ICML 2026 论文列表

We study the problem of transformation inversion on general Lie groups: a datum is transformed by an unknown group element, and the goal is to recover an inverse transformation that maps it back to the original data distribution. Such unknown transformations arise widely in machine learning and scientific modeling, where they can significantly distort observations. We take a probabilistic view and model the posterior over transformations as a Boltzmann distribution defined by an energy function on the data space. To sample from this posterior, we introduce a diffusion process on Lie groups that keeps all updates on-manifold and only requires computations in the associated Lie algebra. Our method, Transformation-Inverting Energy Diffusion (TIED), relies on a new trivialized target-score identity that enables efficient score-based sampling of the transformation posterior. As a key application, we focus on test-time equivariance, where the objective is to improve the robustness of pretrained neural networks to input transformations. Experiments on image homographies and PDE symmetries demonstrate that TIED can restore transformed inputs to the training distribution at test time, showing improved performance over strong canonicalization and sampling baselines.

Learning discrete neural samplers is challenging due to the lack of gradients and combinatorial complexity. While stochastic optimal control (SOC) and Schrödinger bridge (SB) provide principled solutions, efficient SOC solvers like adjoint matching (AM), which excel in continuous domains, remain unexplored for discrete spaces. We bridge this gap by revealing that the core mechanism of AM is *state-space agnostic*, and introduce **discrete ASBS**, a unified framework that extends AM and adjoint Schrödinger bridge sampler (ASBS) to discrete spaces. Theoretically, we analyze the optimality conditions of the discrete SB problem and its connection to SOC, identifying a necessary cyclic group structure on the state space to enable this extension. Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability. Our code is available at https://github.com/AlexandreGUO2001/DASBS.

We study the problem of verifying whether certain properties such as robustness or fairness hold in an ensemble of decision trees. This problem is known to be NP-hard, with most research targeting a solution to a specific verification task. We explore the problem through the lens of an ensemble's OC-space: the set of all possible combinations of the individual trees' predictions. This provides a unifying view that yields a more generic and flexible approach to verification. We show that a wide variety of existing verification tasks can be (1) framed as simple searches through OC-space, and (2) answered in time linear or quadratic in the size of the OC-space. Moreover, the search can be made more efficient by using spatial index structures. Interestingly, while the OC-space can grow exponentially with the ensemble's size, in practice it is often feasible to enumerate all output configurations. Empirically, we show that our generic approach can be faster than approaches targeting a single verification task.

Multimodal fusion object detection faces a substantial modality gap at the same backbone stage. This makes predefined stage-aligned fusion insufficient for cross-stage interactions. We propose MFH-NAS, a hybrid neural architecture search framework that automatically discovers fusion architectures to better leverage cross-modal complementarity. MFH-NAS searches both local fusion primitives and stage-level fusion connectivity. It targets fusion operator design and fusion stage selection. It couples differentiable search with evolutionary search. Differentiable search learns architecture parameters for local fusion primitives. Evolutionary search explores global fusion topologies, including stage selection and cross-stage connection patterns. The joint search balances exploitation and exploration and mitigates premature convergence. It yields fusion structures that strengthen cross-stage interactions.We evaluate MFH-NAS on three public benchmarks, LLVIP, RGBT-Tiny, and M3FD. MFH-NAS consistently outperforms handcrafted fusion-stage designs and prior stage-searching NAS baselines, improving mAP@0.5 from 85.3% to 88.2% over strong fixed-stage fusion methods and delivering gains across all benchmarks.The code is available at https://github.com/someboy0/MFH-NAS.

Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the unconditioned dynamics rarely reach the terminal state. In this work, we propose a novel approach for learning diffusion bridges based on a self-consistency property of the optimal control. The resulting algorithm learns the conditioned dynamics in an iterative online manner, and exhibits strong performance in a range of empirical settings without requiring differentiation through simulated trajectories. Beyond the diffusion bridge setting, we draw connections between our self-consistency framework and recent advances in the wider stochastic optimal control literature.

Hamiltonian Monte Carlo and underdamped Langevin Monte Carlo are state-of-the-art methods for taking samples from high-dimensional distributions with a differentiable density function. To generate samples, they numerically integrate Hamiltonian or Langevin dynamics. This numerical integration introduces an asymptotic bias in Monte Carlo estimators of expectation values, which can be eliminated by adjusting the dynamics with a Metropolis-Hastings (MH) proposal step. Alternatively, one can trade bias for variance by avoiding MH, and select an integration step size that ensures sufficiently small asymptotic bias, relative to the variance inherent in a finite set of samples. Such \emph{unadjusted} methods often significantly outperform their adjusted counterparts in high-dimensional problems where sampling would otherwise be prohibitively expensive, yet are rarely used in statistical applications due to the absence of an automated way of choosing a step size. We propose just such an automatic tuning scheme that takes a user-provided asymptotic bias tolerance and selects a step size that ensures it. The key to the method is a relationship we establish between the energy change during integration and the asymptotic bias. We show that this procedure rigorously bounds the asymptotic bias for Gaussian target distributions. We then numerically show that the procedure works beyond Gaussians. To demonstrate the practicality of the proposed scheme, we provide a comprehensive comparison of adjusted and unadjusted samplers on Bayesian inference problems and on a statistical physics model in more than one million parameters. With our tuning scheme, the unadjusted methods achieve close to optimal performance, significantly and consistently outperforming their adjusted counterparts.

