ICLR 2026 Papers

Large Language Models (LLMs) have made remarkable progress in mathematical reasoning, but still continue to struggle with high-precision tasks like numerical computation and formal symbolic manipulation. Integrating external tools has emerged as a promising approach to bridge this gap. Despite recent advances, existing methods struggle with three key challenges: constructing tool-integrated reasoning data, performing fine-grained optimization, and enhancing inference. To overcome these limitations, we propose THOR (Tool-Integrated Hierarchical Optimization via RL). First, we introduce TIRGen, a multi-agent based pipeline for constructing high-quality datasets of tool-integrated reasoning paths, aligning with the policy and generalizing well across diverse models. Second, to perform fine-grained hierarchical optimization, we introduce an RL strategy that jointly optimizes for both episode-level problem solving and step-level code generation. This is motivated by our key insight that the success of an intermediate tool call is a strong predictor of the final answer's correctness. Finally, THOR incorporates a self-correction mechanism that leverages immediate tool feedback to dynamically revise erroneous reasoning paths during inference. Our approach demonstrates strong generalization across diverse models, performing effectively in both reasoning and non-reasoning models. It further achieves state-of-the-art performance for models of a similar scale on multiple mathematical benchmarks, while also delivering consistent improvements on code benchmarks. Our code will be publicly available at https://github.com/JingMog/THOR.

Large language models (LLMs) are increasingly integrated in software development, but ensuring correctness in LLM-generated code remains challenging and often requires costly manual review. Verifiable code generation---jointly generating code, specifications, and proofs of code-specification alignment---offers a promising path to address this limitation and further unleash LLMs' benefits in coding. Yet, there exists a significant gap in evaluation: current benchmarks often focus on only individual components rather than providing a holistic evaluation framework of all tasks. In this paper, we introduce VERINA (Verifiable Code Generation Arena), a high-quality benchmark enabling a comprehensive and modular evaluation of code, specification, and proof generation as well as their compositions. VERINA consists of 189 manually curated coding tasks in Lean, with detailed problem descriptions, reference implementations, formal specifications, and extensive test suites. Our extensive evaluation of state-of-the-art LLMs reveals significant challenges in verifiable code generation, especially in proof generation, underscoring the need for improving LLM-based theorem provers in verification domains. The best model, OpenAI o3, achieves a 72.6% code correctness rate, 52.3% for specification soundness and completeness, and a mere 4.9% proof success rate (based on one trial per task). We hope VERINA will catalyze progress in verifiable code generation by providing a rigorous and comprehensive benchmark.

We introduce spatially informed variational autoencoders (SI-VAE) as self-supervised deep-learning models that use stochastic point processes to predict spatial organization patterns from images. Existing approaches to learning visual representations based on variational autoencoders (VAE) struggle to capture spatial correlations between objects or events, focusing instead on pixel intensities. We address this limitation by incorporating a point-process likelihood, derived from the Papangelou conditional intensity, as a self-supervision target. This results in a hybrid model that learns statistically interpretable representations of spatial localization patterns and enables zero-shot conditional simulation directly from images. Experiments with synthetic images show that SI-VAE improve the classification accuracy of attractive, repulsive, and uncorrelated point patterns from 48% (VAE) to over 80% in the worst case and 90% in the best case, while generalizing to unseen data. We apply SI-VAE to a real-world microscopy data set, demonstrating its use for studying the spatial organization of proteins in human cells and for using the representations in downstream statistical analysis.

One central challenge in Neural Combinatorial Optimization (NCO) is handling hard constraints efficiently. Beyond the two classic paradigms, i.e., Local Construction (LC), which sequentially builds feasible solutions but scales poorly, and Global Prediction (GP), which produces one-shot heatmaps yet struggles with constraint conflicts, the recently proposed Adaptive Expansion (AE) shares the advantages of both by progressively growing partial solutions with instance-wise global awareness. However, existing realizations bolt AE onto external GP predictors, so their solution quality is bounded by the backbone and their inference cost scales with repeated global calls. In this paper, we fundamentally rethink adaptive expansion and make it native to a generative model, acting as its intrinsic decoding principle rather than an external wrapper. We propose NEXCO, a CO-specific masked diffusion framework that turns adaptive expansion into the model’s own iterative unmasking process. Specifically, it involves a solution-expansion training procedure with a time-agnostic GNN denoiser, which learns diffusion trajectories between fully masked solutions and ground-truth solutions. With the trained time-agnostic denoiser, we introduce a novel solution expansion scheme at the solving stage, enabling adaptive control over the intermediate solution states. It is achieved by constructing candidate sets according to confidence scores and applying feasibility projection to expand the solution while respecting constraints. In this way, ``adaptive" is not an afterthought but the decoding itself: intermediate diffusion states are meaningful partial solutions and progress is instance-adaptive rather than schedule-bound. Extensive experiments on representative CO problems show that NEXCO achieves approximately 50\% improvement in solution quality and up to $4\times$ faster inference compared to prior state-of-the-art solvers.

