ICLR 2026 Papers

Language model (LM)-based embodied agents are increasingly deployed in real-world settings. Yet, their adaptability remains limited in dynamic environments, where constructing accurate and flexible world models is crucial for effective reasoning and decision-making. To address this challenge, we extend the Mixture-of-Experts (MoE) paradigm to embodied agents. While conventional MoE architectures modularize knowledge into expert components with pre-trained routing, they remain rigid once deployed, making them less effective for adapting to unseen domains in dynamic environments. We therefore propose Test-time Mixture of World Models (TMoW), a framework that enhances adaptability to unseen and evolving domains. TMoW updates its routing function over world models at test time, unlike conventional MoE where the function remains fixed, enabling agents to recombine existing models and integrate new ones for continual adaptation. It achieves this through (i) multi-granular prototype-based routing, which adapts mixtures across object- to scene-level similarities, (ii) test-time refinement that aligns unseen domain features with prototypes during inference, and (iii) distilled mixture-based augmentation, which efficiently constructs new models from few-shot data and existing prototypes. We evaluate TMoW on VirtualHome, ALFWorld, and RLBench benchmarks, demonstrating strong performance in both zero-shot adaptation and few-shot expansion scenarios, and showing that it enables embodied agents to operate effectively in dynamic environments.

Vision-Language Navigation (VLN) requires an agent to navigate 3D environments following natural language instructions. During navigation, existing agents commonly encounter perceptual uncertainty, such as insufficient evidence for reliable grounding or ambiguity in interpreting spatial cues, yet they typically ignore such information when predicting actions. In this work, we explicitly model three forms of perceptual uncertainty (i.e., geometric, semantic, and appearance uncertainty) and integrate them into the agent’s observation space to enable informed decision-making. Concretely, our agent first constructs a Semantic Gaussian Map (SGM), composed of differentiable 3D Gaussian primitives initialized from panoramic observations, that encodes both the geometric structure and semantic content of the environment. On top of SGM, geometric uncertainty is estimated through variational perturbations of Gaussian position and scale to assess structural reliability; semantic uncertainty is captured by perturbing Gaussian semantic attributes to reveal ambiguous interpretations; and appearance uncertainty is characterized by Fisher Information, which measures the sensitivity of rendered observations to Gaussian-level variations. These uncertainties are incorporated into SGM, extending it into a unified 3D Value Map, which grounds them as affordances and constraints that support reliable navigation. Comprehensive evaluations across multiple VLN benchmarks (i.e., R2R, RxR, REVERIE) demonstrate the effectiveness of our agent. The code will be released.

The past year has witnessed the significant advancement of video-based large language models. However, the challenge of developing a unified model for both short and long video understanding remains unresolved. Most existing video LLMs cannot handle hour-long videos, while methods custom for long videos tend to be ineffective for shorter videos and images. In this paper, we identify the key issue as the redundant content in videos. To address this, we propose a novel pooling strategy that simultaneously achieves token compression and instruction-aware visual feature aggregation. Our model is termed Prompt-guided Pooling LLaVA, or PPLLaVA for short. Specifically, PPLLaVA consists of three core components: the CLIP-based visual-prompt alignment that extracts visual information relevant to the user's instructions, the prompt-guided pooling that compresses the visual sequence to arbitrary scales using convolution-style pooling, and the clip context extension designed for lengthy prompt common in visual dialogue. Extensive experiments have validated the performance of our model. With superior throughput, PPLLaVA achieves better results on image benchmarks as a video LLM, while achieving state-of-the-art performance across various video benchmarks, excelling in tasks ranging from caption generation to multiple-choice questions, and handling video lengths from seconds to hours.

We propose ImitSAT, a branching policy for conflict-driven clause learning (CDCL) solvers based on imitation learning for the Boolean satisfiability problem (SAT). Unlike previous methods that predict instance-level signals to improve CDCL branching indirectly, or rely on reinforcement learning and insufficient CDCL information to enhance branching, ImitSAT learns from expert KeyTrace that collapses a full run into the sequence of surviving decisions. Replaying a KeyTrace on the same instance is nearly conflict-free, providing dense decision- level supervision and directly reducing propagations—the dominant contributor to wall-clock time. This prefix-conditioned supervision enables ImitSAT to reproduce high-quality branches without exploration, yielding faster convergence, stable training, and seamless integration into CDCL. Extensive experiments demonstrate that ImitSAT reduces propagation counts and runtime, outperforming state-of-the-art learned approaches. We released the source code and trained model at https://github.com/zewei-Zhang/ImitSAT.