This paper proposes a synergy of amortised and particle-based methods for sampling from distributions defined by unnormalised density functions. We state a connection between sequential Monte Carlo (SMC) and neural sequential samplers trained by maximum-entropy reinforcement learning (MaxEnt RL), wherein learnt sampling policies and value functions define proposal kernels and twist functions. Exploiting this connection, we introduce an off-policy RL training procedure for the sampler that uses samples from SMC -- using the learnt sampler as a proposal -- as a behaviour policy that better explores the target distribution. We describe techniques for stable joint training of proposals and twist functions and an adaptive weight tempering scheme to reduce training signal variance. Furthermore, building upon past attempts to use experience replay to guide the training of neural samplers, we derive a way to combine historical samples with annealed importance sampling weights within a replay buffer. On synthetic multi-modal targets (in both continuous and discrete spaces) and the Boltzmann distribution of alanine dipeptide conformations, we demonstrate improvements in approximating the true distribution as well as training stability compared to both amortised and Monte Carlo methods.

Scaling inference methods such as Markov chain Monte Carlo to high-dimensional models remains a central challenge in Bayesian deep learning. A promising recent proposal, microcanonical Langevin Monte Carlo, has shown state-of-the-art performance across a wide range of problems. However, its reliance on full-dataset gradients makes it prohibitively expensive for large-scale problems. This paper addresses a fundamental question: Can microcanonical dynamics effectively leverage mini-batch gradient noise? We provide the first systematic study of this problem, establishing a novel continuous-time theoretical analysis of stochastic-gradient microcanonical dynamics. We reveal two critical failure modes: a theoretically derived bias due to anisotropic gradient noise and numerical instabilities in complex high-dimensional posteriors. To tackle these issues, we propose a principled gradient noise preconditioning scheme shown to significantly reduce this bias and develop a novel, energy-variance-based adaptive tuner that automates step size selection and dynamically informs numerical guardrails. The resulting algorithm is a robust and scalable microcanonical Monte Carlo sampler that achieves state-of-the-art performance on challenging high-dimensional inference tasks like Bayesian neural networks. Combined with recent ensemble techniques, our work unlocks a new class of stochastic microcanonical Langevin ensemble (SMILE) samplers for large-scale Bayesian inference.

Sparse Mixture-of-Experts (MoE) language models enable conditional computation but face deployment challenges due to the memory wall: while few experts are activated per token, the entire model must reside in memory. Existing expert pruning methods primarily rely on independent ranking, failing to account for the complex inter-dependencies and redundancies between experts. In this paper, we formulate post-training MoE pruning as a reconstruction-driven subset selection problem, aiming to minimize layer-output distortion under a cardinality constraint. We introduce SCHUR-A*, an algorithm that leverages A* search to achieve globally optimal expert selection within each layer. To maintain computational tractability, we derive a novel, admissible heuristic upper bound using a Schur-complement-based relaxation of the reconstruction objective. This tight bound allows for aggressive pruning of the search space while mathematically guaranteeing optimality. Furthermore, we propose an automated strategy to balance fidelity and memory reduction across heterogeneous layers via knee-point detection. Extensive experiments on Qwen3-30B-A3B demonstrate that SCHUR-A* significantly outperforms greedy and ranking-based baselines, maintaining comparable performance even under aggressive pruning ratios.

Combinatorial generalization remains a central challenge in Deep Reinforcement Learning (DRL). Classical planning provides a simple yet challenging setting to study this problem through explicit relational descriptions, without requiring learning from perception. In sparse-reward domains, standard RL exploration via real-time search is ineffective, and learning-based planning methods often rely on expert demonstrations, hindsight relabeling, or random walks from the goal state. In contrast, planners rely on best-first search methods such as $\mathrm{A}^\star$ to solve problems from scratch. We propose a self-improving $\mathrm{WA}^\star$ learning framework in combination with a value heuristic represented by a Relational Graph Neural Network: the heuristic guides search, and the resulting search data updates the heuristic via $Q$-learning. This loop yields heuristics that can function as general policies and solve new instances even without search, where DRL otherwise fails, as we show on puzzles such as Sokoban, PushWorld, The Witness, and the 2023 International Planning Competition benchmarks. Notably, we demonstrate strong zero-shot generalization: For example, heuristics trained on Blocksworld instances with fewer than $30$ blocks successfully solve instances with $488$ blocks without search.