Visual instruction tuning (VIT) datasets consist of randomly sampled image-question pairs without regard to the informativeness of each pair. Recent dataset selection methods have shown that a small fraction of such datasets enriched with informative samples can lead to efficient finetuning of Multimodal Large Language Models. In this work, we explore the impact of task complexity on informative data curation and introduce COMPACT (COMPositional Atomic-to-complex Visual Capability Tuning), a VIT data recipe that scales training sample complexity by combining multiple atomic visual capabilities in a single training example. Concretely, we synthesize rich and informative text questions for each image, allowing us to significantly reduce the number of training examples required for effective visual instruction tuning. COMPACT demonstrates superior data efficiency compared to existing data reduction methods. When applied to the LLaVA-665K VIT dataset, COMPACT reduces the data budget by 90% while still achieving 100.2% of the full VIT performance (compared to only 97.5% by the state-of-the-art method) across eight multimodal benchmarks. Further, training on the same COMPACT data even improves performance compared to training with full-scale data on particularly complex benchmarks such as MM-Vet (+8.6%) and MMStar (+2.9%). COMPACT offers a scalable and efficient synthetic data generation recipe to improve on visual language tasks.

We aim to learn wavefunctions simulated by time-dependent density functional theory (TDDFT), which can be efficiently represented as linear combination coefficients of atomic orbitals. In real-time TDDFT, the electronic wavefunctions of a molecule evolve over time in response to an external excitation, enabling first-principles predictions of physical properties such as optical absorption, electron dynamics, and high-order response. However, conventional real-time TDDFT relies on time-consuming propagation of all occupied states with fine time steps. In this work, we propose OrbEvo, which is based on an equivariant graph transformer architecture and learns to evolve the full electronic wavefunction coefficients across time steps. First, to account for external field, we design an equivariant conditioning to encode both strength and direction of external electric field and break the symmetry from SO(3) to SO(2). Furthermore, we design two OrbEvo models, OrbEvo-WF and OrbEvo-DM, using wavefunction pooling and density matrix as interaction method, respectively. Motivated by the central role of the density functional in TDDFT, OrbEvo-DM encodes the density matrix aggregated from all occupied electronic states into feature vectors via tensor contraction, providing a more intuitive approach to learn the time evolution operator. We adopt a training strategy specifically tailored to limit the error accumulation of time-dependent wavefunctions over autoregressive rollout. To evaluate our approach, we generate TDDFT datasets consisting of 5,000 different molecules in the QM9 dataset and 1,500 molecular configurations of the malonaldehyde molecule in the MD17 dataset. Results show that our OrbEvo model accurately captures quantum dynamics of excited states under external field, including time-dependent wavefunctions, time-dependent dipole moment, and optical absorption spectra characterized by dipole oscillator strength. It also shows strong generalization capability on the diverse molecules in the QM9 dataset.

Large Language Models (LLMs) are improving at an exceptional rate. With the advent of agentic workflows, multi-turn dialogue has become the de facto mode of interaction with LLMs for completing long and complex tasks. While LLM capabilities continue to improve, they remain increasingly susceptible to jailbreaking, especially in multi-turn scenarios where harmful intent can be subtly injected across the conversation to produce nefarious outcomes. While single-turn attacks have been extensively explored, adaptability, efficiency and effectiveness continue to remain key challenges for their multi-turn counterparts. To address these gaps, we present PLAGUE, a novel plug-and-play framework for designing multi-turn attacks inspired by lifelong-learning agents. PLAGUE dissects the lifetime of a multi-turn attack into three carefully designed phases (Primer, Planner and Finisher) that enable a systematic and information-rich exploration of the multi-turn attack family. Evaluations show that red-teaming agents designed using PLAGUE achieve state-of-the-art jailbreaking results, improving attack success rates (ASR) by more than 30% across leading models in a lesser or comparable query budget. Particularly, PLAGUE enables an ASR (based on StrongReject) of 81.4% on OpenAI's o3 and 67.3% on Claude's Opus 4.1, two models that are considered highly resistant to jailbreaks in safety literature. Our work offers tools and insights to understand the importance of plan initialization, context optimization, and lifelong learning in crafting multi-turn attacks for a comprehensive model vulnerability evaluation.

