ICML 2026 Papers

Large language models (LLMs) have demonstrated significant potential in formal theorem proving, yet state-of-the-art performance often necessitates prohibitive test-time compute via massive roll-outs or extended context windows. In this work, we address this scalability bottleneck by exploiting an informative structure in formal verification: the observation that compilers map a vast space of diverse proof attempts to a compact set of structured failure modes. We introduce a learning-to-refine framework that leverages this compression to perform efficient learning and proof exploration. We perform tree search that corrects errors locally conditioned on explicit verifier feedback, thereby circumventing the costs associated with accumulating a long history of proof attempts. Extensive evaluations show that our method consistently amplifies the reasoning capabilities of base provers across varying scales. Notably, our approach achieves state-of-the-art performance on PutnamBench among publicly reported $\sim$8B and $\sim$32B parameter models under comparable test-time budgets, offering a scalable paradigm for next-generation verifier-guided reasoning.

Advanced autoregressive (AR) video generation models have improved visual fidelity and interactivity, but the quadratic complexity of attention remains a primary bottleneck for efficient deployment. While existing sparse attention solutions have shown promise on bidirectional models, we identify that applying these solutions to AR models leads to considerable performance degradation for two reasons: isolated consideration of chunk generation and insufficient utilization of past informative context. Motivated by these observations, we propose \textsc{Light Forcing}, the \textit{first} sparse attention solution tailored for AR video generation models. It incorporates a \textit{Chunk-Aware Growth} mechanism to quantitatively estimate the contribution of each chunk, which determines their sparsity allocation. This progressive sparsity increase strategy enables the current chunk to inherit prior knowledge in earlier chunks during generation. Additionally, we introduce a \textit{Hierarchical Sparse Attention} to capture informative historical and local context in a coarse-to-fine manner. Such two-level mask selection strategy (i.e., frame and block level) can adaptively handle diverse attention patterns. Extensive experiments demonstrate that our method outperforms existing sparse attention in quality (e.g., 84.5 on VBench) and efficiency (e.g., $1.2{\sim}1.3\times$ end-to-end speedup). Combined with other efficient solutions, \textsc{Light Forcing} further achieves a $2.0{\sim}3.0\times$ end-to-end speedup across diverse GPUs (e.g., 27.4\,FPS on RTX 5090 and 33.9\,FPS on H100). Code is released via this \href{https://github.com/chengtao-lv/LightForcing}{link}.

Differentiable approaches to causal discovery have shown promise in learning DAG structures via continuous optimization, but their theoretical guarantees are largely restricted to models with homoscedastic noise or known noise distribution. In particular, existing methods based on mean squared error fail to identify the true DAG when noise distributions are non-Gaussian and vary in scale. In this paper, we address this gap in nonlinear additive noise models (ANMs) with arbitrary noise. Our approach extends NOTIME (Berrevoets et al. 2025) which minimizes an independence criterion among the residuals. We show that the global minimizer of the independence criterion corresponds to the true underlying DAG up to additional constant edges in general ANMs. To recover the exact structure, we introduce an adaptive group lasso penalty that regularizes entire columns of the first-layer weight matrix of an MLP, enabling the selective pruning of constant edges in a functionally meaningful way. Empirically, our method achieves effective and stable performance across diverse noise types and variances, outperforming prior methods that lack identifiability guarantees in this setting.

Training deep learning models on single-cell datasets with hundreds of millions of cells requires loading data from disk, as these datasets exceed available memory. While random sampling provides the data diversity needed for effective training, it is prohibitively slow due to the random access pattern overhead, whereas sequential streaming achieves high throughput but introduces biases that degrade model performance. We present scDataset, a PyTorch data loader that enables efficient training from on-disk data with seamless integration across diverse storage formats. Our approach combines block sampling and batched fetching to achieve quasi-random sampling that balances I/O efficiency with minibatch diversity. On Tahoe-100M, a dataset of 100 million cells, scDataset achieves more than two orders of magnitude speedup compared to true random sampling while working directly with AnnData files. We provide theoretical bounds on minibatch diversity and empirically show that scDataset matches the performance of true random sampling across multiple classification tasks and model architectures.

