrades attention from a selector to a selector–transformer, and a global spatial token that provides an explicit degradation-aware slot. Together, these additions improve restoration across synthetic, mixed, underwater, and medical benchmarks, with negligible overhead and consistent performance gains. Analyses with foundation model embeddings, spectral statistics, and separability measures further clarify their roles, positioning our study as a step toward rethinking attention primitives for robust all-in-one IR.

Using Large Language Models to produce intermediate thoughts, a.k.a. Chain-of-thought (CoT), before providing an answer has been a successful recipe for solving complex language tasks. In robotics, similar embodied CoT strategies, generating thoughts before actions, have also been shown to lead to improved performance when using Vision-Language-Action models (VLAs). As these techniques increase the length of the model's generated outputs to include the thoughts, the inference time is negatively affected. Delaying an agent's actions in real-world executions, as in robotic manipulation settings, strongly affects the usability of a method, as tasks require long sequences of actions. However, is the generation of long chains-of-thought a strong prerequisite for achieving performance improvements? In this work, we explore the idea of Hybrid Training (HyT), a framework that enables VLAs to learn from thoughts and benefit from the associated performance gains, while enabling the possibility to leave out CoT generation during inference. Furthermore, by learning to conditionally predict a diverse set of outputs, HyT supports flexibility at inference time, enabling the model to either predict actions directly, generate thoughts or follow instructions. We evaluate the proposed method in a series of simulated benchmarks and real-world experiments.

Streaming video generation as one fundamental component in interactive world models and neural game engines aims to generate high-quality, low-latency, and temporally coherent long stream videos. However, most existing work suffers from severe error accumulation that often significantly degrades the generated stream videos over long horizons. We design Rolling Forcing, a novel video generation technique that enables streaming long videos with minimal error accumulation. Rolling Forcing comes with three novel designs. First, instead of iteratively sampling individual frames which accelerates error propagation, we design a joint denoising scheme that simultaneously denoises multiple frames with progressively increasing noise levels. This design relaxes the strict causality across adjacent frames, effectively suppressing error growth. Second, we introduce the attention sink mechanism into the long-horizon stream video generation task, which allows the model to keep key–value states of initial frames as a global context anchor and thereby enhances long-term global consistency. Third, we design an efficient training algorithm that enables few-step distillation over largely extended denoising windows. This algorithm operates on non-overlapping windows and mitigates exposure bias conditioned on self-generated histories. Extensive experiments show that Rolling Forcing enables real-time streaming generation of multi-minute videos on a single GPU, with substantially reduced error accumulation.

Imputing missing values in multivariate time series remains challenging, especially under diverse missing patterns and heavy missingness. Existing methods suffer from suboptimal performance as corrupted temporal features hinder effective cross-variable information transfer, amplifying reconstruction errors. Robust imputation requires both extracting temporal patterns from sparse observations within each variable and selectively transferring information across variables—yet current approaches excel at one while compromising the other. We introduce T1 (Time series imputation with 1-to-1 channel-head binding), a CNN-Transformer hybrid architecture that achieves robust imputation through Channel-Head Binding—a mechanism creating one-to-one correspondence between CNN channels and attention heads. This design enables selective information transfer: when missingness corrupts certain temporal patterns, their corresponding attention pathways adaptively down-weight based on remaining observable patterns while preserving reliable cross-variable connections through unaffected channels. Experiments on 11 benchmark datasets demonstrate that T1 achieves state-of-the-art performance, reducing MSE by 46% on average compared to the second-best baseline, with particularly strong gains under extreme sparsity (70% missing ratio). The model generalizes to unseen missing patterns without retraining and uses a consistent hyperparameter configuration across all datasets. The code is available at https://github.com/Oppenheimerdinger/T1.

