ICLR 2026 论文列表

Dynamical systems modeling is a core pillar of scientific inquiry across natural and life sciences. Increasingly, dynamical system models are learned from data, rendering identifiability a paramount concept. For systems that are not identifiable from data, no guarantees can be given about their behavior under new conditions and inputs, or about possible control mechanisms to steer the system. It is known in the community that "linear ordinary differential equations (ODE) are almost surely identifiable from a single trajectory." However, this only holds for dense matrices. The sparse regime remains underexplored, despite its practical relevance with sparsity arising naturally in many biological, social, and physical systems. In this work, we address this gap by characterizing the identifiability of sparse linear ODEs. Contrary to the dense case, we show that sparse systems are unidentifiable with a positive probability in practically relevant sparsity regimes and provide lower bounds for this probability. We further study empirically how this theoretical unidentifiability manifests in state-of-the-art methods to estimate linear ODEs from data. Our results corroborate that sparse systems are also practically unidentifiable. Theoretical limitations are not resolved through inductive biases or optimization dynamics. Our findings call for rethinking what can be expected from data-driven dynamical system modeling and allows for quantitative assessments of how much to trust a learned linear ODE.

Machine learning (ML) has shown promise for tackling combinatorial optimization (CO), but much of the reported progress relies on small-scale, synthetic benchmarks that fail to capture real-world structure and scale. A core limitation is that ML methods are typically trained and evaluated on synthetic instance generators, leaving open how they perform on irregular, competition-grade, or industrial datasets. We present FrontierCO, a benchmark for evaluating ML-based CO solvers under real-world structure and extreme scale. FrontierCO spans eight CO problems, including routing, scheduling, facility location, and graph problems, with instances drawn from competitions and public repositories (e.g., DIMACS, TSPLib). Each task provides both easy sets (historically challenging but now solvable) and hard sets (open or computationally intensive), alongside standardized training/validation resources. Using FrontierCO, we evaluate 16 representative ML solvers---graph neural approaches, hybrid neural–symbolic methods, and LLM-based agents---against state-of-the-art classical solvers. We find a persistent performance gap that widens under structurally challenging and large instance sizes (e.g., TSP up to 10M nodes; MIS up to 8M), while also identifying cases where ML methods outperform classical solvers. By centering evaluation on real-world structure and orders-of-magnitude larger instances, FrontierCO provides a rigorous basis for advancing ML for CO.

Masked diffusion models (MDMs) for text offer a compelling alternative to traditional autoregressive language models. Parallel generation makes them efficient, but their computational capabilities and the limitations inherent to their parallelism remain largely unexplored. To this end, we characterize what types of reasoning problems MDMs can provably solve and how efficiently. We do this by connecting MDMs to the well-understood reasoning frameworks of chain of thought (CoT) and padded looped transformers (PLTs) in the finite-precision log-width setting: We show that MDMs and polynomially-padded PLTs are, in fact, equivalent in this setting, and that MDMs can solve all problems that CoT-augmented transformers can. Moreover, we showcase classes of problems (including regular languages) for which MDMs are inherently more efficient than CoT transformers, where parallel generation allows for substantially faster reasoning.

Knowledge editing (KE) is crucial for making precise modifications to factual knowledge within large language models (LLMs). Existing KE methods, however, are primarily designed for dense architectures, limiting their applicability to the increasingly popular sparse Mixture-of-Experts (MoE) models that power modern scalable LLMs. While MoEs offer remarkable efficiency and capacity scaling, their unique structure introduces new challenges for KE. Naively adapting dense-model editors to MoEs is not only computationally expensive but also induces routing distribution shifts that degrade model stability and consistency. To address these challenges, we introduce MoEEdit, the first systematic framework for routing-stable knowledge editing in MoE LLMs. Our approach reparameterizes expert updates through per-expert null-space projections, ensuring router inputs remain invariant to suppress these shifts, and solves the resulting block-structured optimization with an efficient block coordinate descent (BCD) solver. Experiments demonstrate that MoEEdit achieves state-of-the-art efficacy and generalization, while maintaining high specificity, routing stability, and superior computational and memory efficiency. Our work establishes a robust foundation for scalable and precise knowledge editing in modern sparse LLMs by highlighting the necessity of routing-stable interventions.

