ICLR 2026 论文列表

Computational models are critical to advance our understanding of how neural, biomechanical, and physical systems interact to orchestrate animal behaviors. Despite the availability of near-complete reconstructions of the Drosophila melanogaster central nervous system, musculature, and exoskeleton, anatomically and physically grounded models of fly leg muscles are still missing. These models provide an indispensable bridge between motor neuron activity and joint movements. Here, we introduce the first 3D, data-driven musculoskeletal model of Drosophila legs, implemented in both OpenSim and MuJoCo simulation environments. Our model incorporates a Hill-type muscle representation based on high-resolution X-ray scans from multiple fixed specimens. We present a pipeline for constructing muscle models using morphological imaging data and for optimizing unknown muscle parameters specific to the fly. We then combine our musculoskeletal models with detailed 3D pose estimation data from behaving flies to achieve muscle-actuated behavioral replay in OpenSim. Simulations of muscle activity across diverse walking and grooming behaviors predict coordinated muscle synergies that can be tested experimentally. Furthermore, by training imitation learning policies in MuJoCo, we test the effect of different passive joint properties on learning speed and find that damping and stiffness facilitate learning. Overall, our model enables the investigation of motor control in an experimentally tractable model organism, providing insights into how biomechanics contribute to generation of complex limb movements. Moreover, our model can be used to control embodied artificial agents to generate naturalistic and compliant locomotion in simulated environments.

Understanding and addressing potential safety alignment risks in large language models (LLMs) is critical for ensuring their safe and trustworthy deployment. In this paper, we highlight an insidious safety threat: a compromised LLM can maintain a facade of proper safety alignment while covertly generating harmful content. To achieve this, we finetune the model to understand and apply a steganographic technique. At inference time, we input a prompt that contains a steganographically embedded malicious target question along with a plaintext cover question. The model, in turn, produces a target response similarly embedded within a benign-looking cover response. In this process, human observers only see the model being prompted with a cover question and generating a corresponding cover response, while the malicious content is hidden from view. We demonstrate this invisible safety threat on GPT-4.1 despite the OpenAI fine-tuning API’s safeguards. The finetuned model produces steganographic malicious outputs in response to hidden malicious prompts, while the user interface displays only a fully benign cover interaction. We also replicate the attack on two open-source models, Phi-4 and Mistral-Small-24B-Base-2501, confirming the generality of our method. We quantitatively evaluate our method on the AdvBench dataset, using Llama-Guard-3-8B for content safety classification. Across all three models, all stegotexts containing malicious content are incorrectly classified as safe.

We prove the first guarantees of sparse recovery for ReLU neural networks, where the sparse network weights constitute the signal to be recovered. Specifically, we study structural properties of the sparse network weights for two-layer, scalar-output networks under which a simple iterative hard thresholding algorithm recovers these weights exactly, using memory that grows linearly in the number of nonzero weights. We validate this theoretical result with simple experiments on recovery of sparse planted MLPs, MNIST classification, and implicit neural representations. Experimentally, we find performance that is competitive with, and often exceeds, a high-performing but memory-inefficient baseline based on iterative magnitude pruning.

Deep generative models have recently garnered significant attention across various fields, from physics to chemistry, where sampling from unnormalized Boltzmann-like distributions represents a fundamental challenge. In particular, autoregressive models and normalizing flows have become prominent due to their appealing ability to yield closed-form probability densities. Moreover, it is well-established that incorporating prior knowledge—such as symmetries—into deep neural networks can substantially improve training performances. In this context, recent advances have focused on developing symmetry-equivariant generative models, achieving remarkable results. Building upon these foundations, this paper introduces Symmetry-Enforcing Stochastic Modulation (SESaMo). Similar to equivariant normalizing flows, SESaMo enables the incorporation of inductive biases (e.g., symmetries) into normalizing flows through a novel technique called \textit{stochastic modulation}. This approach enhances the flexibility of the generative model by enforcing exact symmetries while, for the first time, enabling the model to learn broken symmetries during training. Our numerical experiments benchmark SESaMo in different scenarios, including an 8-Gaussian mixture model and physically relevant field theories, such as the $\phi^4$ theory and the Hubbard model.