Decision tree learning has long been a central topic in theoretical computer science, driven by its practical importance. A fundamental and widely used method for decision tree construction is the top-down greedy heuristic, which recursively splits on the most influential variable. Despite its empirical success, theoretical analysis of this heuristic has been limited. A recent breakthrough by Blanc et al. (ITCS, 2020) provided the first rigorous theoretical guarantees for the greedy approach, but only under the uniform distribution. We extend this analysis to the more general and practically relevant setting of arbitrary product distributions. Our main result shows that for any function $f$ computable by an optimal decision tree of size $s$, maximum depth $D_{\text{opt}}$, and average depth $\Delta_{\text{opt}}$, the greedy heuristic constructs an $\epsilon$-approximating tree whose size grows at most with $\exp(\Delta_{\text{opt}} D_{\text{opt}} \log(e/\epsilon))$. In the special case where the optimal tree is a full binary tree, this bound improves upon the bound of Blanc et al. and holds under a strictly broader class of distributions. Moreover, we present an algorithm based on the top-down greedy heuristic that is entirely **parameter-free**---it requires no prior knowledge of the optimal tree's size or depth---offering a practical advantage over Blanc et al.'s method.

$U$-statistics play a central role in statistical inference. In many modern applications, however, acquiring the labels required for $U$-statistics is costly. Motivated by recent advances in active inference, we develop an active inference framework for $U$-statistics that selectively queries informative labels to improve estimation efficiency under a fixed labeling budget, while preserving valid statistical inference. Our approach is built on the augmented inverse probability weighting $U$-statistic, which is proposed to incorporate the sampling rule and machine learning predictions. We characterize the optimal sampling rule that minimizes its variance and design practical sampling strategies. We further extend the framework to $U$-statistic-based empirical risk minimization. Experiments on real datasets demonstrate substantial gains in estimation efficiency over baseline methods, while maintaining target coverage.

Joint planning through language-based interactions is a key area of human-AI teaming. Planning problems in the open world often involve various aspects of incomplete information and unknowns, e.g., objects involved, human goals/intents -- thus leading to knowledge gaps in joint planning. We consider the problem of discovering optimal interaction strategies for AI agents to actively elicit human inputs in object-driven planning. To this end, we propose Minimal Information Neuro-Symbolic Tree (MINT) to reason about the impact of knowledge gaps and leverage self-play with MINT to optimize the AI agent’s elicitation strategies and queries. More precisely, MINT builds a symbolic tree by making propositions of possible human-AI interactions and by consulting a neural planning policy to estimate the uncertainty in planning outcomes caused by remaining knowledge gaps. Finally, we leverage LLM to search and summarize MINT’s reasoning process and curate a set of queries to optimally elicit human inputs for best planning performance. By considering a family of extended Markov decision processes with knowledge gaps, we analyze the return guarantee for a given MINT with active human elicitation. Our evaluation on three benchmarks involving unseen/unknown objects of increasing realism shows that MINT-based planning attains near-expert returns by issuing a limited number of questions per task while achieving significantly improved rewards and success rates.

Language agents have demonstrated remarkable potential in web search and information retrieval. However, many search-agent benchmarks assume that user queries are complete and unambiguous. This assumption leaves under-tested a practical failure mode: agents may face ambiguous requests where the intended target cannot be identified without clarification. Yet most agents lack interactive mechanisms during the search process, and existing benchmarks cannot assess this capability. To address this gap, we introduce InteractComp, a benchmark designed to evaluate whether search agents can recognize query ambiguity and actively interact to resolve it during search. Following the principle of easy to verify, interact to disambiguate, we construct 210 expert-curated questions across 9 domains through a target-distractor methodology that creates controlled ambiguity resolvable only through interaction. Evaluation of 17 models reveals striking failure: the best model achieves only 13.73% accuracy despite 71.50% with complete context, exposing systematic overconfidence rather than reasoning deficits. Forced interaction produces dramatic gains, demonstrating latent capability current strategies fail to engage. Longitudinal analysis shows interaction capabilities stagnated over 15 months while search performance improved seven-fold, revealing a critical blind spot. This stagnation, coupled with the immediate feedback inherent to search tasks, makes InteractComp a valuable resource for both evaluating and training interaction capabilities in search agents. The code is available at https://github.com/FoundationAgents/InteractComp