Reinforcement learning has emerged as a popular method for post-training large language models (LLMs). While improving the model's performance on downstream tasks, it often reduces the model's output diversity, leading to narrow, canonical responses. Existing methods to enhance diversity are limited, either by operating at inference time or by focusing on lexical differences. We propose a novel training method named DQO (Diversity Quality Optimization) based on determinantal point processes (DPPs) to jointly optimize LLMs for quality and semantic diversity. Our approach samples and embeds a group of responses for each prompt, then uses the determinant of a kernel-based similarity matrix to measure diversity as the volume spanned by the embeddings of these responses. Experiments across instruction-following, summarization, story generation, and reasoning tasks demonstrate that our method substantially improves semantic diversity without sacrificing model quality.

Featurizing odorants to enable robust prediction of their properties is difficult due to the complex activation patterns that odorants evoke in the olfactory system. Structurally similar odorants can elicit distinct activation patterns in both the sensory periphery (i.e., at the receptor level) and downstream brain circuits (i.e., at a perceptual level). Despite efforts to design or discover features for odorants to better predict how they activate the olfactory system, we lack a universally accepted way to featurize odorants. In this work, we demonstrate that feature-based approaches that rely on pre-trained foundation models $\textit{do not}$ significantly outperform classical hand-designed features, but that targeted foundation model fine-turning can increase model performance beyond these limits. To show this, we introduce a new model that creates olfaction-specific representations: $\textbf{L}$oRA-based $\textbf{O}$dorant-$\textbf{R}$eceptor $\textbf{A}$ffinity prediction with $\textbf{CROSS}$-attention ($\textbf{LORAX}$). We compare existing chemical foundation model representations to hand-designed physicochemical descriptors using feature-based methods and identify large information overlap between these representations, highlighting the necessity of fine-tuning to generate novel and superior odorant representations. We show that LORAX produces a feature space more closely aligned with olfactory neural representation, enabling it to outperform existing models on predictive tasks.

Conventional flow matching and diffusion-based policies sample through iterative denoising from standard noise distributions (e.g., Gaussian), and require conditioning modules to repeatedly incorporate visual information during the generative process, incurring substantial time and memory overhead. To reduce the complexity, we develop VITA (Vision-To-Action policy), a noise-free and conditioning-free flow matching policy learning framework that directly flows from visual representations to latent actions. Since the source of the flow is visually grounded, VITA eliminates the need of visual conditioning during generation. As expected, bridging vision and action is challenging, because actions are lower-dimensional, less structured, and sparser than visual representations; moreover, flow matching requires the source and target to have the same dimensionality. To overcome this, we introduce an action autoencoder that maps raw actions into a structured latent space aligned with visual latents, trained jointly with flow matching. To further prevent latent space collapse, we propose flow latent decoding, which anchors the latent generation process by backpropagating the action reconstruction loss through the flow matching ODE (ordinary differential equation) solving steps. We evaluate VITA on 9 simulation and 5 real-world tasks from ALOHA and Robomimic. VITA achieves 1.5x-2x faster inference compared to conventional methods with conditioning modules, while outperforming or matching state-of-the-art policies.

We introduce the *Quartet of Diffusions*, a structure-aware point cloud generation framework that explicitly models part composition and symmetry. Unlike prior methods that treat shape generation as a holistic process or only support part composition, our approach leverages four coordinated diffusion models to learn distributions of global shape latents, symmetries, semantic parts, and their spatial assembly. This structured pipeline ensures guaranteed symmetry, coherent part placement, and diverse, high-quality outputs. By disentangling the generative process into interpretable components, our method supports fine-grained control over shape attributes, enabling targeted manipulation of individual parts while preserving global consistency. A central global latent further reinforces structural coherence across assembled parts. Our experiments show that the Quartet achieves state-of-the-art performance. To our best knowledge, this is the first 3D point cloud generation framework that fully integrates and enforces both symmetry and part priors throughout the generative process.