Diffusion models are powerful generative models for continuous signals, such as images and videos. However, real-world digital data are quantized; hence, they take not continuous values but only a finite set of discrete values. For example, pixels in 8‑bit images can take only 256 discrete values. In existing diffusion models, quantization is either ignored by treating data as continuous, or handled by adding small noise to make the data continuous. Neither approach guarantees that samples from the model will converge to the finite set of quantized points. In this work, we propose a methodology to explicitly account for quantization within diffusion models. Specifically, by adopting a particular form of parameterization, we guarantee that samples from the reverse diffusion process converge to quantized points. In experiments, we demonstrate that our quantization-aware model can substantially improve the performance of diffusion models for density estimation, and achieve state‑of‑the‑art results on pixel‑level image generation in likelihood evaluation. In particular, for CIFAR‑10 image generation, the negative log‑likelihood improves substantially from 2.42 to 0.27, approaching the theoretical lower bound.

State-Space Models (SSMs) have recently been shown to achieve strong empirical performance on a variety of long-range sequence modeling tasks while remaining efficient and highly-parallelizable. However, the theoretical understanding of their expressive power remains limited. In this work, we study the expressivity of input-Dependent Complex-valued Diagonal (DCD) State-Space Models (SSMs) on sequential state-tracking tasks for abstract groups. It is easy to show that a single DCD SSM layer with a universal decoder can track any Abelian group at finite precision by decomposing it into a product of cyclic groups. We show that this is tight by proving that such a model cannot track any non-Abelian group at finite precision. We further establish the expressivity of multi-layer DCD SSMs. We show that a $k$-layer DCD SSM tracks a group if and only if that group has a subnormal series of length at most $k$, with Abelian factor groups. Empirically, while multi-layer models are theoretically expressive enough for solvable non-Abelian groups, we find they often fail to learn such solutions in practice, highlighting a gap between expressivity and learnability.

Transformer-based models for amortized probabilistic inference, such as neural processes, prior-fitted networks, and tabular foundation models, excel at single-pass *marginal* prediction. However, many real-world applications require coherent *joint distributions* that capture dependencies between predictions. While purely autoregressive architectures efficiently generate such distributions, they sacrifice the flexible set-conditioning that makes these models powerful for meta-learning. Conversely, the standard approach to obtain joint distributions from set-based models requires expensive re-encoding of an updated context set at each autoregressive step. We introduce a *causal autoregressive buffer* that preserves the advantages of both paradigms. Our approach decouples context encoding from updating the conditioning set. The model processes the context once and caches it, while a dynamic buffer captures target dependencies: as targets are incorporated, they enter the buffer and attend to both the cached context and previously buffered targets. This enables efficient batched autoregressive generation and one-pass joint predictive density evaluation. Training seamlessly integrates set-based and autoregressive modes at minimal additional cost. Across synthetic functions, EEG signals, cognitive models, and tabular data, our method matches the predictive accuracy of strong baselines while delivering up to $20\times$ faster joint sampling.

We present Lean Finder, a semantic search engine for Lean and mathlib that understands and aligns with the intents of mathematicians. Progress in formal theorem proving is often hindered by the difficulty of locating relevant theorems and the steep learning curve of the Lean 4 language, making advancement slow and labor-intensive. Existing Lean search engines, though helpful, rely primarily on informalizations (natural language translation of the formal statements), while largely overlooking the mismatch with real-world user queries. In contrast, we propose a user-centered semantic search tailored to the needs of mathematicians. Our approach begins by analyzing and clustering the semantics of public Lean discussions, then fine-tuning text embeddings on synthesized queries that emulate user intents. We further align Lean Finder with mathematicians’ preferences using diverse feedback signals, encoding it with a rich awareness of their goals from multiple perspectives. Evaluations on real-world queries, informalized statements, and proof states demonstrate that our Lean Finder achieves over 30% relative improvement compared to previous search engines and GPT-4o. In addition, Lean Finder is compatible with LLM-based theorem provers, bridging retrieval with formal reasoning. Lean Finder is available at: https://leanfinder.github.io.

