ICLR 2026 论文列表

Test-time reasoning significantly enhances pre-trained AI agents’ performance. However, it requires an explicit environment model, often unavailable or overly complex in real-world scenarios. While MuZero enables effective model learning for search in perfect information games, extending this paradigm to imperfect information games presents substantial challenges due to more nuanced look-ahead reasoning techniques and large number of states relevant for individual decisions. This paper introduces an algorithm LAMIR that learns an abstracted model of an imperfect information game directly from the agent-environment interaction. During test time, this trained model is used to perform look-ahead reasoning. The learned abstraction limits the size of each subgame to a manageable size, making theoretically principled look-ahead reasoning tractable even in games where previous methods could not scale. We empirically demonstrate that with sufficient capacity, LAMIR learns the exact underlying game structure, and with limited capacity, it still learns a valuable abstraction, which improves game playing performance of the pre-trained agents even in large games.

We present Riemannian Gaussian Variational Flow Matching (RG-VFM), a geometric extension of Variational Flow Matching (VFM) for generative modeling on manifolds. Motivated by the benefits of VFM, we derive a variational flow matching objective for manifolds with closed-form geodesics based on Riemannian Gaussian distributions. Crucially, in Euclidean space, predicting endpoints (VFM), velocities (FM), or noise (diffusion) is largely equivalent due to affine interpolations. However, on curved manifolds this equivalence breaks down. For this reason, we formally analyze the relationship between our model and Riemannian Flow Matching (RFM), revealing that the RFM objective lacks a curvature-dependent penalty -- encoded via Jacobi fields -- that is naturally present in RG-VFM. Based on this relationship, we hypothesize that endpoint prediction provides a stronger learning signal by directly minimizing geodesic distances. Experiments on synthetic spherical and hyperbolic benchmarks, as well as real-world tasks in material and protein generation, demonstrate that RG-VFM more effectively captures manifold structure and improves downstream performance over Euclidean and velocity-based baselines.

Reinforcement Learning (RL) has proven highly effective at enhancing the complex reasoning abilities of Large Language Models (LLMs), yet underlying mechanisms driving this success remain largely opaque. Our analysis reveals that puzzling phenomena like ``aha moments", ``length-scaling'' and entropy dynamics are not disparate occurrences but hallmarks of an emergent reasoning hierarchy, akin to the separation of high-level strategic planning from low-level procedural execution in human cognition. We uncover a compelling two-phase dynamic: initially, a model is constrained by procedural correctness and must improve its low-level skills. The learning bottleneck then decisively shifts, with performance gains being driven by the exploration and mastery of high-level strategic planning. This insight exposes a core inefficiency in prevailing RL algorithms like GRPO, which apply optimization pressure agnostically and dilute the learning signal across all tokens. To address this, we propose Hierarchy-Aware Credit Assignment (HICRA), an algorithm that concentrates optimization efforts on high-impact planning tokens. Our extensive experiments validate that HICRA significantly outperforms strong baselines, and offer deep insights into how reasoning advances through the lens of strategic exploration.

Mathematical problem synthesis shows promise in resolving data exhaustion, contamination, and leakage for AI training and evaluation. Despite enormous efforts, an **expressiveness-validity-complexity trilemma** remains an open question. Existing methods either lack whole-process verifiability, are constrained to a particular domain, or are bounded by external models. This paper breaks the trilemma by proposing the framework of **DExploration** _(**D**eductive **Exploration**)_, which formulates problem synthesis as a step-by-step exploration process instead of one-shot generation. Agents are equipped with three simple yet powerful atomic actions: _introducing_ variables/hypotheses, _deducing_ new facts, and _submitting_ derived facts. The entire exploration process is formally verified by Lean 4, which encompasses most mathematical domains up to the research level. Once a conclusion is submitted, the framework outputs a formal statement with guaranteed provability, reducing the need for external models. To bootstrap training data for DExploration, we propose **Exploratory Transformation** to distill exploration trajectories from existing large-scale theorem-proving data. It rewrites formal proofs into a deductive style, parses dependencies among variables, hypotheses, and proof steps, then reassembles them into exploration trajectories by a topological order. Experiments validate the effectiveness and efficiency of our methods, achieving an improved success rate ($40.70\\% \mapsto 54.52\\%$), reduced token cost ($52.9\text{K} \mapsto 8.8\text{K}, 83\\%\downarrow$), broader complexity and difficulty distributions, and Pareto optimality. In $2726$ valid generations, three state-of-the-art provers fail on $60$ (Pass@4) and $8$ (Pass@64). Code, data, and models will be available.