3D anime character generation has become increasingly important in digital entertainment, including animation production, virtual reality, gaming, and virtual influencers. Unlike realistic human modeling, anime-style characters require exaggerated proportions, stylized surface details, and artistically consistent garments, posing unique challenges for automated 3D generation. Previous approaches for 3D anime character generation often suffer from low mesh quality and blurry textures, and they typically do not provide corresponding skeletons, limiting their usability in animation. In this work, we present a novel framework for high-quality 3D anime character generation that overcomes these limitations by combining the expressive power of the Skinned Multi-Person Linear (SMPL) model with precise garment generation. Our approach extends the Anime-SMPL model to better capture the distinct features of anime characters, enabling unified skeleton generation and blendshape-based facial expression control. This results in fully animation-ready 3D characters with expressive faces, bodies, and garments. To complement the body model, we introduce a body-aligned component-wise garments generation pipeline (including hairstyles, upper garments, lower garments, and accessories), which models garments as structured components aligned with body geometry. Furthermore, our method produces high-quality skin and facial textures, as well as detailed garment textures, enhancing the visual fidelity of the generated characters. Experimental results demonstrate that our framework significantly outperforms baseline methods in terms of mesh quality, texture clarity, and garment-body alignment, making it suitable for a wide range of applications in anime content creation and interactive media.

Event-based vision encodes dynamic scenes as asynchronous spatio-temporal spikes called events. To leverage conventional image processing pipelines, events are typically binned into frames. However, binning functions are discontinuous, which truncates gradients at the frame level and forces most event-based algorithms to rely solely on frame-based features. Attempts to directly learn from raw events avoid this restriction but instead suffer from biased gradient estimation due to the discontinuities of the binning operation, ultimately limiting their learning efficiency. To address this challenge, we propose a novel framework for unbiased gradient estimation of arbitrary binning functions by synthesizing weak derivatives during backpropagation while keeping the forward output unchanged. The key idea is to exploit integration by parts: lifting the target functions to functionals yields an integral form of the derivative of the binning function during backpropagation, where the cotangent function naturally arises. By reconstructing this cotangent function from the sampled cotangent vector, we compute weak derivatives that provably match long-range finite differences of both smooth and non-smooth targets. Experimentally, our method improves simple optimization-based egomotion estimation with 3.2\% lower RMS error and 1.57$\times$ faster convergence. On complex downstream tasks, we achieve 9.4\% lower EPE in self-supervised optical flow, and 5.1\% lower RMS error in SLAM, demonstrating broad benefits for event-based visual perception.

Transformers have emerged as powerful implicit rendering models, capable of performing geometric reasoning and producing photorealistic novel views in a single feedforward pass. A central challenge in these architectures is how to inject camera parameters into the transformer in a way that generalises across diverse sensing conditions. In this work, we present Rotary Ray Embedding (RoRE), an approach that embeds image patches directly as rays, using a learning based rotary positional embedding (RoPE). This ray-based formulation provides a unified and general representation, improving robustness to unconventional camera geometries and sensing modalities. We evaluate our approach on conventional perspective imagery, fisheye cameras, and multi-modal RGB-thermal setups, showing that a single network can flexibly integrate arbitrary numbers of cameras and modalities into a coherent scene representation. Experiments demonstrate improved generalisation and cross-modal consistency compared to existing methods, highlighting the potential for relative ray-based embeddings to build adaptable, plug-and-play vision systems.