Long-horizon sparse-reward tasks, such as goal-conditioned or robot manipulation tasks, remain challenging in offline reinforcement learning due to the credit assignment problem. Hierarchical methods have been proposed to tackle this problem by introducing sub-goal planning guided by value functions, which in principle can shorten the effective planning horizon for both high-level and low-level planners, and thereby avoiding the credit assignment problem. However, we demonstrate that the sub-goal selection mechanism is unreliable, as it relies on value functions suffering from generalization noise, which misguides value estimation and thus leads to sub-optimal sub-goals. In this work, to provide more reliable sub-goals, we novelly introduce a reliability-driven decision mechanism, and propose Reliability-Driven HRL (RD-HRL) as the solution. The reliability-driven decision mechanism provide decision-level targets from transition regions, thereby providing noise-immune decision spaces for high-level policy, ensuring the reliability of sub-goals (which are termed as action-level targets in this paper). Comprehensive experimental results demonstrate that our approach RD-HRL outperforms baseline methods across multiple benchmarks, highlighting the competitive advantages of RD-HRL. Our code is anonymously available at \url{https://anonymous.4open.science/r/RD-HRL-243D }.

Large-scale atomistic simulations are essential to bridge computational materials and chemistry to realistic materials and drug discovery applications. In the past few years, rapid developments of machine learning interatomic potentials (MLIPs) have offered a solution to scale up quantum mechanical calculations. Parallelizing these interatomic potentials across multiple devices poses a challenging, but promising approach to further extending simulation scales to real-world applications. In this work, we present \textbf{DistMLIP}, an efficient distributed inference platform for MLIPs based on zero-redundancy, graph-level parallelization. In contrast to conventional space-partitioning parallelization, DistMLIP enables efficient MLIP parallelization through graph partitioning, allowing multi-device inference on flexible MLIP model architectures like multi-layer graph neural networks. DistMLIP presents an easy-to-use, flexible, plug-in interface that enables distributed inference of pre-existing MLIPs. We demonstrate DistMLIP on four widely used and state-of-the-art MLIPs: CHGNet, MACE, TensorNet, and eSEN. We show that existing foundation potentials can perform near-million-atom calculations at the scale of a few seconds on 8 GPUs with DistMLIP.

We study the problem of minimizing a convex objective when only noisy gradient estimates are available. Under the mild assumption that the stochastic gradients have finite $\alpha$-th moments for some $\alpha \in (1,2]$, we show that the last iterate of clipped stochastic gradient descent (Clipped-SGD) achieves high-probability convergence of order $1/K^{(2\alpha-2)/(3\alpha)}$ on smooth objectives. Finally, we provide empirical results that support and complement our theoretical analysis.

Reinforcement Learning with Verifiable Rewards (RLVR), particularly with algorithms like Group Relative Policy Optimization (GRPO), has proven highly effective in enhancing the reasoning capabilities of large language models. However, a critical bottleneck in current pipelines lies in the limited diversity of sampled trajectories during group rollouts. Homogeneous trajectories and their associated rewards would diminish the return signals for policy updates, thereby hindering effective policy learning. This lack of diversity stems primarily from token-level stochastic sampling, where local variations are likely to collapse into near-identical reasoning paths. To address this limitation, we propose Lookahead Tree-Based Rollouts (LATR), a novel rollout strategy designed to explicitly promotes trajectory-level diversity by enforcing branching into different candidate tokens likely to yield distinct continuations. Specifically, LATR iteratively operates in three stages: (1) branching at high-uncertainty generation steps, (2) performing lookahead simulation for each new branch, and (3) pruning branches that exhibits prolonged similarity during simulation. Compared with Stochastic Sampling, LATR accelerates policy learning by 131% on average and improves final pass@1 performance by 4.2% on both GRPO and Dynamic sAmpling Policy Optimization (DAPO) algorithms across different reasoning tasks. Our code will be publicly available.