This work introduces a new approximate proximal sampler that operates solely with zeroth-order information of the potential function. Prior theoretical analyses have revealed that proximal sampling corresponds to alternating forward and backward iterations of the heat flow. The backward step was originally implemented by rejection sampling, whereas we directly simulate the dynamics. Unlike diffusion-based sampling methods that estimate scores via learned models or by invoking auxiliary samplers, our method treats the intermediate particle distribution as a Gaussian mixture, thereby yielding a Monte Carlo score estimator from directly samplable distributions. Theoretically, when the score estimation error is sufficiently controlled, our method inherits the exponential convergence of proximal sampling under isoperimetric conditions on the target distribution. In practice, the algorithm avoids rejection sampling, permits flexible step sizes, and runs with a deterministic runtime budget. Numerical experiments demonstrate that our approach converges rapidly to the target distribution, driven by interactions among multiple particles and by exploiting parallel computation.

Autoformalization, the task of translating informal mathematics into formal machine-verifiable languages, has long been challenging, even for individual statements. Beyond the statement level, mathematicians invest substantial effort in formalizing reusable abstractions such as common definitions and relations, based on which a large corpus of statements can be easily formalized. While previous work focuses on fine-tuning models for single statement autoformalization, we introduce $\textit{Divide and Abstract (DNA)}$, an end-to-end framework that not only improves the models' test-time performance at formalizing a corpus of statements, but also learns a library of reusable formal abstractions, which scales to statements outside of the corpus. First, $\textit{DNA}$ extracts common mathematical concepts from the entire informal corpus and formalizes them as reusable abstractions. Conditioned on these learned abstractions, $\textit{DNA}$ decomposes each informal statement in the corpus into a structured collection of informal clauses, translates each clause into its formal correspondents, composes the formal clauses back together, and refines the final formalization given feedback from a symbolic validator. The entire framework requires zero training and thus scales to any formal language, particularly low-resource Domain-Specific Languages (DSL). $\textit{DNA}$ significantly improves performance by up to $\textbf{8.6}\times$, and advances the SOTA by $\textbf{57.8}$\% from $\textbf{40.8}$ to $\textbf{64.4}$.

Increasing the batch size during training --- a “batch ramp'' --- is a promising strategy to accelerate large language model pretraining. While for SGD, doubling the batch size can be equivalent to halving the learning rate, the optimal strategy for adaptive optimizers like Adam is less clear. As a result, any batch-ramp scheduling, if used at all, is typically tuned heuristically. This work develops a principled framework for batch-size scheduling and introduces Seesaw: whenever a standard scheduler would halve the learning rate, Seesaw instead multiplies it by $1/\sqrt{2}$ and doubles the batch size, preserving loss dynamics while reducing serial steps. Theoretically, we provide, to our knowledge, the first finite-sample proof of equivalence between learning-rate decay and batch-size ramp-up for SGD on noisy linear regression, and we extend this equivalence to normalized SGD, a tractable proxy for Adam, under a variance-dominated regime observed in practice. Empirically, on 150M/300M/600M-parameter models trained at Chinchilla scale using a constant (critical) batch size, Seesaw matches cosine decay at equal FLOPs while reducing wall-clock time by $\approx 36\%$, approaching the theoretical limit implied by our analysis.

Feed-forward 3D reconstruction for autonomous driving has advanced rapidly, yet existing methods struggle with the joint challenges of sparse, non-overlapping camera views and complex scene dynamics. We present UniSplat, a general feed-forward framework that learns robust dynamic scene reconstruction through unified latent spatio-temporal fusion. UniSplat constructs a 3D latent scaffold, a structured representation that captures geometric and semantic scene context by leveraging pretrained foundation models. To effectively integrate information across spatial views and temporal frames, we introduce an efficient fusion mechanism that operates directly within the 3D scaffold, enabling consistent spatio-temporal alignment. To ensure complete and detailed reconstructions, we design a dual-branch decoder that generates dynamic-aware Gaussians from the fused scaffold by combining point-anchored refinement with voxel-based generation, and maintain a persistent memory of static Gaussians to enable streaming scene completion beyond current camera coverage. Extensive experiments on real-world datasets demonstrate that UniSplat achieves state-of-the-art performance in novel view synthesis, while providing robust and high-quality renderings even for viewpoints outside the original camera coverage.