Accurately modeling long-range dependencies in graph-structured data is critical for many real-world applications. However, incorporating long-range interactions beyond the nodes' immediate neighborhood in a $\textit{scalable}$ manner remains an open challenge for graph machine learning models. Existing benchmarks for evaluating long-range capabilities either cannot $\textit{guarantee}$ that their tasks actually depend on long-range information or are rather limited. Therefore, claims of long-range modeling improvements based on said performance remain questionable. We introduce the Long-Range Ising Model Graph Benchmark, a physics-based benchmark utilizing the well-studied Ising model whose ground truth $\textit{provably}$ depends on long-range dependencies. Our benchmark consists of ten datasets that scale from 256 to 65k nodes per graph, and provide controllable long-range dependencies through tunable parameters, allowing precise control over the hardness and ``long-rangedness". We provide model-agnostic evidence that local information is insufficient, further validating the design choices of our benchmark. Via experiments on classical message-passing architectures and graph transformers, we show that both perform far from the optimum, especially those with scalable complexity. Our goal is that our benchmark will foster the development of scalable methodologies that effectively model long-range interactions in graphs.

Counting properties (e.g. determining whether certain tokens occur more than other tokens in a given input text) have played a significant role in the study of expressiveness of transformers. In this paper, we provide a formal framework for investigating the counting power of transformers. We argue that all existing results demonstrate transformers' expressivity only for (semi-)linear counting properties, i.e., which are expressible as a boolean combination of linear inequalities. Our main result is that transformers can express counting properties that are highly nonlinear. More precisely, we prove that transformers can capture all semialgebraic counting properties, i.e., expressible as a boolean combination of arbitrary multivariate polynomials (of any degree). Among others, these generalize the counting properties that can be captured by support vector machines via polynomial kernel in the vector space model. To complement this result, we exhibit a natural subclass of (softmax) transformers that completely characterizes semialgebraic counting properties. Through connections with the Hilbert's tenth problem, this expressivity of transformers also yields a new undecidability result for analyzing an extremely simple transformer model --- surprisingly with neither positional encodings (i.e. NoPE-transformers) nor masking. We also experimentally validate trainability of such counting properties.

This work presents the Large Depth Completion Model (LDCM), a simple, effective, and robust framework for single-view metric depth estimation with sparse observations. Without relying on complex architectural designs, LDCM generates metric-accurate dense depth maps in one large transformer. It outperforms existing approaches across diverse datasets and sparse observations. We achieve this from two key perspectives: (1) maximizing the potential of existing monocular foundation models to improve sparse observations preprocessing, and (2) reformulating training objectives to better capture geometric structure and metric consistency. Specifically, a Poisson-based depth initialization module is firstly introduced to generate a uniform coarse dense depth map from diverse sparse observations, which serves as a strong structural prior for the network. Regarding the training objective, we replace the conventional depth head with a point map head that regresses per-pixel 3D coordinates in camera space, enabling the model to directly learn the underlying 3D scene structure instead of performing pixel-wise depth map restoration. Moreover, this design eliminates the need for camera intrinsic parameters, allowing LDCM to naturally produce metric-scaled 3D point maps. Extensive experiments demonstrate that LDCM consistently outperforms state-of-the-art methods across multiple benchmarks and varying sparsity priors in both depth completion and point map estimation, showcasing its effectiveness and strong generalization to unseen data distributions.

Simultaneously achieving robust classification and high-fidelity generative modeling within a single framework presents a significant challenge. Hybrid approaches, such as Joint Energy-Based Models (JEM), interpret classifiers as EBMs but are often limited by the instability and poor sample quality inherent in training based on Stochastic Gradient Langevin Dynamics (SGLD). We address these limitations by proposing a novel training framework that integrates adversarial training (AT) principles for both discriminative robustness and stable generative learning. The proposed method introduces three key innovations: (1) the replacement of SGLD-based JEM learning with a stable, AT-based approach that optimizes the energy function through a Binary Cross-Entropy (BCE) loss that discriminates between real data and contrastive samples generated via Projected Gradient Descent (PGD); (2) adversarial training for the discriminative component that enhances classification robustness while implicitly providing the gradient regularization needed for stable EBM training; and (3) a two-stage training strategy that addresses normalization-related instabilities and enables leveraging pretrained robust classifiers, generalizing effectively across diverse architectures. Experiments on CIFAR-10/100 and ImageNet demonstrate that our approach: (1) is the first EBM-based hybrid to scale to high-resolution datasets with high training stability, simultaneously achieving state-of-the-art discriminative and generative performance on ImageNet 256$\times$256; (2) uniquely combines generative quality with adversarial robustness, enabling faithful counterfactual explanations; and (3) functions as a competitive standalone generative model, matching the generative quality of autoregressive methods (VAR-d16) and surpassing diffusion models while offering unique versatility. Code is available at https://github.com/xuwangyin/DAT.