Evaluating generative models is challenging because standard metrics often fail to reflect human preferences. Human evaluations are more reliable but costly and noisy, as participants vary in expertise, attention, and diligence. Pairwise comparisons improve consistency, yet aggregating them into overall quality scores requires careful modeling. Bradley-Terry-based methods update item scores from comparisons, but existing approaches either ignore rater variability or lack convergence guarantees, limiting robustness and interpretability. We introduce BBQ, a Bayesian Bradley-Terry variant that explicitly models rater quality, downweighting or removing unreliable participants, and provides guaranteed monotonic likelihood convergence through an Expectation-Maximization algorithm. Empirical results show that BBQ provides efficient inference, well-calibrated uncertainty estimates, and more robust, interpretable rankings compared to baseline Bradley-Terry models, even with noisy or crowdsourced raters. This framework enables more reliable and cost-effective human evaluation of generative models.

Existing preference datasets for text-to-image models typically store only the final winner/loser images. This representation is insufficient for rectified flow (RF) models, whose generation is naturally indexed by a specific prior noise sample and follows a nearly straight denoising trajectory. In contrast, prior DPO-style alignment for diffusion models commonly estimates trajectories using an independent forward noising process, which can be mismatched to the true reverse dynamics and introduces unnecessary variance. We propose Prior Noise-Aware Preference Optimization (PNAPO), an off-policy alignment framework specialized for rectified flow. PNAPO augments preference data by retaining the paired prior noises used to generate each winner/loser image, turning the standard (prompt, winner, loser) triplet into a sextuple. Leveraging the straight-line property of RF, we estimate intermediate states via noise-image interpolation, which constrains the trajectory estimation space and yields a tighter surrogate objective for preference optimization. In addition, we introduce a dynamic regularization strategy that adapts the DPO regularization based on (i) the reward gap between winner and loser and (ii) training progress, improving stability and sample efficiency. Experiments on state-of-the-art RF T2I backbones show that PNAPO consistently improves preference metrics while substantially reducing training compute.

Domain-specific large language models (LLMs), typically developed by fine-tuning a pre-trained general-purpose LLM on specialized datasets, represent a significant advancement in applied AI. A common strategy in LLM fine-tuning is curriculum learning, which pre-orders training samples based on metrics like difficulty to improve learning efficiency compared to a random sampling strategy. However, most existing methods for LLM fine-tuning rely on a static curriculum, designed prior to training, which lacks adaptability to the model's evolving needs during fine-tuning. To address this, we propose EDCO, a novel framework based on two key concepts: \textit{inference entropy} and \textit{dynamic curriculum orchestration}. Inspired by recent findings that maintaining high answer entropy benefits long-term reasoning gains, EDCO prioritizes samples with high inference entropy in a continuously adapted curriculum. EDCO integrates three core components: an efficient entropy estimator that uses prefix tokens to approximate full-sequence entropy, an entropy-based curriculum generator that selects data points with the highest inference entropy, and an LLM trainer that optimizes the model on the selected curriculum. Comprehensive experiments in communication, medicine and law domains, EDCO outperforms traditional curriculum strategies for fine-tuning Qwen3-4B and Llama3.2-3B models under supervised and reinforcement learning settings. Furthermore, the proposed efficient entropy estimation reduces computational time by 83.5\% while maintaining high accuracy. The code is available at https://github.com/GTS-AIData/EDCO.

