ICLR 2026 Papers

Scientific Large Language Models (Sci-LLMs) have emerged as a promising frontier for accelerating biological discovery. However, these models face a fundamental challenge when processing raw biomolecular sequences: the tokenization dilemma. Whether treating sequences as a specialized language, risking the loss of functional motif information, or as a separate modality, introducing formidable alignment challenges, current strategies fundamentally limit their reasoning capacity. We challenge this sequence-centric paradigm by positing that a more effective strategy is to provide Sci-LLMs with high-level structured context derived from established bioinformatics tools, thereby bypassing the need to interpret low-level noisy sequence data directly. Through a systematic comparison of leading Sci-LLMs on biological reasoning tasks, we tested three input modes: sequence-only, context-only, and a combination of both. Our findings are striking: the context-only approach consistently and substantially outperforms all other modes. Even more revealing, the inclusion of the raw sequence alongside its high-level context consistently degrades performance, indicating that raw sequences act as informational noise, even for models with specialized tokenization schemes. These results suggest that the primary strength of existing Sci-LLMs lies not in their nascent ability to interpret biomolecular syntax from scratch, but in their profound capacity for reasoning over structured, human-readable knowledge. Therefore, we argue for reframing Sci-LLMs not as sequence decoders, but as powerful reasoning engines over expert knowledge. This work lays the foundation for a new class of hybrid scientific AI agents, repositioning the developmental focus from direct sequence interpretation towards high-level knowledge synthesis.

The recent success in using human preferences to align large language models (LLMs) has significantly improved their performance in various downstream tasks, such as question answering, mathematical reasoning, and code generation. However, achieving effective LLM alignment depends on high-quality human preference datasets. Collecting these datasets requires human preference annotation, which is costly and resource-intensive, necessitating efficient active data selection methods. Existing methods either lack a strong theoretical foundation or depend on restrictive reward function assumptions, such as linear latent reward function. To this end, we propose an algorithm, ActiveDPO, that uses a theoretically grounded data selection criterion for non-linear reward functions while directly leveraging the LLM itself to parameterize the reward model that is used for active data selection. As a result, ActiveDPO explicitly accounts for the influence of LLM on data selection, unlike methods that select the data without considering the LLM that is being aligned, thereby leading to more effective and efficient data collection. Our extensive experiments demonstrate that ActiveDPO outperforms existing methods across various models and real-life preference datasets.

Although Large Language Models (LLMs) have demonstrated impressive formal reasoning abilities, they often break down when problems require complex proof planning. One promising approach for improving LLM reasoning abilities involves translating problems into formal logic and using a logic solver. Although off-the-shelf logic solvers are in principle substantially more efficient than LLMs at logical reasoning, they assume that all relevant facts are provided in a question and are unable to deal with missing commonsense relations. In this work, we propose a novel method that uses feedback from the logic solver to augment a logic problem with commonsense relations provided by the LLM, in an iterative manner. This involves a search procedure through potential commonsense assumptions to maximize the chance of finding useful facts while keeping cost tractable. On a collection of pure-logical reasoning datasets, from which some commonsense information has been removed, our method consistently achieves considerable improvements over existing techniques, demonstrating the value in balancing neural and symbolic elements when working in human contexts.

Post-hoc explanations aim at understanding which input features (or groups thereof) are the most impactful toward certain model decisions. Many such methods have been proposed (ArchAttribute, Occlusion, SHAP, RISE, LIME, Integrated Gradient) and it is hard for practitioners to understand the differences between them. Even worse, faithfulness metrics, often used to quantitatively compare explanation methods, also exhibit inconsistencies. To address these issues, recent work has unified explanation methods through the lens of Functional Decomposition. We extend such work to scenarios where input features are partitioned into groups (e.g. pixel patches) and prove that disagreements between explanation methods and faithfulness metrics are caused by between-group interactions. Crucially, getting rid of between-group interactions would lead to a single explanation that is optimal according to all faithfulness metrics. We finally show how to reduce the disagreements by adaptively grouping features/pixels on tabular/image data.