Diffusion Language Models (DLMs) generate text by iteratively denoising a masked sequence, repeatedly deciding which positions to commit at each step. Standard decoding follows a greedy rule, unmasking the most confident positions, yet this local choice can lock the model into a suboptimal unmasking order, especially on reasoning-heavy prompts. We present Search Or AcceleRate (SOAR), a training-free decoding algorithm that adapts its behavior to the model’s uncertainty. When confidence is low, SOAR briefly widens the search over alternative unmasking decisions to avoid premature commitments; when confidence is high, it collapses the search and decodes many positions in parallel to reduce the number of denoising iterations. Across mathematical reasoning and code generation benchmarks (GSM8K, MBPP, HumanEval) on Dream-7B and LLaDA-8B, SOAR improves generation quality while maintaining competitive inference speed, offering a practical way to balance quality and efficiency in DLM decoding.

As large language models increasingly function as autonomous coding agents, code documentation should be designed not for human readability, but for agent executability — serving as repo-specific playbooks that specify precise behaviors agents can follow. We formulate agent-oriented documentation generation as a black-box optimization problem over the documentation space, where quality is defined solely by downstream code correctness. A central challenge for conventional LLM refinement methods is output coupling—program entities are interdependent, and refining the documentation of one entity can invalidate its callers, resulting in a persistent whack-a-mole phenomenon during inference-time scaling. We propose DocSearch, a dependency-guided bi-level search framework that systematically exploits test-time feedback. The outer level conducts a priority search over the program-entity dependency DAG, enforcing a callee-before-caller refinement order to prevent downstream interference. The inner level performs a beam search over documentation refinements, using diversified error message sampling from self-generated unit tests to better exploit diagnostic signals and escape local optima. On DevEval+, DocSearch achieves 90.7\% solve rate with GPT-4o, outperforming the strongest baseline by 32.6\%. Cross-language experiments further demonstrate that optimized documentation transfers effectively to different target programming languages. Code is available at https://github.com/ccsnow127/docsearch.

Information-theoretic acquisition functions such as Entropy Search (ES) offer a principled exploration–exploitation framework for Bayesian optimization (BO). However, their practical implementation relies on complicated and slow approximations, i.e., a Monte Carlo estimation of the information gain. This complexity can introduce numerical errors and requires specialized, hand-crafted implementations. We propose a two-stage amortization strategy that learns to approximate entropy search-based acquisition functions using Prior-data Fitted Networks (PFNs) in a single forward pass. A first PFN is trained to be conditioned on information about the optima; second, the α-PFN is trained to predict the expected information gain by training on information gains measured with the first PFN. The α-PFN offers a flexible learned approximation, which replaces the complex heuristic approximations with a single forward pass per candidate, enabling rapid and extensible acquisition evaluation. Empirically, our approach is competitive with state-of-the-art entropy search implementations on synthetic and real-world benchmarks, while accelerating the different entropy search variants across all our experiments, with speed ups over 50x.

Large Vision-Language Models (LVLMs) are rapidly evolving toward true multimodal reasoning, with visual search representing a concrete instantiation of the thinking-with-images paradigm. However, LVLM visual search faces two key challenges: incompatibility among intrinsic capabilities after post-training, and interference in long multi-step reasoning contexts. To address these, we identify two novel insights. First, self-regulation between pre- and post-training LVLMs leverages the intrinsic single-step capabilities of the pre-training model to mitigate capability deterioration and long-context interference. Second, probability-based prophetic sampling, replacing naive prompting, provides a probabilistic interface where the pre-training model acts as a prophet and the post-training model selectively accepts prophetic tokens under its output distribution, preserving coherent multi-step reasoning. Building on these insights, we introduce SeProD, a self-prophetic decoding framework that leverages intrinsic single-step capabilities to enable coherent multi-step reasoning in a training-free, plug-and-play manner. Experiments show that SeProD consistently improves multiple visual-search LVLMs across all 12 splits of 4 visual search benchmarks, as well as across general VQA benchmarks, without added computational overhead, thanks to its parallel prophetic acceptance mechanism.

We propose ***Var**iance **D**riven **E**xploration* (VarDE), a principled approach for pure exploration in *highly stochastic environments*, where the exploration process is dominated by stochastic variance. VarDE is built on a fundamental principle: *sampling effort should be allocated to minimize the uncertainty of the final decision*. We formalize the uncertainty of the final decision through a smooth decision function and derive allocation rules that explicitly capture how stochastic noise in individual components affects the reliability of the final output. We apply this methodology to three core problems of pure exploration -- Best Arm Identification (BAI), Monte Carlo Tree Search (MCTS), and Best-Policy Identification (BPI) -- with theoretical guarantees on variance decay and simple regret. Empirically, we demonstrate consistent and significant improvements of VarDE over existing methods, with especially strong gains in highly stochastic environments.