UV unwrapping is an essential task in computer graphics, enabling various visual editing operations in rendering pipelines. However, existing UV unwrapping methods struggle with time-consuming, fragmentation, lack of semanticity, and irregular UV islands, limiting their practical use. An artist-style UV map must not only satisfy fundamental criteria, such as overlap-free mapping and minimal distortion, but also uphold higher-level standards, including clean boundaries, efficient space utilization, and semantic coherence. We introduce ArtUV, a fully automated, end-to-end method for generating artist-style UV unwrapping. We simulates the professional UV mapping process by dividing it into two stages: surface seam prediction and artist-style UV parameterization. In the seam prediction stage, SeamGPT is used to generate semantically meaningful cutting seams. Then, in the parameterization stage, a rough UV obtained from an optimization-based method, along with the mesh, is fed into an Auto-Encoder, which refines it into an artist-style UV map. Our method ensures semantic consistency and preserves topological structure, making the UV map ready for 2D editing. We evaluate ArtUV across multiple benchmarks and show that it serves as a versatile solution, functioning seamlessly as either a plug-in for professional rendering tools or as a standalone system for rapid, high-quality UV generation.

Information processing in neural populations is inherently constrained by metabolic resource limits and noise properties, with dynamics that are not accurately described by existing mathematical models. Recent data, for example, shows that neurons in mouse visual cortex go into a "low power mode" in which they maintain firing rate homeostasis while expending less energy. This adaptation leads to increased neuronal noise and tuning curve flattening in response to metabolic stress. We have developed a theoretical population coding framework that captures this behavior using two novel, surprisingly simple constraints: an approximation of firing rate homeostasis and an energy limit tied to noise levels via biophysical simulation. A key feature of our contribution is an energy budget model directly connecting adenosine triphosphate (ATP) use in cells to a fully explainable mathematical framework that generalizes existing optimal population codes. Specifically, our simulation provides an energy-dependent dispersed Poisson noise model, based on the assumption that the cell will follow an optimal decay path to produce the least-noisy spike rate that is possible at a given cellular energy budget. Each state along this optimal path is associated with properties (resting potential and leak conductance) which can be measured in electrophysiology experiments and have been shown to change under prolonged caloric deprivation. We analytically derive the optimal coding strategy for neurons under varying energy budgets and coding goals, and show how our method uniquely captures how populations of tuning curves adapt while maintaining homeostasis, as has been observed empirically.

In this paper, we introduce SemHiTok, a unified image Tokenizer via Semantic-Guided Hierarchical codebook (SGHC) that provides consistent discrete representations for multimodal understanding and generation. Recently, unified image tokenizers have sparked exploration within the research community, which is designed to capture high-level semantic features for understanding and retaining low-level pixel features for generation. Previous works attempt to train a unified image tokenizer by combining loss for semantic distillation and pixel reconstruction. However, due to the differing levels of features prioritized by multimodal understanding and generation, joint training methods face significant challenges in achieving a good trade-off. SemHiTok addresses this challenge through a novel semantic-guided hierarchical codebook, which builds pixel sub-codebooks on a pretrained semantic codebook. This design decouples semantic and pixel in both terms of structure and training strategy, enabling the tokenizer to capture pixel features while retaining its ability to comprehend high-level semantic information. Our experiments demonstrate that SemHiTok achieves SOTA performance in image reconstruction and multimodal understanding under the LLaVA-v1.5 setting. Further, we develop a unified MLLM with SemHiTok, which exhibits superior performance across multimodal understanding and generation tasks. For understanding, SemHiTok achieves impressive performance on most benchmarks. For generation, our model achieves SOTA performance on MJHQ30K in unified MLLMs. Our code and models will be open source.