Generative retrieval (GR) reformulates information retrieval (IR) by framing it as the generation of document identifiers (docids), thereby enabling an end-to-end optimization and seamless integration with generative language models (LMs). Despite notable progress under supervised training, GR still struggles to generalize to zero-shot IR scenarios, which are prevalent in real-world applications. To tackle this challenge, we propose ZeroGR, a zero-shot generative retrieval framework that leverages natural language instructions to extend GR across a wide range of IR tasks. Specifically, ZeroGR is composed of three key components: (i) an LM-based docid generator that unifies heterogeneous documents (e.g., text, tables, code) into semantically meaningful docids; (ii) an instruction-tuned query generator that generates diverse types of queries from natural language task descriptions to enhance corpus indexing; and (iii) a reverse annealing decoding strategy to balance precision and recall during docid generation. We investigate the impact of instruction fine-tuning scale and find that performance consistently improves as the number of IR tasks encountered during training increases. Empirical results on the BEIR and MAIR benchmarks demonstrate that \textsc{ZeroGR} outperforms strong dense retrieval and generative baselines in zero-shot settings, establishing a new state-of-the-art for instruction-driven GR.

Text-to-image (T2I) models offer great potential for creating virtually limitless synthetic data, a valuable resource compared to fixed and finite real datasets. Previous works evaluate the utility of synthetic data from T2I models on three key desiderata: quality, diversity, and consistency. While prompt engineering is the primary means of interacting with T2I models, the systematic impact of prompt complexity on these critical utility axes remains underexplored. In this paper, we first conduct synthetic experiments to motivate the difficulty of generalization w.r.t. prompt complexity and explain the observed difficulty with theoretical derivations. Then, we introduce a new evaluation framework that can compare the utility of real data and synthetic data, and present a comprehensive analysis of how prompt complexity influences the utility of synthetic data generated by commonly used T2I models. We conduct our study across diverse datasets, including CC12M, ImageNet-1k, and DCI, and evaluate different inference-time intervention methods. Our synthetic experiments show that generalizing to more general conditions is harder than the other way round, since the former needs an estimated likelihood that is not learned by diffusion models. Our large-scale empirical experiments reveal that increasing prompt complexity results in lower conditional diversity and prompt consistency, while reducing the synthetic-to-real distribution shift, which aligns with the synthetic experiments. Moreover, current inference-time interventions can augment the diversity of the generations at the expense of moving outside the support of real data. Among those interventions, prompt expansion, by deliberately using a pre-trained language model as a likelihood estimator, consistently achieves the highest performance in both image diversity and aesthetics, even higher than that of real data. Combining advanced guidance interventions with prompt expansion results in the most appealing utility trade-offs of synthetic data.

Large-scale deep learning models are known to *memorize* parts of the training set. In machine learning theory, memorization is often framed as interpolation or label fitting, and classical results show that this can be achieved when the number of parameters $p$ in the model is larger than the number of training samples $n$. In this work, we consider memorization from the perspective of *data reconstruction*, demonstrating that this can be achieved when $p$ is larger than $dn$, where $d$ is the dimensionality of the data. More specifically, we show that, in the random features model, when $p \gg dn$, the subspace spanned by the training samples in feature space gives sufficient information to identify the individual samples in input space. Our analysis suggests an optimization method to reconstruct the dataset from the model parameters, and we demonstrate that this method performs well on various architectures (random features, two-layer fully-connected and deep residual networks). Our results reveal a *law of data reconstruction*, according to which the entire training dataset can be recovered as $p$ exceeds the threshold $dn$.

