ICLR 2026 Papers

Mathematical problem solving remains a challenging test of reasoning for large language and multimodal models, yet existing benchmarks are limited in size, language coverage, and task diversity. We introduce *MathNet*, a large-scale, high-quality, multilingual, and multimodal dataset of Olympiad-level problems. MathNet spans 40 countries, 10 languages, and two decades of competitions, comprising 17,512 **expert-authored problems with solutions** across diverse domains. *MathNet* supports three tasks: (i) *mathematical comprehension*, (ii) *mathematical retrieval*, an underexplored but essential capability and (iii) *Math RAG*, which evaluates how retrieval-augmented generation improves problem solving. For retrieval, we construct 39K pairs of mathematically equivalent problems to enable equivalence-based evaluation, in addition to 70 expert-curated pairs from real competitions. Experimental results show that even state-of-the-art reasoning models (76.8% for GPT-5 and 46.8% for Claude 4.5 Opus) are challenged, while embedding models struggle to retrieve equivalent problems. Finally, we show that LLM performance in RAG-based math problem solving is highly sensitive to retrieval quality; for example, DeepSeek-V3.2-Speciale achieves gains of up to 12%, obtaining the highest scores on the benchmark. *MathNet* provides the largest high-quality Olympiad dataset and the first retrieval benchmark for problem equivalence. We publicly release both the dataset and benchmark at http://mathnet.netlify.app/.

Spatial reasoning is fundamental to auditory perception, yet current audio large language models (ALLMs) largely rely on unstructured binaural cues and single- step inference. This limits both perceptual accuracy in direction and distance estimation and the capacity for interpretable reasoning. Recent work such as BAT demonstrates spatial QA with binaural audio, but its reliance on coarse categorical labels (left, right, up, down) and the absence of explicit geometric supervision constrain resolution and robustness. We introduce the $\textbf{Spatial-Acoustic Geometry Encoder (SAGE}$), a geometry-aware audio encoder that aligns binaural acoustic features with 3D spatial structure using panoramic depth images and room-impulse responses at training time, while requiring only audio at inference. Building on this representation, we present $\textbf{OWL}$, an ALLM that integrates $\textbf{SAGE}$ with a spatially grounded chain-of-thought to rationalize over direction-of-arrivals (DoA) and distance estimates. Through curriculum learning from perceptual QA to multi-step reasoning, $\textbf{OWL}$ supports o’clock-level azimuth and DoA estimation. To enable large-scale training and evaluation, we construct and release $\textbf{BiDepth}$, a dataset of over one million QA pairs combining binaural audio with panoramic depth images and room impulse responses across both in-room and out-of-room scenarios. Across two benchmark datasets, our new $\textbf{BiDepth}$ and the public SpatialSoundQA, $\textbf{OWL}$ reduces mean DoA error by $\textbf{11$^{\circ}$}$ through $\textbf{SAGE}$ and improves spatial reasoning QA accuracy by up to $\textbf{25}$% over BAT. Our dataset and code are available at: https://anonymous.4open.science/r/OWL-ICLR-26/

Modern machine learning problems are frequently formulated in federated learning domain and incorporate inherently heterogeneous data. Weighting methods operate efficiently in terms of iteration complexity and represent a common direction in this setting. At the same time, they do not address directly the main obstacle in federated and distributed learning -- communication bottleneck. We tackle this issue by incorporating compression into the weighting scheme. We establish the convergence under a convexity assumption, considering both exact and stochastic oracles. Finally, we evaluate the practical performance of the proposed method on real-world problems.