Large Language Models (LLMs) have impressive multilingual capabilities, but they suffer from unexpected code-switching, also known as language mixing, which involves switching to unexpected languages in the model response. This problem leads to poor readability and degrades the usability of model responses. However, existing work on this issue lacks a mechanistic analysis and shows limited effectiveness. In this paper, we first provide an in-depth analysis of unexpected code-switching using sparse autoencoders and find that when LLMs switch to a language, the features of that language exhibit excessive pre-activation values. Based on our findings, we propose $\textbf{S}$parse $\textbf{A}$utoencoder-guided $\textbf{S}$upervised $\textbf{F}$ine$\textbf{t}$uning (SASFT), which teaches LLMs to maintain appropriate pre-activation values of specific language features during training. Experiments on five models across three languages demonstrate that SASFT consistently reduces unexpected code-switching by more than 50\% compared to standard supervised fine-tuning, with complete elimination in four cases. Moreover, SASFT maintains or even improves the models' performance on six multilingual benchmarks, showing its effectiveness in addressing code-switching while preserving multilingual capabilities. The code and data are available at https://anonymous.4open.science/r/SASFT-71CC.

We propose a new method for controlling linear dynamical systems under adversarial disturbances and cost functions. Our algorithm achieves a running time that scales polylogarithmically with the inverse of the stability margin, improving upon prior methods with polynomial dependence maintaining the same regret guarantees. The technique, which may be of independent interest, is based on a novel convex relaxation that approximates linear control policies using spectral filters constructed from the eigenvectors of a specific Hankel matrix.

Recently, visualization-of-thought (VoT) has unlocked new opportunities for complex spatial reasoning in multimodal large language models (MLLMs) by complementing verbal reasoning with visual thinking. However, the autoregressive accumulation of lengthy and redundant tokens substantially increases computation and memory costs. In this paper, we present a new efficient framework for multimodal spatial reasoning, named *DARE*, designed to adaptively prune multimodal tokens across different network depths, reasoning hops, and modalities. First, *DARE* devises an intra- and inter-hop-aware differentiable retention mechanism to dynamically estimate token importance both within each reasoning step and across successive hops. Recognizing that deeper network layers encode visual cues into verbal streams, *DARE* introduces an asymmetric compression strategy that prunes tokens according to modality-specific redundancy and semantic importance. Furthermore, *DARE* incorporates a progressive KV-cache retention policy aligned with cross-modal fusion dynamics, further reducing memory overhead during autoregressive reasoning. Our method delivers substantial reductions in computation and memory footprint, averaging a 40.37\% reduction in FLOPs and 46.07\% reduction in KV caches usage, while consistently preserving or even improving reasoning performance across seven multimodal spatial reasoning benchmarks, and further generalizing to broader multimodal reasoning tasks, establishing a scalable and robust recipe for efficient multimodal reasoning.

Fine-tuning large vision models (LVMs) and large language models (LLMs) under differentially private federated learning (DPFL) is hindered by a fundamental privacy-utility trade-off. Low-Rank Adaptation (LoRA), a promising parameter-efficient fine-tuning (PEFT) method, reduces computational and communication costs by introducing two trainable low-rank matrices while freezing pre-trained weights. However, directly applying LoRA in DPFL settings leads to performance degradation, especially in LVMs. Our analysis reveals three previously underexplored challenges: (1) gradient coupling caused by the simultaneous update of two asymmetric low-rank matrices, (2) compounded noise amplification under differential privacy, and (3) sharpness of the global aggregated model in the parameter space. To address these issues, we propose LA-LoRA (\textbf{L}ocal \textbf{A}lternating \textbf{LoRA}), a novel approach that decouples gradient interactions and aligns update directions across clients to enhance robustness under stringent privacy constraints. Theoretically, LA-LoRA strengthens convergence guarantees in noisy federated environments. Extensive experiments demonstrate that LA-LoRA achieves state-of-the-art (SOTA) performance on Swin Transformer and RoBERTa models, showcasing robustness to DP noise and broad applicability across both LVMs and LLMs. For example, when fine-tuning the Swin-B model on the Tiny-ImageNet dataset under a strict privacy budget ($\epsilon = 1$), LA-LoRA outperforms the best baseline, RoLoRA, by 16.83\% in test accuracy. Code is provided in the Appendix.