Diffusion-based policies have gained growing popularity in solving a wide range of decision-making tasks due to their superior expressiveness and controllable generation during inference. However, effectively training large diffusion policies using reinforcement learning (RL) remains challenging. Existing methods either suffer from unstable training due to directly maximizing value objectives, or face computational issues due to relying on crude Gaussian likelihood approximation, which requires a large amount of sufficiently small denoising steps. In this work, we propose DIPOLE (Dichotomous diffusion Policy improvement), a novel RL algorithm designed for stable and controllable diffusion policy optimization. We begin by revisiting the KL-regularized objective in RL, which offers a desirable weighted regression objective for diffusion policy extraction, but often struggles to balance greediness and stability. We then formulate a greedified policy regularization scheme, which naturally enables decomposing the optimal policy into a pair of stably learned dichotomous policies: one aims at reward maximization, and the other focuses on reward minimization. Under such a design, optimized actions can be generated by linearly combining the scores of dichotomous policies during inference, thereby enabling flexible control over the level of greediness.Evaluations in offline and offline-to-online RL settings on ExORL and OGBench demonstrate the effectiveness of our approach. We also use DIPOLE to train a large vision-language-action (VLA) model for end-to-end autonomous driving (AD) and evaluate it on the large-scale real-world AD benchmark NAVSIM, highlighting its potential for complex real-world applications.

Large language models (LLMs), such as OpenAI-o1 and DeepSeek-R1, excel in contextual reasoning by leveraging extensive world knowledge and deep contextual understanding. However, their high computational costs limit deployment in resource-constrained settings. Conversely, small language models (SLMs) are more computationally efficient but often struggle with contextual reasoning due to limited parameter capacity and challenges like catastrophic forgetting. Existing enhancement methods for SLMs—such as knowledge distillation and data synthesis—still depend on additional training and face inherent limitations. To address this, we propose Navigation, a novel training-free framework that improves SLMs’ contextual reasoning by distilling LLM-derived contextual processing expertise into generalizable navigation templates. These templates, stored in a scalable Navigation database, guide SLMs through a three-stage process—Generation, Utilization, and Update—to locate and process critical information within complex contexts. Experiments demonstrate that our approach yields an average 10.7\% accuracy gain with a template count equivalent to no more than 2.1\% of the dataset size, enabling models such as Qwen2.5-3B-Instruct and Llama-3.2-3B-Instruct to outperform GPT-3.5-Turbo on diverse contextual reasoning tasks.

KV caching is a fundamental technique for accelerating Large Language Model (LLM) inference by reusing key-value (KV) pairs from previous queries, but its effectiveness under limited memory is highly sensitive to the eviction policy. The default Least Recently Used (LRU) eviction algorithm struggles with dynamic online query arrivals, especially in multi-LLM serving scenarios, where balancing query load across workers and maximizing cache hit rate of each worker are inherently conflicting objectives. We give the first unified mathematical model that captures the core trade-offs between KV cache eviction and query routing. Our analysis reveals the theoretical limitations of existing methods and leads to principled algorithms that integrate provably competitive randomized KV cache eviction with learning-based methods to adaptively route queries with evolving patterns, thus balancing query load and cache hit rate. Our theoretical results are validated by extensive experiments across 4 benchmarks and 3 prefix-sharing settings, demonstrating improvements of up to **6.92$\times$** in cache hit rate, **11.96$\times$** reduction in latency, **14.06$\times$** reduction in time-to-first-token (TTFT), and **77.4%** increase in throughput over the state-of-the-art methods. Our code is available at https://github.com/fzwark/KVRouting.

The Transformer architecture, despite its widespread success, struggles with long-context scenarios due to quadratic computation and linear memory growth. While various linear attention variants mitigate these efficiency constraints by compressing context into fixed-size states, they often degrade performance in tasks such as in-context retrieval and reasoning. To address this limitation and achieve more effective context compression, we propose two key innovations. First, we introduce a row-sparse update formulation for linear attention by conceptualizing state updating as information classification. This enables sparse state updates via softmax-based top-$k$ hard classification, thereby extending receptive fields and reducing inter-class interference. Second, we present Sparse State Expansion (SSE) within the sparse framework, which expands the contextual state into multiple partitions, effectively decoupling parameter size from state capacity while maintaining the sparse classification paradigm. Supported by efficient parallelized implementations, our design achieves effective classification and highly discriminative state representations. We extensively validate SSE in both pure linear and hybrid (SSE-H) architectures across language modeling, in-context retrieval, and mathematical reasoning benchmarks. SSE demonstrates strong retrieval performance and scales favorably with state size. Moreover, after reinforcement learning (RL) training, our 2B SSE-H model achieves state-of-the-art mathematical reasoning performance among small reasoning models, scoring 64.5 on AIME24 and 50.2 on AIME25, significantly outperforming similarly sized open-source Transformers. These results highlight SSE as a promising and efficient architecture for long-context modeling.