Sudden concept drift makes previously trained predictors unreliable, yet deciding when to retrain and what post-drift data size is sufficient is rarely addressed. We propose CALIPER —a detector- and model-agnostic, data-only test that estimates the post-drift data size required for stable retraining. CALIPER exploits state dependence in streams generated by dynamical systems: we run a single-pass weighted local regression over the post-drift window and track a one-step proxy error as a function of a locality parameter $\theta$. When an effective sample size gate is satisfied, a monotonically non-increasing trend in this error with increasing a locality parameter indicates that the data size is sufficiently informative for retraining. We also provide a theoretical analysis of our method, and we show that the algorithm has a low per-update time and memory. Across datasets from four heterogeneous domains, three learner families, and two detectors, CALIPER consistently matches or exceeds the best fixed data size for retraining while incurring negligible overhead and often outperforming incremental updates. CALIPER closes the gap between drift detection and data-sufficient adaptation in streaming learning.

Although large language models (LLMs) have achieved remarkable success across various domains, their considerable scale necessitates substantial computational resources, posing significant challenges for deployment in resource-constrained environments. Layer pruning, as a simple yet effective compression method, removes layers of a model directly, reducing computational overhead. However, what are the best practices for layer pruning in LLMs? Are sophisticated layer selection metrics truly effective? Does the LoRA (Low-Rank Approximation) family, widely regarded as a leading method for pruned model fine-tuning, truly meet expectations when applied to post-pruning fine-tuning? To answer these questions, we dedicate thousands of GPU hours to benchmarking layer pruning in LLMs and gaining insights across multiple dimensions. Our results demonstrate that a simple approach, i.e., pruning the final layers followed by fine-tuning the lm\_head and the remaining last three layers, yields remarkably strong performance. These pruning strategies are further supported by theoretical analyses based on the gradient flow. Following this guide, our method surpasses existing state-of-the-art pruning methods by $5.62\%$–$17.27\%$ on Llama-3.1-8B-It, by $2.36\%$–$19.45\%$ on Llama-3-8B and by $4.34\%$–$9.59\%$ on Llama-3-70B. The code is available at at https://github.com/yaolu-zjut/Navigation_LLM_layer_pruning.

The rapid advancement of text-to-image (T2I) models has increased the need for reliable human preference modeling, a demand further amplified by recent progress in reinforcement learning for preference alignment. However, existing approaches typically quantify the quality of a generated image using a single scalar, limiting their ability to provide comprehensive and interpretable feedback on image quality. To address this, we introduce ImageDoctor, a unified multi-aspect T2I model evaluation framework that assesses image quality across four complementary dimensions: plausibility, semantic alignment, aesthetics, and overall quality. ImageDoctor also provides pixel-level flaw indicators in the form of heatmaps, which highlight misaligned or implausible regions, and can be used as a dense reward for T2I model preference alignment. Inspired by the diagnostic process, we improve the detail sensitivity and reasoning capability of ImageDoctor by introducing a ``look-think-predict" paradigm, where the model first localizes potential flaws, then generates reasoning, and finally concludes the evaluation with quantitative scores. Built on top of a vision-language model and trained through a combination of supervised fine-tuning and reinforcement learning, ImageDoctor demonstrates strong alignment with human preference across multiple datasets, establishing its effectiveness as an evaluation metric. Furthermore, when used as a reward model for preference tuning, ImageDoctor significantly improves generation quality—achieving an improvement of 10% over scalar-based reward models.

Despite significant progress in post-hoc explanation methods for neural networks, many remain heuristic and lack provable guarantees. A key approach for obtaining explanations with provable guarantees is by identifying a cardinally-minimal subset of input features which by itself is provably sufficient to determine the prediction. However, for standard neural networks, this task is often computationally infeasible, as it demands a worst-case exponential number of verification queries in the number of input features, each of which is NP-hard. In this work, we show that for Neural Additive Models (NAMs), a recent and more interpretable neural network family, we can efficiently generate explanations with such guarantees. We present a new model-specific algorithm for NAMs that generates provably cardinally-minimal explanations using only a logarithmic number of verification queries in the number of input features, after a parallelized preprocessing step with logarithmic runtime in the required precision is applied to each small univariate NAM component. Our algorithm not only makes the task of obtaining cardinally-minimal explanations feasible, but even outperforms existing algorithms designed to find the relaxed variant of subset-minimal explanations - which may be larger and less informative but easier to compute - despite our algorithm solving a much more difficult task. Our experiments demonstrate that, compared to previous algorithms, our approach provides provably smaller explanations than existing works and substantially reduces the computation time. Moreover, we show that our generated provable explanations offer benefits that are unattainable by standard sampling-based techniques typically used to interpret NAMs.