Knowledge Base Question Answering (KBQA) challenges models to bridge the gap between natural language and strict knowledge graph schemas by generating executable logical forms. While Large Language Models (LLMs) have advanced this field, current approaches often struggle with a dichotomy of failure: they either generate hallucinated queries without verifying schema existence or exhibit rigid, template-based reasoning that mimics synthesized traces without true comprehension of the environment. To address these limitations, we present **KBQA-R1**, a framework that shifts the paradigm from text imitation to interaction optimization via Reinforcement Learning. Treating KBQA as a multi-turn decision process, our model learns to autonomously navigate the knowledge base using a structured action space, refining its reasoning strategies based on concrete execution feedback rather than static supervision. Furthermore, we introduce Referenced Rejection Sampling (RRS), a data synthesis method that resolves cold-start challenges by strictly aligning reasoning traces with ground-truth action sequences. Extensive experiments on WebQSP, GrailQA, and GraphQuestions demonstrate that KBQA-R1 achieves state-of-the-art performance. Code is available at https://anonymous.4open.science/r/KBQA-R1-814F.

Cross-device Federated Learning (FL) is frequently bottlenecked by the prohibitive memory and communication costs of training deep neural networks on resource-constrained edge hardware. While federated dynamic sparse training aims to alleviate these costs by adjusting sparse structures during training, existing methods rely on magnitude-based heuristics that are fundamentally ill-suited for the non-convergent, heterogeneous environments inherent to FL. To address this challenge, we propose FedFit, a federated dynamic sparse training framework that replaces simple heuristics with optimization-centric criteria for structure adjustment. By leveraging a second-order approximation of the loss landscape via the Fisher Information Matrix, FedFit enables precise and efficient structure adjustment without the overhead of explicit Hessian computation. Empirical evaluations across computer vision and natural language processing benchmarks demonstrate that FedFit significantly narrows the sparse-to-dense accuracy gap, outperforming state-of-the-art methods while maintaining high communication efficiency. Our code is available at https://github.com/Serena-28/Fedfit.git.

Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modeling. Existing methods for uncertainty modeling face a fundamental dilemma: Bayesian approaches provide principled estimates but remain computationally prohibitive, while efficient second-order predictors lack rigorous connections between their specific objectives and epistemic uncertainty quantification. To resolve this dilemma, we introduce **D**irichlet-**a**pproximated **p**ossibilistic **p**osterior p**r**edictions (DAPPr), a principled framework grounded in possibility theory. We define a possibilistic posterior over parameters, project it to the prediction space via supremum operators, and approximate the projected posterior using learnable Dirichlet possibility functions. This projection-and-approximation strategy yields a simple training objective with closed-form solutions. Despite its simplicity, extensive experiments across diverse benchmarks show that DAPPr achieves competitive or superior uncertainty quantification performance over state-of-the-art second-order predictors while maintaining both principled derivation and computational efficiency.

Collaborative perception enhances environment understanding through multi-agent information sharing, but its performance in real-world scenarios is constrained by heterogeneous sensor modalities and model architectures. Recent protocol-based two-stage methods alleviate this problem by mapping heterogeneous features into a shared protocol space; however, independently trained modality-specific converters often generate modality-specific pseudo-protocol distributions, leading to semantic inconsistency and error accumulation, which is particularly pronounced in scenarios with large modality discrepancies. To address this issue, we propose CauseCollab, a causal unified and modality-agnostic network. CauseCollab formulates representation learning in the protocol space from a causal perspective, explicitly disentangling semantic factors from modality-specific statistical confounders via causal metric learning. Meanwhile, CauseCollab adopts context-guided Unified Converter for heterogeneous modalities to ensure cross-modal semantic consistency. In addition, integrating new modalities only requires training adapters with minimal parameters. Extensive experiments on the OPV2V and DAIR-V2X datasets demonstrate that CauseCollab achieves state-of-the-art performance, with more significant gains in scenarios involving large modality gaps.