Large language models (LLMs) are increasingly deployed as part of compound AI systems which coordinate multiple modules (e.g., retrievers, tools, verifiers) over long-horizon workflows. Although recent frameworks that propagate textual feedback globally (e.g., TextGrad make it feasible to optimize such pipelines, we identify two depth-scaling failure modes in long-horizon agentic workflows: 1) exploding textual gradient, where textual feedback grows exponentially with depth, leading to prohibitively long message and amplifies evaluation biases; and 2) vanishing textual gradient, where limited long-context ability causes models overemphasize recent or early feedback, while compression of lengthy feedback causes downstream messages to lose specificity gradually as they propagate many hops upstream. To mitigate these issues, we introduce Textual Equilibrium Propagation (TEP), a local learning principle inspired by Equilibrium Propagation in energy-based models. TEP includes two phases: 1) a free phase where a local LLM critics iteratively refine prompts until reaching equilibrium (no further improvements are suggested); and 2) a nudged phase which applies proximal prompt edits with bounded modification intensity, using task-level objectives that propagate via forward signaling rather than backward feedback chains. This design supports local prompt optimization followed by controlled adaptation toward global goals without the computational burden and signal degradation of global textual backpropagation. Across long-horizon QA benchmarks and multi-agent tool-use dataset, TEP consistently improves accuracy and efficiency over global propagation methods such as TextGrad, with gains that increase at greater depths, while preserving the practicality of black-box LLM components in deep compound AI system.

Recent studies have shown that combining parameter-efficient fine-tuning (PEFT) with mixture-of-experts (MoE) is an effective strategy for adapting large language models (LLMs) to the downstream tasks. However, most existing approaches rely on conventional TopK routing, which requires careful hyperparameter tuning and assigns a fixed number of experts to each token. In this work, we propose LD-MoLE, a Learnable Dynamic routing mechanism for Mixture of LoRA Experts that enables adaptive, token-dependent, and layer-wise expert allocation. Our method replaces the non-differentiable TopK selection with a differentiable routing function and a closed-form solution. Moreover, our design allows the model to adaptively determine the number of experts to activate for each token at different layers. In addition, we introduce an analytical sparsity control objective to regularize the number of activated experts. Extensive experiments on the Qwen3-1.7B and Llama-3.2-3B models show that LD-MoLE achieves the highest average scores compared to state-of-the-art baselines, across a diverse set of benchmarks. Our method not only achieves superior performance, but also demonstrates the ability to learn token-dependent and layer-wise expert allocation.

Unsupervised 3D representation learning reduces the burden of labeling multimodal 3D data for fusion perception tasks. Among different pre-training paradigms, differentiable-rendering-based methods have shown most promise. However, existing works separately conduct pre-training for each modalities due to computational costs of processing large point clouds with images. As such, mutual benefit of high-level semantics (from image) and 3D structure (from point cloud) has not been exploited. To address this gap, we propose a joint unsupervised differentiable-rendering-based pre-training method for images and point clouds, termed CLAP, short for Curvature sampLing and leArnable Prototype. Specifically, our method overcomes the computational hurdle by Curvature Sampling to select the more informative points/pixels for pre-training. To uncover the performance benefits brought by their complementarity, we propose to use learnable prototypes to represent parts of the 3D scenes in a common feature space and an Expectation-Maximization training scheme to associate embeddings of each modality to prototypes. We further propose a swapping prediction loss that explores their interplay through prototypes along with a Gram Matrix Regularization term to maintain training stability. Experiments on NuScenes and Waymo datasets show that CLAP achieves up to 100% more performance gain as compared to previous SOTA pre-training methods. Codes and models will be released.