Live Photo captures both a high-quality key photo and a short video clip to preserve the precious dynamics around the captured moment. While users may choose alternative frames as the key photo to capture better expressions or timing, these frames often exhibit noticeable quality degradation, as the photo capture ISP pipeline delivers significantly higher image quality than the video pipeline. This quality gap highlights the need for dedicated restoration techniques to enhance the reselected key photo. To this end, we propose LiveMoments, a reference-guided image restoration framework tailored for the reselected key photo in Live Photos. Our method employs a two-branch neural network: a reference branch that extracts structural and textural information from the original high-quality key photo, and a main branch that restores the reselected frame using the guidance provided by the reference branch. Furthermore, we introduce a unified Motion Alignment module that incorporates motion guidance for spatial alignment at both the latent and image levels. Experiments on real and synthetic Live Photos demonstrate that LiveMoments significantly improves perceptual quality and fidelity over existing solutions, especially in scenes with fast motion or complex structures.

The impact of misinformation arises not only from factual inaccuracies but also from the misleading narratives that creators deliberately embed. Interpreting such creator intent is therefore essential for multimodal misinformation detection (MMD) and effective information governance. To this end, we introduce DeceptionDecoded, a large-scale benchmark of 12,000 image–caption pairs grounded in trustworthy reference articles, created using an intent-guided simulation framework that models both the desired influence and the execution plan of news creators. The dataset captures both misleading and non-misleading cases, spanning manipulations across visual and textual modalities, and supports three intent-centric tasks: (1) misleading intent detection, (2) misleading source attribution, and (3) creator desire inference. We evaluate 14 state-of-the-art vision–language models (VLMs) and find that they struggle with intent reasoning, often relying on shallow cues such as surface-level alignment, stylistic polish, or heuristic authenticity signals. These results highlight the limitations of current VLMs and position DeceptionDecoded as a foundation for developing intent-aware models that go beyond shallow cues in MMD.

Designing protein sequences that fold into a target 3-D structure, termed as the inverse folding problem, is central to protein engineering. However, it remains challenging due to the vast sequence space and the importance of local structural constraints. Existing deep learning approaches achieve strong recovery rates, however, lack explicit mechanisms to reuse fine-grained structure-sequence patterns conserved across natural proteins. To mitigate this, we present PRISM a multimodal retrieval-augmented generation framework for inverse folding. PRISM retrieves fine-grained representations of potential motifs from known proteins and integrates them with a hybrid self-cross attention decoder. PRISM is formulated as a latent-variable probabilistic model and implemented with an efficient approximation, combining theoretical grounding with practical scalability. Experiments across multiple benchmarks, including CATH-4.2, TS50, TS500, CAMEO 2022, and the PDB date split, demonstrate the fine-grained multimodal retrieval efficacy of PRISM in yielding SoTA perplexity and amino acid recovery, while also improving the foldability metrics (RMSD, TM-score, pLDDT).

Retrieval-Augmented Generation (RAG) systems enhance large language models (LLMs) by incorporating external knowledge bases, significantly improving their factual accuracy and contextual relevance. However, this integration also introduces new privacy vulnerabilities. Existing privacy attacks on RAG systems may trigger data leakage, but they often fail to accurately isolate knowledge base-derived content within mixed responses and perform poorly in multi-domain settings. In this paper, we propose a novel black-box attack framework that exploits knowledge asymmetry between RAG systems and standard LLMs to enable fine-grained privacy extraction across heterogeneous knowledge domains. Our approach decomposes adversarial queries to maximize information divergence between the models, then applies semantic relationship scoring to resolve lexical and syntactic ambiguities. These features are used to train a neural classifier capable of precisely identifying response segments that contain private or sensitive information. Unlike prior methods, our framework generalizes to unseen domains through iterative refinement without requiring prior knowledge of the corpus. Experimental results show that our method achieves over 90\% extraction accuracy in single-domain scenarios and 80\% in multi-domain settings, outperforming baselines by over 30\% in key evaluation metrics. These results represent the first systematic solution for fine-grained privacy localization in RAG systems, exposing critical security vulnerabilities and paving the way for stronger, more resilient defenses.