Explainability is essential for applying time series analysis in high-stakes domains. While Time Series Captioning (TSC) offers a pathway to enhance temporal explainability, achieving reliable caption generation usually necessitates high-quality textual annotations. However, as interpreting abstract temporal dynamics requires specialized domain knowledge, acquiring such caption annotations is challenging, thereby impeding the advancement of TSC. To address this challenge, we introduce a novel Caption Label-Free Learning (CLFL) paradigm. Departing from the supervised learning tradition of imitating human annotations, CLFL formulates captioning as an agentic exploration task optimized by feedback from a proxy reward. Specifically, we propose a Dual Loop Agentic Captioning (DLAC) framework to achieve such an exploration-feedback mechanism. In the inner loop, a Time Series Captioning Agent (TSCAgent) reflectively explores potential semantic captions. In turn, the outer loop evaluates these captions via downstream reasoning to derive proxy reward, which feeds back to optimize the TSCAgent. Empirical results validate the effectiveness of the CLFL, proving that the exploration-feedback mechanism is sufficient for learning complex temporal semantics and autonomously generating captions, without any caption label supervision. Furthermore, we release TFTSC, an industrial expert-level time series caption dataset, which is available at: https://github.com/chunhuiz/TFTSC/tree/master.

As increasingly capable agents are deployed, a central safety challenge is how to retain meaningful human control without modifying the underlying system. We study a minimal control interface in which an agent chooses whether to act autonomously (play) or defer (ask), while a human simultaneously chooses whether to be permissive (trust) or engage in oversight (oversee), and model this interaction as a two-player Markov Game. When this game forms a Markov Potential Game, we prove an alignment guarantee: any increase in the agent's utility from acting more autonomously cannot decrease the human's value. This establishes a form of intrinsic alignment where the agent's incentive to seek autonomy is structurally coupled to the human's welfare. Practically, the framework induces a transparent control layer encouraging the agent to defer when risky and act when safe. While we use gridworld simulations to illustrate the emergence of this collaboration, our primary validation involves an agentic tool-use task where two 30B-parameter language models are fine-tuned via independent policy gradient. We demonstrate that even as the agents learn to coordinate on the fly, this framework effectively reduces safety violations in realistic, open-ended environments.

Test-time guidance is a widely used mechanism for steering pretrained diffusion models toward outcomes specified by a reward function. Existing approaches, however, focus on maximizing reward rather than sampling from the true Bayesian posterior, leading to miscalibrated inference. In this work, we show that common test-time guidance methods do not recover the correct posterior distribution and identify the structural approximations responsible for this failure. We then propose consistent alternative estimators that enable calibrated sampling from the Bayesian posterior. We significantly outperform previous methods on a set of Bayesian inference tasks, and set a new state-of-the-art PSNR in black hole image reconstruction. We publish our code at https://github.com/mandt-lab/Calibrated-Guidance.

Mixture-of-Experts (MoE) language models organize knowledge into explicitly routed expert modules, making expert-level representations traceable and analyzable. By analyzing expert activation patterns in MoE language large models (LLMs), we find that a subset of experts is consistently activated across diverse knowledge domains. These common experts encode cross-domain, generalizable knowledge that is closely related to model generalization, naturally raising the question of how such identifiable expert knowledge can be practically reused. Motivated by this observation, we propose XPERT, a training-free framework that extracts, consolidates, and reuses expert knowledge from pre-trained MoE LLMs to support effective training of language models across different model scales. XPERT identifies cross-domain experts via inference-only analysis, refines their representations through tensor decomposition, and adapts the extracted knowledge to be reused in downstream models. Experiments on language understanding and dialogue generation benchmarks show that models benefiting from reused expert knowledge achieve consistently stronger performance and faster convergence compared to strong baselines. These results highlight MoE LLMs as structured and reusable knowledge sources, and demonstrate the value of expert-level knowledge reuse for improving model training.