Despite strong single-turn performance, diffusion-based image compositing often struggles to preserve coherent spatial relations in pairwise or sequential edits, where subsequent insertions may overwrite previously generated content and disrupt physical consistency. We introduce PICS, a self-supervised composition-by-decomposition paradigm that composes objects in parallel while explicitly modeling the compositional interactions among (fully-/partially-)visible objects and background. At its core, an Interaction Transformer employs mask-guided Mixture-of-Experts to route background, exclusive, and overlap regions to dedicated experts, with an adaptive $\alpha$-blending strategy that infers a compatibility-aware fusion of overlapping objects while preserving boundary fidelity. To further enhance robustness to geometric variations, we incorporate geometry-aware augmentations covering both out-of-plane and in-plane pose changes of objects. Our method delivers superior pairwise compositing quality and substantially improved stability, with extensive evaluations across virtual try-on, indoor, and street scene settings showing consistent gains over state-of-the-art baselines.

Variance-dependent regret bounds for linear contextual bandits, which improve upon the classical $\tilde{O}(d\sqrt{K})$ regret bound to $\tilde{O}(d\sqrt{\sum_{k=1}^K\sigma_k^2})$, where $d$ is the context dimension, $K$ is the number of rounds, and $\sigma^2_k$ is the noise variance in round $k$, has been widely studied in recent years. However, most existing works focus on the regret upper bounds instead of lower bounds. To our knowledge, the only lower bound is from Jia et al. (2024), which proved that for any eluder dimension $d_{\textbf{elu}}$ and total variance budget $\Lambda$, there exists an instance with $\sum_{k=1}^K\sigma_k^2\leq \Lambda$ for which any algorithm incurs a variance-dependent lower bound of $\Omega(\sqrt{d_{\textbf{elu}}\Lambda})$. However, this lower bound has a $\sqrt{d}$ gap with existing upper bounds. Moreover, it only considers a fixed total variance budget $\Lambda$ and does not apply to a general variance sequence $\{\sigma_1^2,\ldots,\sigma_K^2\}$. In this paper, to overcome the limitations of Jia et al. (2024), we consider the general variance sequence under two settings. For a prefixed sequence, where the entire variance sequence is revealed to the learner at the beginning of the learning process, we establish a variance-dependent lower bound of $\Omega(d \sqrt{\sum_{k=1}^K\sigma_k^2 }/\log K)$ for linear contextual bandits. For an adaptive sequence, where an adversary can generate the variance $\sigma_k^2$ in each round $k$ based on historical observations, we show that when the adversary must generate $\sigma_k^2$ before observing the decision set $D_k$, a similar lower bound of $\Omega(d\sqrt{ \sum_{k=1}^K\sigma_k^2} /\log^6(dK))$ holds. In both settings, our results match the upper bounds of the SAVE algorithm (Zhao et al. 2023) up to logarithmic factors. Furthermore, if the adversary can generate the variance $\sigma_k$ after observing the decision set $D_k$, we construct a counter-example showing that it is impossible to construct a variance-dependent lower bound if the adversary properly selects variances in collaboration with the learner. Our lower bound proofs use a novel peeling technique that groups rounds by variance magnitude. For each group, we construct separate instances and assign the learner distinct decision sets. We believe this proof technique may be of independent interest.

Multimodal Large Language Models (MLLMs) have shown remarkable performance in vision-language tasks, such as image captioning and visual question answering. However, these models often struggle with fine-grained visual understanding and are prone to hallucinations, primarily due to over-reliance on linguistic priors that distract them from leveraging actual visual information. This results in outputs that are often unanchored in the visual content, leading to errors. To address these challenges, we introduce MMGrounded-PostAlign, a post-multimodal alignment framework designed to enhance the visual understanding capabilities of MLLMs and mitigate hallucinations. In the framework, the visual grounding module identifies the referred objects in the image, while the textual grounding module generates the rationale for the final answer. This dual grounding approach ensures that outputs are firmly anchored in both visual and textual evidence. In particular, we incorporate a negative rejection mechanism within the visual grounding module to distinguish between grounded entities and non-existent objects influenced by linguistic biases. Moreover, we propose a selective reasoning mechanism within the textual grounding module to adjust the model’s reasoning strategy based on the complexity of the query. These innovations together work to resolve the issues associated with hallucinations and enhance the overall alignment between visual and textual modalities. Extensive evaluations on benchmarks such as POPE, HaloQuest, ReasonSeg, MME, and MMBench demonstrate significant improvements in fine-grained visual understanding and hallucination suppression, showcasing the effectiveness of our approach in real-world multimodal tasks.