Large language models (LLMs) have achieved impressive performance on knowledge-intensive tasks, yet they often struggle with multi-step reasoning due to the unstructured nature of retrieved context. While retrieval-augmented generation (RAG) methods provide external information, the lack of explicit organization among retrieved passages limits their effectiveness, leading to brittle reasoning pathways. Recent interpretability studies highlighting the importance of structured intermediate reasoning further align with this perspective. We propose Retrieval-And-Structuring (RAS), a framework that dynamically constructs question-specific knowledge graphs through iterative retrieval and structured knowledge building. RAS interleaves targeted retrieval planning with incremental graph construction, enabling models to assemble and reason over evolving knowledge structures tailored to each query. On seven knowledge-intensive benchmarks, RAS consistently outperforms strong baselines, achieving up to 8.7\% and 7.0\% gains with proprietary and open-source LLMs, respectively. Our results demonstrate that dynamic, question-specific knowledge structuring offers a robust path to improving reasoning accuracy and robustness in language model generation.

Associative memory systems face significant challenges in efficiently retrieving semantically related information from large document collections, particularly when queries require traversing complex relationships between concepts. Traditional retrieval-augmented generation (RAG) approaches often struggle to capture intricate associative patterns and relationships embedded within textual data. To address this limitation, we propose BrowseNet, a novel associative memory framework that leverages query-specific subgraph exploration within a named-entity-based graph for enhanced information retrieval. Our method transforms unstructured text into a graph-of-chunks representation, where nodes encode document chunks with semantic embeddings and edges capture lexical relationships between content segments. By dynamically traversing the graph-of-chunks based on query characteristics, BrowseNet emulates content-addressable memory systems that enable efficient pattern matching and associative recall. The framework incorporates both structural similarity derived from lexical relationships and semantic similarity based on embedding representations to optimize retrieval performance. We evaluate BrowseNet against established RAG baselines and state-of-the-art (SOTA) pipelines using publicly available datasets that require associative reasoning across multiple information sources. Experimental results demonstrate that BrowseNet achieves SOTA performance in exact match score over both the graph-based RAG approaches and the dense retrieval methods. The two-pronged approach combining structural graph traversal with semantic embeddings enables more effective associative memory retrieval, particularly for queries requiring the integration of disparate but related information. The code and datasets are open-sourced at: https://github.com/bisect-group/BrowseNet

While recent generative models synthesize high-quality visual content, they still struggle with generating rare or fine-grained concepts. To address this challenge, we explore the usage of Retrieval-Augmented Generation (RAG) for image generation, and introduce ImageRAG, a training-free method for rare concept generation. Using a Vision Language Model (VLM), ImageRAG identifies generation gaps between an input prompt and a generated image dynamically, retrieves relevant images, and uses them as context to guide the generation process. Prior approaches that use retrieved images require training models specifically for retrieval-based generation. In contrast, ImageRAG leverages existing image conditioning models, and does not require RAG-specific training. We demonstrate our approach is highly adaptable through evaluation over different backbones, including models trained to receive image inputs and models augmented with a post-training image-prompt adapter. Through extensive quantitative, qualitative, and subjective evaluation, we show that incorporating retrieved references consistently improves the generation abilities of rare and fine-grained concepts across three datasets and three generative models.

Retrieval-Augmented Generation (RAG) improves the factuality of large language models (LLMs) by grounding outputs in retrieved evidence, but faithfulness failures, where generations contradict or extend beyond the provided sources, remain a critical challenge. Existing hallucination detection methods for RAG often rely either on large-scale detector training, which requires substantial annotated data, or on querying external LLM judges, which leads to high inference costs. Although some approaches attempt to leverage internal representations of LLMs for hallucination detection, their accuracy remains limited. Motivated by recent advances in mechanistic interpretability, we employ sparse autoencoders (SAEs) to disentangle internal activations, successfully identifying features that are specifically triggered during RAG hallucinations. Building on a systematic pipeline of information-based feature selection and additive feature modeling, we introduce RAGLens, a lightweight hallucination detector that accurately flags unfaithful RAG outputs using LLM internal representations. RAGLens not only achieves superior detection performance compared to existing methods, but also provides interpretable rationales for its decisions, enabling effective post-hoc mitigation of unfaithful RAG. Finally, we justify our design choices and reveal new insights into the distribution of hallucination-related signals within LLMs. The code is available at https://github.com/Teddy-XiongGZ/RAGLens.