This paper studies the problem of data-specific neural representations, aiming for compact, flexible, and modality-agnostic storage of individual visual data using neural networks. Our approach considers a visual datum as a set of discrete observations of an underlying continuous signal, thus requiring models capable of capturing the inherent structure of the signal. For this purpose, we investigate state-space models (SSMs), which are well-suited for modeling latent signal dynamics. We first explore the appealing properties of SSMs for data-specific neural representation and then present a novel framework that integrates SSMs into the representation pipeline. The proposed framework achieved compact representations and strong reconstruction performance across a range of visual data formats, suggesting the potential of SSMs for data-specific neural representations.

3D medical imaging is in high demand and essential for clinical diagnosis and scientific research. Currently, diffusion models have become an effective tool for medical imaging reconstruction thanks to their ability to learn rich, high‑quality data priors. However, learning the 3D data distribution with diffusion models in medical imaging is challenging, not only due to the difficulties in data collection but also because of the significant computational burden during model training. A common compromise is to train the diffusion model on 2D data priors and reconstruct stacked 2D slices to address 3D medical inverse problems. However, the intrinsic randomness of diffusion sampling causes severe inter‑slice discontinuities of reconstructed 3D volumes. Existing methods often enforce continuity regularizations along the $z$‑axis, which introduces sensitive hyper‑parameters and may lead to over-smoothing results. In this work, we revisit the origin of stochasticity in diffusion sampling and introduce Inter‑Slice Consistent Stochasticity (ISCS), a simple yet effective strategy that encourages inter‑slice consistency during diffusion sampling. Our key idea is to control the consistency of stochastic noise components during diffusion sampling, thereby aligning their sampling trajectories without adding any new loss terms or optimization steps. Importantly, the proposed ISCS is plug‑and‑play and can be dropped into any 2D‑trained diffusion‑based 3D reconstruction pipeline without additional computational cost. Experiments on several medical imaging problems show that our method can effectively improve the performance of medical 3D imaging problems based on 2D diffusion models. Our findings suggest that controlling inter‑slice stochasticity is a principled and practically attractive route toward high‑fidelity 3D medical imaging with 2D diffusion priors. The code is available at: [https://anonymous.4open.science/r/ICLR-ISCS-3281](https://anonymous.4open.science/r/ICLR-ISCS-3281).

Large reasoning models (LRMs) often consume excessive tokens, inflating computational cost and latency. We challenge the assumption that longer responses improve accuracy. By penalizing the reasoning tokens using a discounted reinforcement-learning setup (interpretable as a small per-token cost) and analyzing Blackwell optimality in restricted policy classes, we encourage concise yet accurate reasoning; in practice we discount only the environment (correctness) reward. Experiments confirm our theoretical results that this approach shortens chains of thought while preserving accuracy.

Large language models rely on attention mechanisms with a softmax activation. Yet the dominance of softmax over alternatives (e.g., component-wise or linear) remains poorly understood, and many theoretical works have focused on the easier-to-analyze linearized attention. In this work, we address this gap through a principled study of the single-location regression task, where the output depends on a linear transformation of a single input token at a random location. Building on ideas from statistical physics, we develop an analysis of attention-based predictors in the high-dimensional limit, where generalization performance is captured by a small set of order parameters. At the population level, we show that softmax achieves the Bayes risk, whereas linear attention fundamentally falls short. We then examine other activation functions to identify which properties are necessary for optimal performance. Finally, we analyze the finite-sample regime: we provide an asymptotic characterization of the test error and show that, while softmax is no longer Bayes-optimal, it consistently outperforms linear attention. We discuss the connection with optimization by gradient-based algorithms.