The reasoning process of Large Language Models (LLMs) is often plagued by hallucinations and missing facts in question-answering tasks. A promising solution is to ground LLMs' answers in verifiable knowledge sources, such as Knowledge Graphs (KGs). Prevailing KG-enhanced methods typically constrained LLM reasoning either by enforcing rules during generation or by imitating paths from a fixed set of demonstrations. However, they naturally confined the reasoning patterns of LLMs within the scope of prior experience or fine-tuning data, limiting their generalizability to out-of-distribution graph reasoning problems. To tackle this problem, in this paper, we propose Explore-on-Graph (EoG), a novel framework that encourages LLMs to autonomously explore a more diverse reasoning space on KGs. To incentivize exploration and discovery of novel reasoning paths, we propose to introduce reinforcement learning during training, whose reward is the correctness of the reasoning paths' final answers. To enhance the efficiency and meaningfulness of the exploration, we propose to incorporate path information as additional reward signals to refine the exploration process and reduce futile efforts. Extensive experiments on five KGQA benchmark datasets demonstrate that, to the best of our knowledge, our method achieves state-of-the-art performance, outperforming not only open-source but also even closed-source LLMs.

Recent 3D feed-forward models, such as the Visual Geometry Grounded Transformer (VGGT), have shown strong capability in inferring 3D attributes of static scenes. However, since they are typically trained on static datasets, these models often struggle in real-world scenarios involving complex dynamic elements, such as moving humans or deformable objects like umbrellas. To address this limitation, we introduce PAGE-4D, a feedforward model that extends VGGT to dynamic scenes, enabling camera pose estimation, depth prediction, point cloud reconstruction, and point tracking—all without post-processing. Training a geometry transformer for dynamic scenes from scratch, however, demands large-scale dynamic datasets and substantial computational resources, which are often impractical. To overcome this, we propose an efficient fine-tuning strategy that allows PAGE-4D to generalize to dynamic scenarios using only limited dynamic data and compute. In particular, we design a dynamics-aware aggregator that disentangles dynamic from static content for downstream scene understanding tasks: it first predicts a dynamics-aware mask, which then guides a dynamics-aware global attention mechanism. Extensive experiments show that PAGE-4D consistently outperforms the original VGGT in dynamic scenarios, achieving superior results in camera pose estimation, monocular and video depth estimation, and dense point map reconstruction. The source code and pretrained model weights are provided in the supplementary material.

Boolean Satisfiability (SAT) solvers are foundational to computer science, yet their performance typically hinges on hand-crafted heuristics. This work introduces Reinforcement Learning from Algorithm Feedback (RLAF) as a paradigm for learning to guide SAT solver branching heuristics with Graph Neural Networks (GNNs). Central to our approach is a novel and generic mechanism for injecting inferred variable weights and polarities into the branching heuristics of existing SAT solvers. In a single forward pass, a GNN assigns these parameters to all variables. Casting this one-shot guidance as a reinforcement learning problem lets us train the GNN with off-the-shelf policy-gradient methods, such as GRPO, directly using the solver's computational cost as the sole reward signal. Extensive evaluations demonstrate that RLAF-trained policies significantly reduce the mean solve times of different base solvers across diverse SAT problem distributions, achieving more than a 2x speedup in some cases, while generalizing effectively to larger and harder problems after training. Notably, these policies consistently outperform expert-supervised approaches based on learning handcrafted weighting heuristics, offering a promising path towards data-driven heuristic design in combinatorial optimization.

