ICLR 2026 论文列表

Spatiotemporal partial differential equations (PDEs) underpin a wide range of scientific and engineering applications, yet classical solvers are computationally costly on large or irregular domains. Neural PDE solvers have emerged as an efficient alternative, but they struggle to generalize to unseen source terms, which represent external forcing such as heat generation, body forces, or reaction rates. Since existing models typically mix the source with the system state, they lack a principled mechanism to capture source responses. We propose DGNet, a discrete Green network that explicitly decouples system evolution from source response. The key idea is to transform the classical Green’s function---a cornerstone of PDE theory---into a graph-based discrete formulation, preserving the superposition principle in a computable update rule. To ensure fidelity on irregular meshes, we construct a hybrid operator by combining physics-based discretizations with GNN-based corrections, while a lightweight residual GNN captures dynamics beyond the operator. Across three categories of spatiotemporal PDE scenarios, DGNet consistently achieves state-of-the-art accuracy. In particular, on the most challenging setting with entirely novel source terms, DGNet maintains stable performance while existing approaches collapse.

We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $\Pi$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem for backpropagation. We deploy $\Pi$net as a feasible-by-design optimization proxy for parametric constrained optimization problems and obtain modest-accuracy solutions faster than traditional solvers when solving a single problem, and significantly faster for a batch of problems. We surpass state-of-the-art learning approaches by orders of magnitude in terms of training time, solution quality, and robustness to hyperparameter tuning, while maintaining similar inference times. Finally, we tackle multi-vehicle motion planning with non-convex trajectory preferences and provide $\Pi$net as a GPU-ready package implemented in JAX.

Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is equivariant under general conformal transformations. To achieve this, we lift data from flat Euclidean space to Anti de Sitter (AdS) space. This allows us to exploit a known correspondence between conformal transformations of flat space and isometric transformations on the Anti de Sitter space. We then build upon the fact that such isometric transformations have been extensively studied on general geometries in the geometric deep learning literature. In particular, we employ message-passing layers conditioned on the proper distance, yielding a computationally efficient framework. We validate our model on tasks from computer vision and statistical physics, demonstrating strong performance, improved generalization capacities, and the ability to extract conformal data such as scaling dimensions from the trained network.

Spiking Neural Networks (SNNs) process information via discrete spikes, enabling them to operate at remarkably low energy levels. However, our experimental observations reveal a striking vulnerability when SNNs are trained using the mainstream method—direct encoding combined with backpropagation through time (BPTT): even a single backward pass on data drawn from a slightly different distribution can lead to catastrophic network collapse. We refer to this phenomenon as the heterogeneous training vulnerability of SNNs. Our theoretical analysis attributes this vulnerability to the repeated inputs inherent in direct encoding and the gradient accumulation characteristic of BPTT, which together produce an exceptional large Hessian spectral radius. To address this challenge, we develop a hyperparameter-free method called Dominant Singular Deflation (DSD). By orthogonally projecting the dominant singular components of gradients, DSD effectively reduces the Hessian spectral radius, thereby preventing SNNs from settling into sharp minima. Extensive experiments demonstrate that DSD not only mitigates the vulnerability of SNNs under heterogeneous training, but also significantly enhances overall robustness compared to key baselines, providing strong support for safer SNNs.

As Generative AI (GenAI) systems see growing adoption, a key concern involves the external validity of evaluations, or the extent to which they generalize from lab-based to real-world deployment conditions. Threats to the external validity of GenAI evaluations arise when the source sample of human raters and system outputs used to obtain a system quality estimate differs from the target distribution at deployment time. In this work, we propose a doubly-robust estimation framework designed to address this evaluation sampling bias. Key to our approach is the use of synthetic "persona" ratings -- produced by prompting an LLM evaluator (i.e., an LLM-as-a-judge) to behave as a human rater with specific sociodemographic characteristics. Our doubly-robust framework combines these informative yet imperfect persona ratings with human ratings obtained under evaluation sampling bias to produce statistically valid system quality estimates. In particular, we show that our approach yields valid system quality estimates when either: (i) a model trained to predict human ratings using persona ratings and source data observed under sampling bias, or (ii) a reweighting model that corrects for sampling bias is of sufficient quality. We validate our framework theoretically and via a novel Persona Simulation Framework (PSF) designed to systematically manipulate persona quality and the degree of evaluation sampling bias present in source data. Our work provides a principled foundation for combining imperfect persona ratings with human ratings observed under sampling bias to obtain valid system quality estimates.