State-space language models such as Mamba match Transformer quality while permitting linear complexity inference, yet still comprise billions of parameters that hinder deployment. While existing one-shot pruning methods are effective for generic linear and attention blocks, they are not designed with the overall Mamba architecture in mind and fail to account for the time-shared and discretized state-transition matrix at the heart of the selective state-space module (SSM). In this paper, we introduce SparseSSM, the first training-free pruning framework that extends the classic optimal brain surgeon (OBS) framework to state space architectures. Our layer-wise algorithm (i) derives an approximate second-order saliency score that aggregates Hessian-trace information across time steps, (ii) incorporates a component sensitivity analysis to guide feed-forward network (FFN) pruning, which also sheds light on where redundancy resides in mamba architecture, (iii) can be easily extended to semi-structured and structured sparsity, and generalized to other SSM-based architectures. Empirically, we prune 50% of SSM weights without fine-tuning and observe only limited performance degradation, achieving the current state-of-the-art one-shot pruning algorithm for Mamba-based LLMs.

EEG foundation models aim to learn transferable representations, yet EEG recordings are dominated by high-frequency noise and large cross-subject variability. Existing pretraining strategies such as masked autoencoding or autoregressive modeling often treat waveform reconstruction as the learning signal, making the objective sensitive to stochastic fluctuations rather than consistent neurophysiological structure. To address this overlap, we propose PATCHCODE, a region-aware discrete predictive learning framework that keeps the encoder input continuous while introducing region-aware discrete codes as stable supervision targets. We pretrain a masked predictive encoder on continuous EEG patches with dual-granularity learning: it predicts missing patch-level representations to preserve fine spatiotemporal structure, while aligning them to discretized code targets from a frozen tokenizer to anchor robust semantics. Extensive experiments across sixteen downstream datasets spanning emotion recognition, motor imagery, sleep staging, seizure detection, vigilance estimation, stress detection, and clinical diagnosis demonstrate that PATCHCODE achieves competitive performance compared to state-of-the-art baselines, with notable gains in data efficiency under limited labels. Our code is available at https://github.com/kierenyyu/Patchcode.

Supervised fine-tuning (SFT) is a commonly used technique to adapt large language models (LLMs) to downstream tasks. In practice, SFT on a full dataset is computationally expensive and sometimes suffers from overfitting or bias amplification. This facilitates the rise of data curation in SFT, which prioritizes the most valuable data to optimze. This work studies the online batch selection family that dynamically scores and filters samples during the training process. However, existing popular methods often (i) rely merely on the utility of data to select a subset while neglecting other crucial factors like diversity, (ii) rely on external resources such as reference models or validation sets, and (iii) incur extra training time over full-dataset training. To address these limitations, this work develops UDS (Utility-Diversity Sampling), a framework for efficient online batch selection in SFT. UDS leverages the nuclear norm of the logits matrix to capture both data utility and intra-sample diversity, while estimating inter-sample diversity through efficient low-dimensional embedding comparisons with a lightweight memory buffer of historical samples. Such a design eliminates the need for external resources and unnecessary backpropagation, securing computational efficiency. Experiments on multiple benchmarks demonstrate that UDS consistently outperforms state-of-the-art online batch selection methods under varying data budgets, and significantly reduces training time compared to full-dataset fine-tuning.

Multimodal Process Reward Models (MPRMs) are central to step-level supervision for visual reasoning in MLLMs. Training MPRMs typically requires large-scale Monte Carlo (MC)-annotated corpora, incurring substantial training cost. This paper studies the data efficiency for MPRM training. Our preliminary experiments reveal that MPRM training quickly saturates under random subsampling of the training data, indicating substantial redundancy within existing MC-annotated corpora. To explain this, we formalize a theoretical framework and reveal that informative gradient updates depend on two factors: label mixtures of positive/negative steps and label reliability (average MC scores of positive steps). Guided by these insights, we propose the Balanced-Information Score (BIS), which prioritizes both mixture and reliability based on existing MC signals at the rollout level, without incurring any additional cost. Across two backbones (InternVL2.5-8B and Qwen2.5-VL-7B) on VisualProcessBench, BIS-selected subsets consistently match and even surpass the full-data performance at small fractions. Notably, the BIS subset reaches full-data performance using only 10% of the training data, improving over random subsampling by a relative 4.1%.