Large language models (LLMs) excel at complex reasoning but remain limited by static and incomplete parametric knowledge. Retrieval-augmented generation (RAG) mitigates this by incorporating external knowledge, yet existing RAGs struggle with knowledge-intensive tasks due to fragmented information and weak modeling of knowledge structure. Graphs offer a natural way to model relationships within knowledge, but LLMs are inherently unstructured and cannot effectively reason over graph-structured data. Recent graph-enhanced RAG (GraphRAG) attempts to bridge this gap by constructing tailored graphs and enabling LLMs to reason on them. However, these methods often depend on ad-hoc graph designs, heuristic search, or costly agent pipelines, which hinder scalability and generalization. To address these challenges, we present G-reasoner, a unified framework that integrates graph and language foundation models for scalable reasoning over diverse graph-structured knowledge. Central to our approach is QuadGraph, a standardized four-layer abstraction that unifies heterogeneous knowledge sources into a common graph representation. Building on this, we introduce a 34M-parameter graph foundation model (GFM) that jointly captures graph topology and textual semantics, and is integrated with LLMs to enhance reasoning in downstream applications. To ensure scalability and efficiency, mixed-precision training and distributed message-passing are implemented to scale GFM with more GPUs. Extensive experiments on six benchmarks show that G-reasoner consistently outperforms state-of-the-art baselines, significantly enhances LLM reasoning, and achieves strong efficiency and cross-graph generalization.

LLMs can perform multi-step reasoning through Chain-of-Thought (CoT), but they cannot reliably verify their own logic. Even when they reach correct answers, the underlying reasoning may be flawed, undermining trust in high-stakes scenarios. To mitigate this issue, we introduce VeriCoT, a neuro-symbolic method that extracts and verifies formal logical arguments from CoT reasoning. VeriCoT formalizes each CoT reasoning step into first-order logic and identifies premises that ground the argument in source context, commonsense knowledge, or prior reasoning steps. The symbolic representation enables automated solvers to verify logical validity while the NL premises allow humans and systems to identify ungrounded or fallacious reasoning steps. Experiments on the ProofWriter, LegalBench, and BioASQ datasets show VeriCoT effectively identifies flawed reasoning, and serves as a strong predictor of final answer correctness. We also leverage VeriCoT’s verification signal for (1) inference-time self-reflection, (2) supervised fine-tuning (SFT) on VeriCoT-distilled datasets and (3) preference fine-tuning (PFT) with direct preference optimization (DPO) using verification-based pairwise rewards, further improving reasoning validity and accuracy.

We introduce WARP (**W**eight-space **A**daptive **R**ecurrent **P**rediction), a simple yet powerful model that unifies weight-space learning with linear recurrence to redefine sequence modeling. Unlike conventional recurrent neural networks (RNNs) which collapse temporal dynamics into fixed-dimensional hidden states, WARP explicitly parametrizes its hidden state as the weights and biases of a distinct auxiliary neural network, and uses input differences to drive its recurrence. This brain-inspired formulation enables efficient gradient-free adaptation of the auxiliary network at test-time, in-context learning abilities, and seamless integration of domain-specific physical priors. Empirical validation shows that WARP matches or surpasses state-of-the-art baselines on diverse classification tasks, featuring in the top three in 4 out of 6 real-world challenging datasets. Furthermore, extensive experiments across sequential image completion, multivariate time series forecasting, and dynamical system reconstruction demonstrate its expressiveness and generalization capabilities. Remarkably, a physics-informed variant of our model outperforms the next best model by more than 10x. Ablation studies confirm the architectural necessity of key components, solidifying weight-space linear RNNs as a transformative paradigm for adaptive machine intelligence.