Adam [Kingma & Ba, 2015] is the de facto optimizer in deep learning, yet its theoretical understanding remains limited. Prior analyses show that Adam favors solutions aligned with $\ell_\infty$-geometry, but these results are restricted to the full-batch regime. In this work, we study the implicit bias of incremental Adam (using one sample per step) for logistic regression on linearly separable data, and show that its bias can deviate from the full-batch behavior. As an extreme example, we construct datasets on which incremental Adam provably converges to the $\ell_2$-max-margin classifier, in contrast to the $\ell_\infty$-max-margin bias of full-batch Adam. For general datasets, we characterize its bias using a proxy algorithm for the $\beta_2 \to 1$ limit. This proxy maximizes a data-adaptive Mahalanobis-norm margin, whose associated covariance matrix is determined by a data-dependent dual fixed-point formulation. We further present concrete datasets where this bias reduces to the standard $\ell_2$- and $\ell_\infty$-max-margin classifiers. As a counterpoint, we prove that Signum [Bernstein et al., 2018] converges to the $\ell_\infty$-max-margin classifier for any batch size. Overall, our results highlight that the implicit bias of Adam crucially depends on both the batching scheme and the dataset, while Signum remains invariant.

Code data has been shown to enhance the reasoning capabilities of large language models (LLMs), but it remains unclear which aspects of code are most responsible. We investigate this question with a systematic, data-centric framework. We construct parallel instruction datasets in ten programming languages and apply controlled perturbations that selectively disrupt structural or semantic properties of code. We then finetune LLMs from five model families and eight scales on each variant and evaluate their performance on natural language, math, and code tasks. Across 3,331 experiments, our results show that LLMs are more vulnerable to structural perturbations than semantic ones, particularly on math and code tasks. Appropriate abstractions like pseudocode and flowcharts can be as effective as code, while encoding the same information with fewer tokens without adhering to original syntax can often retain or even improve performance. Remarkably, even corrupted code with misleading signals remains competitive when surface-level regularities persist. Finally, syntactic styles also shape task-specific gains with Python favoring natural language reasoning and lower-level languages such as Java and Rust favoring math. Through our systematic framework, we aim to provide insight into how different properties of code influence reasoning and inform the design of training data for enhancing LLM reasoning capabilities.

We study the problem of graph and hypergraph sparsification in insertion-only data streams. The input is a hypergraph $H=(V, E, w)$ with $n$ nodes, $m$ hyperedges, and rank $r$, and the goal is to compute a hypergraph $\widehat{H}$ that preserves the energy of each vector $x \in \mathbb{R}^n$ in $H$, up to a small multiplicative error. In this paper, we give a streaming algorithm that achieves a $(1+\varepsilon)$-approximation, using $\mathcal{O}\left(\frac{rn}{\varepsilon^2} \log^2 n \log r\right) \cdot$ poly $(\log \log m)$ bits of space, matching the sample complexity of the best known offline algorithm up to poly $(\log \log m)$ factors. Our approach also provides a streaming algorithm for graph sparsification that achieves a $(1+\varepsilon)$-approximation, using $\mathcal{O}\left(\frac{n}{\varepsilon^2} \log n\right)\cdot\text{poly}(\log\log n)$ bits of space, improving the current bound by $\log n$ factors. Furthermore, we give a space-efficient streaming algorithm for min-cut approximation. Along the way, we present an online algorithm for $(1+\varepsilon)$-hypergraph sparsification, which is optimal up to poly-logarithmic factors. Hence, we achieve $(1+\varepsilon)$-hypergraph sparsification in the sliding window model, with space optimal up to poly-logarithmic factors. Lastly, we give an adversarially robust algorithm for hypergraph sparsification using $\frac{n}{\varepsilon^2} \cdot $ poly $(r, \log n, \log r, \log \log m)$ bits of space.

With the rapid growth of spatio-temporal data fueled by IoT deployments and urban infrastructure expansion, accurate and efficient continual forecasting has become a critical challenge. Most existing Spatio-Temporal Graph Neural Networks rely on static graph structures and offline training, rendering them inadequate for real-world streaming scenarios characterized by graph expansion and distribution shifts. Although Continual Spatio-Temporal Forecasting methods have been proposed to tackle these issues, they often adopt backbones with limited modeling capacity and lack effective mechanisms to balance stability and adaptability. To overcome these limitations, we propose STBP, a novel framework that integrates a general spatio-temporal backbone with a scalable contextual pattern bank. The backbone extracts stable representations in the frequency domain and captures dynamic spatial correlations through lightweight linear graph attention. To support continual adaptation and mitigate catastrophic forgetting, the contextual pattern bank is updated incrementally via parameter expansion, enabling the capture of evolving node-level heterogeneity and relevance. During incremental training, the backbone remains fixed to preserve general knowledge, while the pattern bank adapts to new scenarios and distributions. Extensive experiments demonstrate that STBP outperforms state-of-the-art baselines in both forecasting accuracy and scalability, validating its effectiveness for continual spatio-temporal forecasting. Code is available at https://github.com/Aoyu-Liu/STBP.