As large language models (LLMs) expand into high-stakes domains like network system operations, evaluating their real-world reliability becomes increasingly critical. However, existing benchmarks risk contamination due to static design, show high statistical variance from limited dataset size, and fail to reflect the complexity of production environments. We introduce NetArena, a dynamic benchmark generation framework for network applications. NetArena features a novel abstraction and unified interface that generalizes across applications, effec- tively addressing the challenges of dynamic benchmarking posed by the diversity of network tasks. At runtime, users can generate unlimited queries on demand. NetArena integrates with network emulators to provide execution-time feedback on correctness, safety, and latency. We demonstrate NetArena on three repre- sentative applications and find that (1) it significantly improve statistical reliability among LLM agents (confidence interval overlap reduced from 85% to 0), (2) agents achieve only 13–38% average performance (as low as 3%) for large-scale, realistic queries, (3) it reveals finer-grained behaviors missed by static, correctness-only benchmarks. NetArena also enables use cases such as SFT and RL fine-tuning on network system tasks. Code is available anonymously at https://anonymous.4open.science/r/netarena_iclr2026-BE94/README.md

Identifying the structure of a partially observed causal system is essential to various scientific fields. Recent advances have focused on constraint-based causal discovery to solve this problem, and yet in practice these methods often face challenges related to multiple testing and error propagation. These issues could be mitigated by a score-based method and thus it has raised great attention whether there exists a score-based greedy search method that can handle the partially observed scenario. In this work, we propose the first score-based greedy search method for the identification of structure involving latent variables with identifiability guarantees. Specifically, we propose Generalized N Factor Model and establish the global consistency: the true structure including latent variables can be identified up to the Markov equivalence class by using score. We then design Latent variable Greedy Equivalence Search (LGES), a greedy search algorithm for this class of model with well-defined operators, which search very efficiently over the graph space to find the optimal structure. Our experiments on both synthetic and real-life data validate the effectiveness of our method.

Complex vehicle routing problems (VRPs) remain a fundamental challenge, demanding substantial expert effort for intent interpretation and algorithm design. While large language models (LLMs) offer a promising path toward automation, current approaches still rely on external intervention, which restrict autonomy and often lead to execution errors and low solution feasibility. To address these challenges, we propose an Agentic Framework with LLMs (AFL) for solving complex vehicle routing problems, achieving full automation from problem instance to solution. AFL directly extracts knowledge from raw inputs and enables self-contained code generation without handcrafted modules or external solvers. To improve trustworthiness, AFL decomposes the overall pipeline into three manageable subtasks and employs four specialized agents whose coordinated interactions enforce cross-functional consistency and logical soundness. Extensive experiments on 20 complex VRPs, ranging from standard benchmarks to practical variants, validate the effectiveness and generality of our framework, showing comparable performance against meticulously designed algorithms. Notably, it substantially outperforms existing LLM-based baselines in both code reliability and solution feasibility, achieving rates close to 100% on the evaluated benchmarks.

Generative sequence models are typically trained on sample sequences from natural or formal languages. It is a crucial question whether—or to what extent—sample-based training is able to capture the true structure of these languages, often referred to as the "world model". Theoretical results indicate that we can hope for soundness at best, that is, generating valid sequences, but not necessarily all of them. However, it is still important to have practical tools that are able to verify whether a given sequence model is sound. In this study, we focus on chess, as it is a domain that provides enough complexity while having a simple rule-based world model. We propose adversarial sequence generation for verifying the soundness of the sequence model. Our adversaries generate valid sequences so as to force the sequence model to generate an invalid next move prediction. Apart from the falsification of soundness, this method is also suitable for a more fine-grained analysis of the failure modes and the effects of different choices during training. To demonstrate this, we propose a number of methods for adversarial sequence generation and evaluate the approach on a large set of chess models. We train models on random as well as high-quality chess games, using several training recipes. We find that none of the models are sound, but some training techniques and dataset choices are able to improve soundness remarkably. We also investigate the potential application of board state probes in both our training and attack methods. Our findings indicate that the extracted board states have no causal role in next token prediction in most of the models.