Embodied navigation is a foundational challenge for intelligent robots, demanding the ability to comprehend visual environments, follow natural language instructions, and explore autonomously. However, existing models struggle to provide a unified solution across heterogeneous navigation paradigms, often yielding low success rates and limited generalization. We present OmniNav, a unified framework that handles instruct-goal, object-goal, point-goal navigation, and frontier-based exploration within a single architecture. First, we introduce a lightweight, low-latency policy that predicts continuous-space waypoints (coordinates and orientations) with high accuracy, outperforming action-chunk methods in precision and supporting real-world deployment with control frequencies up to 5 Hz. Second, at the architectural level, OmniNav proposes a fast-slow system design: a fast module performs waypoint generation from relatively short-horizon visual context and subtasks, while a slow module conducts deliberative planning using long-horizon observations and candidate frontiers to select the next subgoal and subtask. This collaboration improves path efficiency and maintains trajectory coherence in exploration and memory-intensive settings. Notably, we find that the primary bottleneck lies not in navigation policy learning per se, but in robust understanding of general instructions and objects. To enhance generalization, we incorporate large-scale general-purpose training datasets including those used for image captioning and referring/grounding into a joint multi-task regimen, which substantially boosts success rates and robustness. Extensive experiments demonstrate state-of-the-art performance across diverse navigation benchmarks, and real-world deployment further validates the approach. OmniNav offers practical insights for embodied navigation and points to a scalable path toward versatile, highly generalizable robotic intelligence.

Tool use represents a critical capability for AI agents, with recent advances focusing on leveraging reinforcement learning (RL) for test-time scaling to achieve better performance through more deliberate reasoning. However, there are some key challenges in current RL-based scaling approaches: (a) direct RL training often struggles to scale up thinking length sufficiently to solve complex problems, and (b) scaled-up models tend to overthink simpler problems, resulting in substantial token inefficiency. To address these challenges, we propose a novel training paradigm that first employs warm-up supervised fine-tuning to help models distinguish between simple and complex problems, followed by RL that enable models to automatically determine appropriate reasoning trajectories. Furthermore, to tackle the issue of automatic thinking-length scaling, we discover that entropy-based optimization objectives effectively maintain model diversity while successfully unlocking the model's scaling capabilities. Based on this insight, we introduce an entropy-based long-short reasoning fusion RL strategy. Our experiments on three benchmarks demonstrate that model successfully achieves auto-scaling for efficient tool use, achieving significant 9.8\% accuracy improvements while reducing computational overhead by ~81\%.

Generative classifiers, which leverage conditional generative models for classification, have recently demonstrated desirable properties such as robustness to distribution shifts. However, recent progress in this area has been largely driven by diffusion-based models, whose substantial computational cost limits their scalability in practice. To address the efficiency concern, we investigate generative classifier built upon recent advances in visual autoregressive (VAR) modeling. Owing to their tractable likelihood, VAR-based generative classifier enable significantly more efficient inference compared to diffusion-based counterparts. Building on this foundation, we introduce the Adaptive VAR Classifier$^+$ (A-VARC$^+$), which further improves accuracy while reducing computational cost, substantially enhancing practical usability. Beyond efficiency, we also study several properties of VAR-based generative classifiers that distinguish them from conventional discriminative models. In particular, the tractable likelihood facilitates visual explainability via token-wise mutual information, and the model naturally adapts to class-incremental learning without requiring additional replay data.