Membrane potential perturbation dynamic (MPPD) is an emerging approach to capture perturbation intensity and stabilize the performance of spiking neural networks (SNN). It discards the neuronal reset part to intuitively reduce fluctuations of dynamics, but this treatment may be insufficient in perturbation characterization. In this study, we prove that MPPD is total variation (TV), which is a widely-used methodology for robust signal reconstruction. Moreover, we propose a novel TV-$\ell_1$ framework for MPPD, which allows for a wider range of network functions and has better denoising advantage than the existing TV-$\ell_2$ framework, based on the coarea formula. Experiments show that MPPD-TV-$\ell_1$ achieves robust performance in both Gaussian noise training and adversarial training for image classification tasks. This finding may provide a new insight into the essence of perturbation characterization.

Quality-Diversity (QD) algorithms constitute a branch of optimization that is concerned with discovering a diverse and high-quality set of solutions to an optimization problem. Current QD methods commonly maintain diversity by dividing the behavior space into discrete regions, ensuring that solutions are distributed across different parts of the space. The QD problem is then solved by searching for the best solution in each region. This approach to QD optimization poses challenges in large solution spaces, where storing many solutions is impractical, and in high-dimensional behavior spaces, where discretization becomes ineffective due to the curse of dimensionality. We present an alternative framing of the QD problem, called \emph{Soft QD}, that sidesteps the need for discretizations. We validate this formulation by demonstrating its desirable properties, such as monotonicity, and by relating its limiting behavior to the widely used QD Score metric. Furthermore, we leverage it to derive a novel differentiable QD algorithm, \emph{Soft QD Using Approximated Diversity (SQUAD)}, and demonstrate empirically that it is competitive with current state of the art methods on standard benchmarks while offering better scalability to higher dimensional problems.

Autoregressive models (ARMs) are hindered by slow sequential inference. While masked diffusion models (MDMs) offer a parallel alternative, they suffer from critical drawbacks: high computational overhead from precluding Key-Value (KV) caching, and incoherent generation arising from learning dependencies over an intractable space of token combinations. To address these limitations, we introduce ReFusion, a novel masked diffusion model that achieves superior performance and efficiency by elevating parallel decoding from the token level to a higher slot level, where each slot is a fixed-length, contiguous sub-sequence. This is achieved through an iterative ``plan-and-infill'' decoding process: a diffusion-based planning step first identifies a set of weakly dependent slots, and an autoregressive infilling step then decodes these selected slots in parallel. The slot-based design simultaneously unlocks full KV cache reuse with a unified causal framework and reduces the learning complexity from the token combination space to a manageable slot-level permutation space. Extensive experiments on seven diverse benchmarks show that ReFusion not only overwhelmingly surpasses prior MDMs with 32\% performance gains and an over 10$\times$ speedup on average, but also bridges the performance gap to strong ARMs while maintaining a 1.4$\times$ average speedup.

Although multi-view multi-label learning has been extensively studied, research on the dual-missing scenario, where both views and labels are incomplete, remains largely unexplored. Existing methods mainly rely on contrastive learning or information bottleneck theory to learn consistent representations under missing-view conditions, but relying solely on loss-based constraints limits the ability to capture stable and discriminative shared semantics. To address this issue, we introduce a more structured mechanism for consistent representation learning: we learn discrete consistent representations through a multi-view shared codebook and cross-view reconstruction, which naturally align different views within the limited shared codebook embeddings and reduce redundant features. At the decision level, we design a weight estimation method that evaluates the ability of each view to preserve label correlation structures, assigning weights accordingly to enhance the quality of the fused prediction. In addition, we introduce a fused-teacher self-distillation framework, where the fused prediction guides the training of view-specific classifiers and feeds the global knowledge back into the single-view branches, thereby enhancing the generalization ability of the model under missing-label conditions. The effectiveness of our proposed method is thoroughly demonstrated through extensive comparative experiments with advanced methods on five benchmark datasets.