When formulating safety as limits of cumulative cost, safe reinforcement learning (RL) learns policies that maximize rewards subject to these constraints during both data collection and deployment. While off-policy methods offer high sample efficiency, their application to safe RL faces substantial challenges from constraint violations caused by the cost-agnostic exploration and the underestimation bias in the cost value function. To address these challenges, we propose Constrained Optimistic eXploration Q-learning (COX-Q), an off-policy primal-dual safe RL method that integrates cost-bounded exploration and conservative distributional RL. First, we introduce a novel cost-constrained optimistic exploration strategy that resolves gradient conflicts between reward and cost in the action space, and adaptively adjusts the trust region to control constraint violation in exploration. Second, we adopt truncated quantile critics to mitigate the underestimation bias in costs. The quantile critics also quantify distributional, risk-sensitive epistemic uncertainty for guiding exploration. Experiments across velocity-constrained robot locomotion, safe navigation, and complex autonomous driving tasks demonstrate that COX-Q achieves high sample efficiency, competitive safety performance during evaluation, and controlled data collection cost in exploration. The results highlight the proposed method as a promising solution for safety-critical RL.

Sparse autoencoders (SAEs) are a cornerstone of interpretability for large language models (LLMs), aiming to decompose hidden states into meaningful semantic features. While several SAE variants have been proposed, there remains no principled framework to derive SAEs from the original dictionary learning formulation. In this work, we introduce such a framework by unrolling the proximal gradient method for sparse coding. We show that a single-step update naturally recovers common SAE variants, including ReLU, JumpReLU, and TopK. Through this lens, we reveal a fundamental limitation of existing SAEs: their sparsity-inducing regularizers enforce non-negativity, preventing a single feature from representing bidirectional concepts (e.g., male vs. female). This structural constraint fragments semantic axes into separate, redundant features, limiting representational completeness. To address this issue, we propose AbsTopK SAE, a new variant derived from the $\ell_0$ sparsity constraint that applies hard thresholding over the largest-magnitude activations. By preserving both positive and negative activations, AbsTopK uncovers richer, bidirectional conceptual representations. Comprehensive experiments across four LLMs and seven probing and steering tasks show that AbsTopK improves reconstruction fidelity, enhances interpretability, and enables single features to encode contrasting concepts. Remarkably, AbsTopK matches or even surpasses the Difference-in-Mean method—a supervised approach that requires labeled data for each concept and has been shown in prior work to outperform SAEs.

Matrix factorization mechanisms for differentially private training have emerged as a promising approach to improve model utility under privacy constraints. In practical settings, models are typically trained over multiple epochs, requiring matrix factorizations that account for repeated participation. Existing theoretical upper and lower bounds on multi-epoch factorization error leave a significant gap. In this work, we introduce a new explicit factorization method, Banded Inverse Square Root (BISR), which imposes a banded structure on the inverse correlation matrix. This factorization enables us to derive an explicit and tight characterization of the multi-epoch error. We further prove that BISR achieves asymptotically optimal error by matching the upper and lower bounds. Empirically, BISR performs on par with the state of the art factorization methods, while being simpler to implement, computationally efficient, and easier to analyze.