Low-Rank Adaptation is a widely used finetuning method for large models. Its small memory footprint allows practitioners to adapt large models to specific tasks at a fraction of the cost of full finetuning. Different modifications have been proposed to enhance its efficiency by, for example, setting the learning rate, the rank, and the initialization. Another improvement axis is adapter placement strategy: when using LoRA, practitioners usually pick \emph{module types} to adapt with LoRA, such as Query and Key modules. Few works have studied the problem of adapter placement, with nonconclusive results: original LoRA paper suggested placing adapters in attention modules, while other works suggested placing them in the MLP modules. Through an intuitive theoretical analysis, we introduce PLoP (Precise LoRA Placement), a lightweight method that allows automatic identification of module types where LoRA adapters should be placed, given a pretrained model and a finetuning task. We demonstrate that PLoP consistently outperforms, and in the worst case competes, with commonly used placement strategies through comprehensive experiments on supervised finetuning and reinforcement learning for reasoning.

Offline–to–online deployment of reinforcement learning (RL) agents often stumbles over two fundamental gaps: (1) the sim-to-real gap, where real-world systems exhibit latency and other physical imperfections not captured in simulation; and (2) the interaction gap, where policies trained purely offline face out-of-distribution (OOD) issues during online execution, as collecting new interaction data is costly or risky. As a result, agents must generalize from static, delay-free datasets to dynamic, delay-prone environments. In this work, we propose $\textbf{DT-CORL}$ ($\textbf{D}$elay-$\textbf{T}$ransformer belief policy $\textbf{C}$onstrained $\textbf{O}$ffline $\textbf{RL}$), a novel framework for learning delay-resilient policies solely from static, delay-free offline data. DT-CORL introduces a transformer-based belief model to infer latent states from delayed observations and jointly trains this belief with a constrained policy objective, ensuring that value estimation and belief representation remain aligned throughout learning. Crucially, our method does not require access to delayed transitions during training and outperforms naive history-augmented baselines, SOTA delayed RL methods, and existing belief-based approaches. Empirically, we demonstrate that DT-CORL achieves strong delay-robust generalization across both locomotion and goal-conditioned tasks in the D4RL benchmark under varying delay regimes. Our results highlight that joint belief-policy optimization is essential for bridging the sim-to-real latency gap and achieving stable performance in delayed environments.

Modern methods of generative modelling and unpaired data translation based on Schrodinger bridges and stochastic optimal control theory aim to transform an initial density to a target one in an optimal way. In the present paper, we assume that we only have access to i.i.d. samples from initial and final distributions. This makes our setup suitable for both generative modelling and unpaired data translation. Relying on the stochastic optimal control approach, we choose an Ornstein-Uhlenbeck process as the reference one and estimate the corresponding Schrodinger potential. Introducing a risk function as the Kullback-Leibler divergence between couplings, we derive tight bounds on generalization ability of an empirical risk minimizer in a class of Schrodinger potentials including Gaussian mixtures. Thanks to the mixing properties of the Ornstein-Uhlenbeck process, we almost achieve fast rates of convergence up to some logarithmic factors in favourable scenarios. We also illustrate performance of the suggested approach with numerical experiments.

Contact forces introduce discontinuities into robot dynamics that severely limit the use of simulators for gradient-based optimization. Penalty-based simulators such as MuJoCo, soften contact resolution to enable gradient computation. However, realistically simulating hard contacts requires stiff solver settings, which leads to incorrect simulator gradients when using automatic differentiation. Contrarily, using non-stiff settings strongly increases the sim-to-real gap. We analyze penalty-based simulators to pinpoint why gradients degrade under hard contacts. Building on these insights, we propose DiffMJX, which couples adaptive time integration with penalty-based simulation to substantially improve gradient accuracy. A second challenge is that contact gradients vanish when bodies separate. To address this, we introduce contacts from distance (CFD) which combines penalty-based simulation with straight-through estimation. By applying CFD exclusively in the backward pass, we obtain informative pre-contact gradients while retaining physical realism.