Imputing missing node features in graphs is challenging, particularly under high missing rates. Existing methods based on latent representations or global diffusion often fail to produce reliable estimates, and may propagate errors across the graph. We propose FSD-CAP, a two-stage framework designed to improve imputation quality under extreme sparsity. In the first stage, a graph-distance-guided subgraph expansion localizes the diffusion process. A fractional diffusion operator adjusts propagation sharpness based on local structure. In the second stage, imputed features are refined using class-aware propagation, which incorporates pseudo-labels and neighborhood entropy to promote consistency. We evaluated FSD-CAP on multiple datasets. With 99.5% of features missing across five benchmark datasets, FSD-CAP achieves average accuracies of 80.06% (structural) and 81.01% (uniform) in node classification, close to the 81.31% achieved by a standard GCN with full features. For link prediction under the same setting, it reaches AUC scores of 91.65% (structural) and 92.41% (uniform), compared to 95.06% for the fully observed case. Furthermore, FSD-CAP demonstrates superior performance on both large-scale and heterophily datasets when compared to other models. Code conducting all experiments can be found at https://anonymous.4open.science/r/FSD-CAP-50E8.

We present Aurelius, a new framework that enables relation aware text-to-audio (TTA) generation research at scale. Given the lack of essential audio event and relation corpora, \emph{Aurelius} contributes a large-scale audio event corpus \emph{AudioEventSet} and another large-scale relation corpus \emph{AudioRelSet}. Comprising 110 event categories, AudioEventSet maximally covers all commonly heard audio events and each event is unique, realistic and of high-quality. AudioRelSet consists of 100 relations, comprehensively covering the relations that present in the physical world or can be neatly described by text. As the two corpora provide audio event and relation independently, they can be combined to create massive <text,audio> pairs with our pair generation strategy to support relation aware TTA investigation at scale. We comprehensively benchmark all existing TTA models from both general and relation aware evaluation perspective. We further provide in-depth investigation on scaling up existing TTA models' relation aware generation by either training from scratch or leveraging cross-domain general TTA knowledge. The introduced corpora and the findings through investigation in this work potentially facilitate future research on relation aware TTA generation.

Fairness has become an arising concern in machine learning with its prevalence in decision-making processes, and the trade-offs between various fairness notions and between fairness and accuracy has been empirically observed. However, the inheritance of such trade-offs, as well as the quantification of the best achievable trade-offs, i.e., the Pareto optimal trade-offs, under varied constraints on fairness notions has been rarely and improperly discussed. Owing to the sub-optimality of fairness interventions, existing work fails to provide informative characterization regarding these trade-offs. In light of existing limitations, in this work, we propose a reformulation of the model-specific (MS) Pareto optimal trade-off, where we frame it as convex optimization problems involving fairness notions and accuracy w.r.t. the confusion vector. Our formulation provides an efficient approximation of the best achievable accuracy under dynamic fairness constraints, and yields systematical analysis regarding the fairness-accuracy trade-off. Going beyond the discussion on fairness-accuracy trade-offs, we extend the discussion to the trade-off between fairness notions, which characterizes the impact of accuracy on the compatibility between fairness notions. Inspired by our reformulation, we propose a last-layer retraining framework with group-dependent bias, and we prove theoretically the superiority of our method over existing baselines. Experimental results demonstrate the effectiveness of our method in achieving better fairness-accuracy trade-off, and that our MS Pareto frontiers sufficiently quantify the two trade-offs.

We study the learnability of languages in the *Next Symbol Prediction* (NSP) setting, where a learner receives only positive examples from a language together with, for every prefix, (i) whether the prefix itself is in the language and (ii) which next symbols can lead to an accepting string. This setting has been used in prior work to empirically analyze neural sequence models, and additionally, we observe that efficient algorithms for the NSP setting can be used to learn the (truncated) support of language models. We first show that the class of DFAs with at most $n$ states is identifiable from positive examples augmented with these NSP labels. Nevertheless, even with this richer supervision, we show that PAC-learning DFAs remains computationally hard, and exact identification using only membership queries cannot be achieved in polynomial time. We then present $\mathrm{L_{nsp}^{\star}}$, an extension of Angluin’s $\mathrm{L}^{\star}$ algorithm, and show that DFAs can be PAC-learned efficiently using a language-model–based teacher that answers membership queries and generates valid strings conditioned on prefix prompts. Finally, we conduct a comprehensive experimental evaluation on 11 regular languages of varying complexity. Using $\mathrm{L}^{\star}_{\text{nsp}}$, we extract DFAs from Transformer-based language models trained on regular languages to evaluate the algorithm’s effectiveness and identify erroneous examples.