Diffusion models excel at short-horizon robot planning, yet scaling them to long-horizon tasks remains challenging due to computational constraints and limited training data. Existing compositional approaches stitch together short segments by separately denoising each component and averaging overlapping regions. However, this suffers from instability as the factorization assumption breaks down in noisy data space, leading to inconsistent global plans. We propose that the key to stable compositional generation lies in enforcing boundary agreement on the estimated clean data (Tweedie estimates) rather than on noisy intermediate states. Our method formulates long-horizon planning as inference over a chain-structured factor graph of overlapping video chunks, where pretrained short-horizon video diffusion models provide local priors. At inference time, we enforce boundary agreement through a novel combination of synchronous and asynchronous message passing that operates on Tweedie estimates, producing globally consistent guidance without requiring additional training. Our training-free framework demonstrates significant improvements over existing baselines across 100 simulation tasks spanning 4 diverse scenes, effectively generalizing to unseen start-goal combinations that were not present in the original training data. Project website: https://comp-visual-planning.github.io/

Unified multimodal understanding–generation models have shown promising results in image generation and editing, but remain largely constrained to the image domain. In this work, we present VOGUE, a versatile framework that extends unified modeling to the video domain. VOGUE adopts a dual-stream design, combining a Multimodal Large Language Model (MLLM) for instruction understanding with a Multimodal DiT (MMDiT) for video generation. This design enables accurate interpretation of complex multimodal instructions while preserving visual consistency. Built on this architecture, VOGUE unifies diverse video generation and editing tasks under a single multimodal instruction paradigm and is jointly trained across them. Extensive experiments demonstrate that VOGUE matches or surpasses state-of-the-art task-specific baselines in visual understanding, text/image-to-video generation, in-context video editing and generation. Beyond these core capabilities, the unified design allows VOGUE to generalize to unseen free-form editing tasks, such as green-screening characters or novel task composition (e.g., editing + style transfer) in a single instruction. Notably, VOGUE is the first system to support visual-prompt-based video generation in a unified model, where the MLLM interprets visual prompts and guides the MMDiT in synthesis. To foster future research, our model and code will be released.

E-commerce agents contribute greatly to helping users complete their e-commerce needs. To promote further research and application of e-commerce agents, benchmarking frameworks are introduced for evaluating LLM agents in the e-commerce domain. Despite the progress, current benchmarks lack evaluating agents' capability to handle mixed-type e-commerce dialogue and complex domain rules. To address the issue, this work first introduces a novel corpus, termed Mix-ECom, which is constructed based on real-world customer-service dialogues with post-processing to remove user privacy and add CoT process. Specifically, Mix-ECom contains 4,799 samples with multiply dialogue types in each e-commerce dialogue, covering four dialogue types (QA, recommendation, task-oriented dialogue, and chit-chat), three e-commerce task types (pre-sales, logistics, after-sales), and 82 e-commerce rules. Furthermore, this work build baselines on Mix-Ecom and propose a dynamic framework to further improve the performance. Results show that current e-commerce agents lack sufficient capabilities to handle e-commerce dialogues, due to the hallucination cased by complex domain rules. The dataset will be publicly available.

Large language models (LLMs) often generate hallucinations---unsupported content that undermines reliability. While most prior works frame hallucination detection as a binary task, many real-world applications require identifying hallucinated spans, which is a multi-step decision making process. This naturally raises the question of whether explicit reasoning can help the complex task of detecting hallucination spans. To answer this question, we first evaluate pretrained models with and without Chain-of-Thought (CoT) reasoning, and show that CoT reasoning has the potential to generate at least one correct answer when sampled multiple times. Motivated by this, we propose RL4HS, a reinforcement learning framework that incentivizes reasoning with a span-level reward function. RL4HS builds on Group Relative Policy Optimization and introduces Class-Aware Policy Optimization to mitigate reward imbalance issue. Experiments on the RAGTruth benchmark (summarization, question answering, data-to-text) show that RL4HS surpasses pretrained reasoning models and supervised fine-tuning, demonstrating the necessity of reinforcement learning with span-level rewards for detecting hallucination spans.