Activation sparsity is an intriguing property of deep neural networks that has been extensively studied in ReLU-based models, due to its advantages for efficiency, robustness, and interpretability. However, methods relying on exact zero activations do not directly apply to modern Large Language Models (LLMs), leading to fragmented, model-specific strategies for LLM activation sparsity and a gap in its general understanding. In this work, we introduce a general framework for evaluating sparsity robustness in contemporary LLMs and conduct a systematic investigation of this phenomenon in their feedforward~(FFN) layers. Our results uncover universal properties of activation sparsity across diverse model families and scales. Importantly, we observe that the potential for effective activation sparsity grows with model size, highlighting its increasing relevance as models scale. Furthermore, we present the first study of activation sparsity in diffusion-based LLMs. Overall, our work provides a comprehensive perspective and practical guidance for harnessing activation sparsity in LLM design and acceleration.

Aligning large generative models with human feedback is a critical challenge. In speech synthesis, this is particularly pronounced due to the lack of a large-scale human preference dataset, which hinders the development of models that truly align with human perception. To address this, we introduce ***SpeechJudge***, a comprehensive suite comprising a dataset, a benchmark, and a reward model centered on naturalness—one of the most fundamental subjective metrics for speech synthesis. First, we present ***SpeechJudge-Data***, a large-scale human feedback corpus of 99k speech pairs. The dataset is constructed using a diverse set of advanced zero-shot text-to-speech (TTS) models across diverse speech styles and multiple languages, with human annotations for both intelligibility and naturalness preference. From this, we establish ***SpeechJudge-Eval***, a challenging benchmark for speech naturalness judgment. Our evaluation reveals that existing metrics and AudioLLMs struggle with this task; the best-performing model, Gemini-2.5-Flash, achieves less than 70% agreement with human judgment, highlighting a significant gap for improvement. To bridge this gap, we develop ***SpeechJudge-GRM***, a generative reward model (GRM) based on Qwen2.5-Omni-7B. It is trained on SpeechJudge-Data via a two-stage post-training process: Supervised Fine-Tuning (SFT) with Chain-of-Thought rationales followed by Reinforcement Learning (RL) with GRPO on challenging cases. On the SpeechJudge-Eval benchmark, the proposed SpeechJudge-GRM demonstrates superior performance, achieving 77.2% accuracy (and 79.4% after inference-time scaling @10) compared to a classic Bradley-Terry reward model (72.7%). Furthermore, SpeechJudge-GRM can be also employed as a reward function during the post-training of speech generation models to facilitate their alignment with human preferences.

Fine-grained time series data with high temporal resolution is critical for accurate analytics across a wide range of applications. However, the acquisition of such data is often limited by cost and feasibility. This problem can be tackled by reconstructing high-resolution signals from low-resolution inputs based on specific priors, known as super-resolution. While extensively studied in computer vision, directly transferring image super-resolution techniques to time series is not trivial. To address this challenge at a fundamental level, we propose **S**uper-**R**esolution for **T**ime series (SRT), a novel framework that reconstructs temporal patterns lost in low-resolution inputs via disentangled rectified flow. SRT decomposes the input into trend and seasonal components, aligns them to the target resolution using an implicit neural representation, and leverages a novel cross-resolution attention mechanism to guide the generation of high-resolution details. We further introduce SRT-large, a scaled-up version with extensive pretraining, which enables strong zero-shot super-resolution capability. Extensive experiments on nine public datasets demonstrate that SRT and SRT-large consistently outperform existing methods across multiple scale factors, showing both robust performance and the effectiveness of each component in our architecture.