Recent advancements in diffusion-based text synthesis have demonstrated significant performance in inserting and editing text within images via inpainting. However, despite the potential of text inpainting methods, three key limitations hinder their applicability to broader Text Image Manipulation (TIM) tasks: (i) the inability to remove text, (ii) the lack of control over the style of rendered text, and (iii) a tendency to generate duplicated letters. To address these challenges, we propose OmniText, a training-free generalist capable of performing a wide range of TIM tasks. Specifically, we investigate two key properties of cross- and self-attention mechanisms to enable text removal and to provide control over both text styles and content. Our findings reveal that text removal can be achieved by applying self-attention inversion, which mitigates the model's tendency to focus on surrounding text, thus reducing text hallucinations. Additionally, we redistribute cross-attention, as increasing the probability of certain text tokens reduces text hallucination. For controllable inpainting, we introduce novel loss functions in a latent optimization framework: a cross-attention content loss to improve text rendering accuracy and a self-attention style loss to facilitate style customization. Furthermore, we present OmniText-Bench, a benchmark dataset for evaluating diverse TIM tasks. It includes input images, target text with masks, and style references, covering diverse applications such as text removal, rescaling, repositioning, and insertion and editing with various styles. Our OmniText framework is the first generalist method capable of performing diverse TIM tasks. It achieves state-of-the-art performance across multiple tasks and metrics compared to other text inpainting methods and is comparable with specialist methods.

Multimodal Large Language Models (MLLMs) have achieved significant advances in integrating visual and linguistic information, yet their ability to reason about complex and real-world scenarios remains limited. Existing benchmarks are usually constructed in a task-oriented manner, without a guarantee that different task samples come from the same data distribution. Therefore, they often fall short in evaluating the synergistic effects of lower-level perceptual capabilities on higher-order reasoning. To lift this limitation, we contribute Lens, a multi-level evaluation benchmark of multimodal reasoning with with 3.4K contemporary images and 60K+ human-authored questions covering eight tasks and 12 daily scenarios, forming three progressive task tiers, i.e., perception, understanding, and reasoning. One feature is that each image is equipped with rich annotations for all tasks. Thus, this data set intrinsically supports evaluating MLLMs to handle image-invariable prompts, from basic perception to compositional reasoning. In addition, our images have been collected manually from social media, with $53$% published after Jan. 2025. We evaluate 15+ frontier MLLMs such as Qwen2.5-VL, InternVL3, GPT-4o and two reasoning models QVQ-Max and Kimi-VL. Most models were released in 2025, and none of them achieve an accuracy beyond $60$% in the reasoning tasks. Furthermore, we propose the Self-Driven Multi-Expert Collaborative Framework (SMEC), a framework designed for MLLMs that simulates a panel of experts discussing and exchanging viewpoints via self-generated role-specific prompts. The experimental results confirm the existence of synergistic effects in a hierarchical task structure, where low-level tasks facilitate the reasoning of MLLMs on more complex, high-level tasks. Statistical analysis and ablation studies further demonstrate the comprehensiveness of our dataset and the superiority of our methodology.

Semantic caches return cached responses for semantically similar prompts to reduce LLM inference latency and cost. They embed cached prompts and store them alongside their response in a vector database. Embedding similarity metrics assign a numerical score to quantify the similarity between a request and its nearest neighbor prompt from the cache. Existing systems use the same static similarity threshold across all requests to determine whether two prompts can share similar responses. However, we observe that static thresholds do not give formal correctness guarantees, result in unexpected error rates, and lead to suboptimal cache hit rates. This paper proposes vCache, the first verified semantic cache with user-defined error rate guarantees for predictable performance. It employs an online learning algorithm to estimate an optimal threshold for each cached prompt, enabling reliable cache responses without additional training. Our experiments show that vCache consistently meets the specified error bounds while outperforming state-of-the-art static-threshold and fine-tuned embedding baselines with up to 12.5$\times$ higher cache hit and 26$\times$ lower error rates. We release the vCache implementation and four benchmarks to support future research.

We propose a statistical benchmark for diffusion posterior sampling (DPS) algorithms in linear inverse problems. Our test signals are discretized Lévy processes whose posteriors admit efficient Gibbs methods. These Gibbs methods provide gold-standard posterior samples for direct, distribution-level comparisons with DPS algorithms. They can also sample the denoising posteriors in the reverse diffusion, which enables the arbitrary-precision Monte Carlo estimation of various objects that may be needed in the DPS algorithms, such as the expectation or the covariance of the denoising posteriors. In turn, this can be used to isolate algorithmic errors from the errors due to learned components. We instantiate the benchmark with the minimum-mean-squared-error optimality gap and posterior-coverage tests and evaluate popular algorithms on the inverse problems of denoising, deconvolution, imputation, and reconstruction from partial Fourier measurements. We release the benchmark code at https://github.com/emblem-saying/dps-benchmark and invite the community to contribute and report results.