Estimating epistemic uncertainty in value functions is a crucial challenge for many aspects of reinforcement learning (RL), including efficient exploration, safe decision-making, and offline RL. While deep ensembles provide a robust method for quantifying value uncertainty, they come with significant computational overhead. Single-model methods, while computationally favorable, often rely on heuristics and typically require additional propagation mechanisms for myopic uncertainty estimates. In this work we introduce universal value-function uncertainties (UVU), which, similar in spirit to random network distillation (RND), quantify uncertainty as squared prediction errors between an online learner and a fixed, randomly initialized target network. Unlike RND, UVU errors reflect policy-conditional $\textit{value uncertainty}$, incorporating the future uncertainties $\textit{any policy}$ may encounter. This is due to the training procedure employed in UVU: the online network is trained using temporal difference learning with a synthetic reward derived from the fixed, randomly initialized target network. We provide an extensive theoretical analysis of our approach using neural tangent kernel (NTK) theory and show that in the limit of infinite network width, UVU errors are exactly equivalent to the variance of an ensemble of independent universal value functions. Empirically, we show that UVU achieves equal performance to large ensembles on challenging multi-task offline RL settings, while offering simplicity and substantial computational savings.

Prevailing autoregressive (AR) models for text-to-image generation either rely on heavy, computationally-intensive diffusion models to process continuous image tokens, or employ vector quantization (VQ) to obtain discrete tokens with quantization loss. In this paper, we push the autoregressive paradigm forward with NextStep-1, a 14B autoregressive model paired with a 157M flow matching head, training on discrete text tokens and continuous image tokens with next-token prediction objectives. NextStep-1 achieves state-of-the-art performance for autoregressive models in text-to-image generation tasks, exhibiting strong capabilities in high-fidelity image synthesis. Furthermore, our method shows strong performance in image editing, highlighting the power and versatility of our unified approach. To facilitate open research, we will release our code and models to the community.

Mixture-of-Experts (MoE) has become a cornerstone in recent state-of-the-art large language models (LLMs). Traditionally, MoE relies on $\mathrm{Softmax}$ as the router score function to aggregate expert output, a designed choice that has persisted from the earliest MoE models to modern LLMs, and is now widely regarded as standard practice. However, the necessity of using $\mathrm{Softmax}$ to project router weights into a probability simplex remains an unchallenged assumption rather than a principled design choice. In this work, we first revisit the classical Nadaraya–Watson regression and observe that MoE shares the same mathematical formulation as Nadaraya–Watson regression. Furthermore, we show that both feed-forward neural network (FFN) and Mixture-of-Experts (MoE) can be interpreted as a special case of Nadaraya–Watson regression, where the kernel function corresponds to the input neurons of the output layer. Motivated by these insights, we propose the **zero-additional-cost** Kernel Inspired Router with Normalization ($\mathrm{KERN}$), an FFN-style router function, as an alternative to $\mathrm{Softmax}$. We demonstrate that this router generalizes both $\mathrm{Sigmoid}$- and $\mathrm{Softmax}$-based routers. **Based on empirical observations and established practices in FFN implementation, we recommend the use of $\mathrm{ReLU}$ activation and $\ell_2$-normalization in $\mathrm{KERN}$ router function.** Comprehensive experiments in MoE and LLM validate the effectiveness of the proposed FFN-style router function $\mathrm{KERN}$.

Existing studies on bias mitigation methods for large language models (LLMs) use diverse baselines and metrics to evaluate debiasing performance, leading to inconsistent comparisons among them. Moreover, their evaluations are mostly based on the comparison between LLMs' probabilities of biased and unbiased contexts, which ignores the gap between such evaluations and real-world use cases where users interact with LLMs by reading model responses and expect fair and safe outputs rather than LLMs' probabilities. To enable consistent evaluation across debiasing methods and bridge this gap, we introduce **BiasFreeBench**, an empirical benchmark that comprehensively compares eight mainstream bias mitigation techniques (covering four prompting-based and four training-based methods) on two test scenarios (multi-choice QA and open-ended multi-turn QA) by reorganizing existing datasets into a unified query-response setting. We further introduce a response-level metric, **Bias-Free Score**, to measure the extent to which LLM responses are fair, safe, and anti-stereotypical. Debiasing performances are systematically compared and analyzed across key dimensions: the prompting vs. training paradigm, model size, and generalization of different training strategies to unseen bias types. We release our benchmark, aiming to establish a unified testbed for bias mitigation research [https://github.com/xxupiano/BiasFreeBench](https://github.com/xxupiano/BiasFreeBench).