Offline reinforcement learning often relies on behavior regularization that enforces policies to remain close to the dataset distribution. However, such approaches fail to distinguish between high-value and low-value actions in their regularization components. We introduce Guided Flow Policy (GFP), which couples a multi-step flow-matching policy with a distilled one-step actor. The actor directs the flow policy through weighted behavior cloning to focus on cloning high-value actions from the dataset rather than indiscriminately imitating all state-action pairs. In turn, the flow policy constrains the actor to remain aligned with the dataset's best transitions while maximizing the critic. This mutual guidance enables GFP to achieve state-of-the-art performance across 144 state and pixel-based tasks from the OGBench, Minari, and D4RL benchmarks, with substantial gains on suboptimal datasets and challenging tasks.

Modern neural architectures are fundamentally constrained by their reliance on fixed activation functions, limiting their ability to adapt representations to task-specific structure and efficiently capture high-order interactions. We introduce deep low-rank separated neural networks (LRNNs), a novel architecture generalizing MLPs that achieves enhanced expressivity by learning adaptive, factorized activation functions. LRNNs generalize the core principles underpinning continuous low-rank function decomposition to the setting of deep learning, constructing complex, high-dimensional neuron activations through a multiplicative composition of simpler, learnable univariate transformations. This product structure inherently captures multiplicative interactions and allows each LRNN neuron to learn highly flexible, data-dependent activation functions. We provide a detailed theoretical analysis that establishes the universal approximation property of LRNNs and reveals why they are capable of excellent empirical performance. Specifically, we show that LRNNs can mitigate the curse of dimensionality for functions with low-rank structure. Moreover, the learnable product-structured activations enable LRNNs to adaptively control their spectral bias, crucial for signal representation tasks. These theoretical insights are validated through extensive experiments where LRNNs achieve state-of-the-art performance across diverse domains including image and audio representation, numerical solution of PDEs, sparse-view CT reconstruction, and supervised learning tasks. Our results demonstrate that LRNNs provide a powerful and versatile building block with a distinct inductive bias for learning compact yet expressive representations.

Recurrent Neural Networks (RNNs) have found widespread applications in machine learning for time series prediction and dynamical systems reconstruction, and experienced a recent renaissance with improved training algorithms and architectural designs. Understanding why and how trained RNNs produce their behavior is important for scientific and medical applications, and explainable AI more generally. An RNN's dynamical repertoire depends on the topological and geometrical properties of its state space. Stable and unstable manifolds of periodic points play a particularly important role: They dissect a dynamical system's state space into different basins of attraction, and their intersections lead to chaotic dynamics with fractal geometry. Here we introduce a novel algorithm for detecting these manifolds, with a focus on piecewise-linear RNNs (PLRNNs) employing rectified linear units (ReLUs) as their activation function. We demonstrate how the algorithm can be used to trace the boundaries between different basins of attraction, and hence to characterize multistability, a computationally important property. We further show its utility in finding so-called homoclinic points, the intersections between stable and unstable manifolds, and thus establish the existence of chaos in PLRNNs. Finally we show for an empirical example, electrophysiological recordings from a cortical neuron, how insights into the underlying dynamics could be gained through our method.

Safety mechanisms for diffusion and flow models have recently been developed along two distinct paths. In robot planning, control barrier functions are employed to guide generative trajectories away from obstacles at every denoising step by explicitly imposing geometric constraints. In parallel, recent data-driven, negative guidance approaches have been shown to suppress harmful content and promote diversity in generated samples. However, they rely on heuristics without clearly stating when safety guidance is actually necessary. In this paper, we first introduce a unified probabilistic framework using a Maximum Mean Discrepancy (MMD) potential for image generation tasks that recasts both Shielded Diffusion and Safe Denoiser as instances of our energy-based negative guidance against unsafe data samples. Furthermore, we leverage control-barrier functions analysis to justify the existence of a critical time window in which negative guidance must be strong; outside of this window, the guidance should decay to zero to ensure safe and high-quality generation. We evaluate our unified framework on several realistic safe generation scenarios, confirming that negative guidance should be applied in the early stages of the denoising process for successful safe generation.