Task-specific fine-tuning of foundation models is critically dependent on the quality and relevance of the instruction data. While prevailing data selection methods rely exclusively on instruction instances X to approximate the target distribution, we argue that selection should align with the joint distribution of instructions and task-specific labels (X,Y), However, task-specific labels Y are typically unavailable in practice. To address this, we reformulate the task-specific data selection problem and present a novel pipeline that leverages the reasoning capabilities of large language models (LLMs) to infer proxy labels, thereby facilitating joint distribution alignment. Our approach begins by propagating proxy labels from a small target set to a large, unlabeled source corpus. A two-stage filtering process then removes instances with label noise and refines the subset through distribution alignment. This strategy produces more semantically meaningful and task-aware selections than conventional similarity measures based on X alone. Experimental results show that fine-tuning on a subset of only 10K samples—selected from a pool of 300K—achieves performance competitive or superior to state-of-the-art methods.

Multi-domain reinforcement learning (RL) for large language models (LLMs) involves highly intricate reward surfaces, posing significant challenges in finding parameters that excel across all domains. Recent empirical studies have further highlighted conflicts among domains, where gains in one capability often come at the expense of another. However, approaches to mitigate such conflicts and enhance multi-domain reasoning remain largely underexplored. To address this challenge, we propose **C**urvature-**G**uided **P**olicy **O**ptimization (**CGPO**), a principled and scalable training framework to advance the multi-domain reasoning of LLMs. Inspired by Newton's method, CGPO exploits the geometric structure in the reward surface, while sidestepping the prohibitive cost of Hessian computation. At each update, CGPO processes domains in random order, preconditioning their gradients with curvature information from other domains to foster richer cross-domain interactions. This mechanism further promotes implicit gradient alignment by maximizing inter-domain inner products in expectation, steering the parameters toward regions that jointly enhance multi-domain performance. Extensive experiments on a mixed dataset covering math, coding, science, and creative writing, evaluated across seven widely-used benchmarks, show that CGPO significantly outperforms all baselines in terms of faster reward improvement and stronger multi-domain capability.

While diffusion models achieve state-of-the-art generation quality, they still suffer from computationally expensive sampling. Recent works address this issue with gradient-based optimization methods that distill a few-step ODE diffusion solver from the full sampling process, reducing the number of function evaluations from dozens to just a few. However, these approaches often rely on intricate training techniques and do not explicitly focus on preserving fine-grained details. In this paper, we introduce the Generalized Solver: a simple parameterization of the ODE sampler that does not require additional training tricks and improves quality over existing approaches. We further combine the original distillation loss with adversarial training, which mitigates artifacts and enhances detail fidelity. We call the resulting method the Generalized Adversarial Solver and demonstrate its superior performance compared to existing solver training methods under similar resource constraints.

We introduce MUSE, a novel watermarking paradigm for tabular generative models. Existing approaches often exploit DDIM invertibility to watermark tabular diffusion models, but tabular diffusion models suffer from poor invertibility, leading to degraded performance. To overcome this limitation, we leverage the computational efficiency of tabular generative models and propose a multi-sample selection paradigm, where watermarks are embedded by generating multiple candidate samples and selecting one according to a specialized scoring function. The key advantages of MUSE include (1) Model-agnostic: compatible with any tabular generative model that supports repeated sampling; (2) Flexible: offers flexible designs to navigate the trade-off between generation quality, detectability, and robustness; (3) Calibratable: theoretical analysis provides principled calibration of watermarking strength, ensuring minimal distortion to the original data distribution. Extensive experiments on five datasets demonstrate that MUSE substantially outperforms existing methods. Notably, it reduces the distortion rates by 84-88% for fidelity metrics compared with the best performing baselines, while achieving 1.0 TPR@0.1%FPR detection rate.