Crime prediction is a critical yet challenging task in urban spatio-temporal forecasting. Sparse crime records alone are insufficient to capture latent high-order patterns shaped by heterogeneous contextual factors with spatial and criminal specificity, while high non-stationarity renders conventional offline models ineffective against concept drift. To tackle these challenges, we propose a Spatio-Temporal Hierarchical Hypergraph Online Learning framework named ST-HHOL. First, we propose a hierarchical hypergraph convolution network that integrates crime data with heterogeneous contextual factors to uncover dual-specific crime patterns and their co-occurrence relations. Second, we introduce an iterative online learning strategy to address concept drift by employing frequent fine-tuning for short-term dynamics and periodic retraining for long-term shifts. Moreover, we adopt a Partially-Frozen LLM that leverages pre-trained sequence priors while adapting its attention mechanisms to crime-specific dependencies, enhancing spatio-temporal reasoning under sparse supervision. Extensive experiments on three real-world datasets demonstrate that ST-HHOL consistently outperforms state-of-the-art methods in terms of accuracy and robustness, while also providing enhanced interpretability. Code is available at https://github.com/777Rebecca/ST-HHOL.

We tackle the task of any-reference video generation, which aims to synthesize videos conditioned on arbitrary types and combinations of reference subjects, together with textual prompts. This task faces persistent challenges, including identity inconsistency, entanglement among multiple reference subjects, and copy-paste artifacts. To address these issues, we introduce MAGREF, a unified and effective framework for any-reference video generation. Our approach incorporates masked guidance and a subject disentanglement mechanism, enabling flexible synthesis conditioned on diverse reference images and textual prompts. Specifically, masked guidance employs a region-aware masking mechanism combined with pixel-wise channel concatenation to preserve appearance features of multiple subjects along the channel dimension. This design preserves identity consistency and maintains the capabilities of the pre-trained backbone, without requiring any architectural changes. To mitigate subject confusion, we introduce a subject disentanglement mechanism which injects the semantic values of each subject derived from the text condition into its corresponding visual region. Additionally, we establish a four-stage data pipeline to construct diverse training pairs, effectively alleviating copy-paste artifacts. Extensive experiments on a comprehensive benchmark demonstrate that MAGREF consistently outperforms existing state-of-the-art approaches, paving the way for scalable, controllable, and high-fidelity any-reference video synthesis. The code and video demos are available in the supplementary materials.

Spiking Neural Networks (SNNs), inspired by biological neurons, are attractive for their event-driven energy efficiency but still fall short of Artificial Neural Networks (ANNs) in accuracy. Knowledge distillation (KD) has emerged as a promising approach to narrow this gap by transferring ANN knowledge into SNNs. Temporal-wise distillation (TWD) leverages the temporal dynamics of SNNs by providing supervision across timesteps, but it applies a constant teacher output to all timesteps, mismatching the inherently evolving temporal process of SNNs. Moreover, while TWD improves per-timestep accuracy, truncated inference still suffers from full-length temporal information loss due to the progressive accumulation process. We propose **MEOM** (**M**any **E**yes, **O**ne **M**ind), a unified KD framework that enriches supervision with diverse temporal perspectives through mask-weighted teacher features and progressively aligns truncated predictions with the full-length prediction, thereby enabling more reliable inference across all timesteps. Extensive experiments and theoretical analyses demonstrate that MEOM achieves state-of-the-art performance on multiple benchmarks. Code is available at https://github.com/KaiSUN1/MEOM.

Training effective Vision-Language Models (VLMs) for GUI agents typically depends on large-scale annotated datasets, whose collection is both labor-intensive and error-prone. We introduce K-step GUI Transition, a self-supervised inverse dynamics task in which VLMs learn GUI dynamics by predicting the initial action that causes a transition between two GUI states. This approach eliminates the need for natural language instructions and enables scalable dataset construction from existing GUI trajectories or automated exploration. Building on this task, we propose GUI-Shift, a reinforcement learning (RL) framework that combines rule-based optimization with data filtering to improve VLM performance. We conduct extensive experiments using multiple VLM backbones across four benchmarks, spanning GUI task automation (AndroidControl, GUI Odyssey) and GUI grounding (ScreenSpot-v2, ScreenSpot-Pro). Our results show that training on GUI-Shift generalizes well to both GUI automation and grounding tasks, yielding up to an 11.2% increase in GUI automation accuracy. This study underscores the potential of self-supervised RL to leverage unlabeled GUI trajectories and offers a scalable alternative to training with annotated samples.