Policy gradient algorithms have been a driver of much recent advancement in language model reasoning. One of their most appealing properties is the ability to learn from exploration on their own trajectories, a process crucial for discovering diverse approaches and fostering creative solutions. As we show in this paper, most policy gradient algorithms naturally reduce the entropy---and thus the diversity of explored trajectories---as part of training, yielding a policy increasingly limited in its ability to explore. However, not all algorithms exhibit this collapse in entropy equally. In this paper, we formally analyze the contributions of leading policy gradient objectives on entropy, show which mechanisms they employ to implicitly limit entropy collapse, and propose a new regularization method, REPO, that stabilizes entropy over training through the use of an adaptive controller. Models trained with REPO preserve entropy throughout training, yielding final policies that are, on average, more performant. By preserving entropy in the final policy, REPO-trained models can even be re-trained on evolving data distributions in new environments, unlike their non-entropy-preserving counterparts.

The rapid development and widespread adoption of Audio Large Language Models (ALLMs) require a rigorous assessment of their trustworthiness. However, existing evaluation frameworks, primarily designed for text, are not equipped to handle the unique vulnerabilities introduced by audio’s acoustic properties. We find that significant trustworthiness risks in ALLMs arise from non-semantic acoustic cues, such as timbre, accent, and background noise, which can be used to manipulate model behavior. To address this gap, we propose AudioTrust, the first framework for large-scale and systematic evaluation of ALLM trustworthiness concerning these audio-specific risks. AudioTrust spans six key dimensions: fairness, hallucination, safety, privacy, robustness, and authenticition. It is implemented through 26 distinct sub-tasks and a curated dataset of over 4,420 audio samples collected from real-world scenarios (e.g., daily conversations, emergency calls, and voice assistant interactions), purposefully constructed to probe the trustworthiness of ALLMs across multiple dimensions. Our comprehensive evaluation includes 18 distinct experimental configurations and employs human-validated automated pipelines to objectively and scalably quantify model outputs. Experimental results reveal the boundaries and limitations of 14 state-of-the-art (SOTA) open-source and closed-source ALLMs when confronted with diverse high-risk audio scenarios, thereby offering critical insights into the secure and trustworthy deployment of future audio models. Our platform and benchmark are publicly available at https://anonymous.4open.science/r/AudioTrust-8715/.

Chirality is a fundamental molecular property that governs stereospecific behavior in chemistry and biology. Capturing chirality in machine learning models remains challenging due to the geometric complexity of stereochemical relationships and the limitations of traditional molecular representations that often lack explicit stereochemical encoding. Existing approaches to chiral molecular representation primarily focus on central chirality, relying on handcrafted stereochemical tags or limited 3D encodings, and thus fail to generalize to more complex forms, such as axial chirality. In this work, we introduce \textbf{ChiDeK} (\textbf{Chi}ral \textbf{De}terminant \textbf{K}ernels), a framework that systematically integrates stereogenic information into molecular representation learning. We propose the chiral determinant kernel to encode the SE(3)-invariant chirality matrix and employ cross-attention to integrate stereochemical information from local chiral centers into the global molecular representation. This design enables explicit modeling of chiral-related features within a unified architecture, capable of jointly encoding central and axial chirality. To support the evaluation of axial chirality, we construct a new benchmark for electronic circular dichroism (ECD) and optical rotation (OR) prediction. Across four tasks, including R/S configuration classification, enantiomer ranking, ECD spectrum prediction, and OR prediction, ChiDeK achieves substantial improvements over state-of-the-art baselines, most notably yielding over 7\% higher accuracy on axially chiral tasks on average.