A popular method to adapt large language models (LLMs) to new tasks is in-context learning (ICL), which is effective but incurs high inference costs as context length grows. In this paper we propose a method to perform instruction induction, where we take training examples and reduce them to a compact but descriptive prompt that can achieve performance comparable to ICL over the full training set. Specifically, we propose Prompt-MII, a reinforcement learning (RL) based framework to meta-learn an instruction induction model that can generate compact instructions on the fly for an arbitrary new dataset. We train on over 3,000 diverse classification datasets from the HuggingFace hub, and evaluate on 90 unseen tasks. Prompt-MII improves downstream model quality by 4-9 F1 points (10-20\% relative), matching ICL performance while requiring 3-13x fewer tokens.

The merit of Conformal Prediction (CP), as a distribution-free framework for uncertainty quantification, depends on generating prediction sets that are efficient, reflected in small average set sizes, while adaptive, meaning they signal uncertainty by varying in size according to input difficulty. A central limitation for deep conformal classifiers is that the nonconformity scores are derived from softmax outputs, which can be unreliable indicators of how certain the model truly is about a given input, sometimes leading to overconfident misclassifications or undue hesitation. In this work, we argue that this unreliability can be inherited by the prediction sets generated by CP, limiting their capacity for adaptiveness. We propose a new approach that leverages information from the pre-softmax logit space, using the Helmholtz Free Energy as a measure of model uncertainty and sample difficulty. By reweighting nonconformity scores with a monotonic transformation of the energy score of each sample, we improve their sensitivity to input difficulty. Our experiments with four state-of-the-art score functions on multiple datasets and deep architectures show that this energy-based enhancement improves the adaptiveness of the prediction sets, leading to a notable increase in both efficiency and adaptiveness compared to baseline nonconformity scores, without introducing any post-hoc complexity.

In large language model (LLM) serving, reusing the key-value (KV) cache of prompts across requests is a key technique for reducing time-to-first-token (TTFT) and lowering serving costs. Cache-affinity scheduling, which co-locates requests with the same prompt prefix to maximize KV cache reuse, often conflicts with load-balancing scheduling, which aims to distribute requests evenly across compute instances. Existing schedulers struggle to reconcile this trade-off, as they operate within a single mapping space, typically applying cache-affinity routing to a subset of requests and load-balanced routing to the rest, without a unified solution to achieve both goals. To overcome this limitation, we propose DualMap, a dual-mapping scheduling strategy for distributed LLM serving that simultaneously enables cache affinity and load balancing. The key idea of DualMap is to map each request to two candidate instances using two independent hash functions based on the request prompt, and then intelligently select the better candidate based on current system states. This design increases the likelihood that requests with shared prefixes are co-located, while evenly dispersing distinct prefixes across the cluster via ``the power of two choices''. To make DualMap robust under dynamic and skewed real-world workloads, we incorporate three techniques: 1) SLO-aware request routing, which prioritizes cache affinity but switches to load-aware scheduling when TTFT exceeds the SLO, enhancing load balance without sacrificing cache reuse; 2) hotspot-aware rebalancing, which dynamically migrates requests from overloaded to underloaded instances, mitigating hotspots and rebalancing the system; 3) lightweight dual-hash-ring scaling, which leverages a dual-hash-ring mapping to support fast and low-overhead instance scaling without costly global remapping. Experiments on real-world workloads show that DualMap improves effective request capacity by up to 2.25$\times$ under the same TTFT SLO constraints, compared with the state-of-the-art work.