ICLR 2026 Papers

Traditional RLHF optimizes language models with coarse, scalar rewards that mask the fine-grained reasons behind success or failure, leading to slow, opaque learning. Recent work augments RL with textual critiques through prompting or reflection, improving interpretability but leaving model parameters untouched. We introduce **Text2Grad**, a reinforcement-learning paradigm that *turns free-form textual feedback into span-level gradients*. Given human (or programmatic) critiques, Text2Grad aligns each feedback phrase with the relevant token spans, converts these alignments into differentiable reward signals, and performs gradient updates that directly refine the offending portions of the model's policy. This yields precise, feedback-conditioned adjustments instead of global nudges. Text2Grad is realized through three components: (1) a high-quality feedback–annotation pipeline that pairs critiques with token spans; (2) a fine-grained reward model that predicts span-level reward on answers while generating explanatory critiques; and (3) a span-level policy optimizer that back-propagates *natural-language gradients*. Across summarization, code generation, and question answering, Text2Grad consistently surpasses scalar-reward RL and prompt-only baselines, providing both higher task metrics and richer interpretability. Our results suggest that natural-language feedback can serve not only as explanations, but also as actionable training signals for fine-grained alignment. The code for our method is available at *[https://github.com/microsoft/Text2Grad](https://github.com/microsoft/Text2Grad)*.

Understanding internal representations of neural models is a core interest of mechanistic interpretability. Due to its large dimensionality, the representation space can encode various aspects about inputs. To what extent are different aspects organized and encoded in separate subspaces? Is it possible to find these "natural" subspaces in a purely unsupervised way? Somewhat surprisingly, we can indeed achieve this and find interpretable subspaces by a seemingly unrelated training objective. Our method, neighbor distance minimization (NDM), learns non-basis-aligned subspaces in an unsupervised manner. Qualitative analysis shows subspaces are interpretable in many cases, and encoded information in obtained subspaces tends to share the same abstract concept across different inputs, making such subspaces similar to "variables" used by the model. We also conduct quantitative experiments using known circuits in GPT-2; results show a strong connection between subspaces and circuit variables. We also provide evidence showing scalability to 2B models by finding separate subspaces mediating context and parametric knowledge routing. Viewed more broadly, our findings offer a new perspective on understanding model internals and building circuits.

Sequence modelling requires determining which past tokens are causally relevant from the context and their importance: a process inherent to the attention layers in transformers, yet whose underlying learned mechanisms remain poorly understood. In this work, we formalize the task of estimating token importance as an in-context learning problem by introducing a novel framework based on Mixture of Transition Distributions, whereby a latent variable, whose distribution is parameterized by a set of unobserved mixture weights, determines the influence of past tokens on the next. To correctly predict the next token, transformers need to learn the mixture weights in-context. We demonstrate that transformers can implement Mirror Descent to learn the mixture weights from the context. To this end, we give an explicit construction of a three-layer transformer that exactly implements one step of Mirror Descent and prove that the resulting estimator is a first-order approximation of the Bayes-optimal predictor. Corroborating our construction and its learnability via gradient descent, we empirically show that transformers trained from scratch converge to this solution: attention maps match our construction, and deeper models’ performance aligns with multi-step Mirror Descent.

Multi-view generation with camera pose control and prompt-based customization are both essential elements for achieving controllable generative models. However, existing multi-view generation models do not support customization with geometric consistency, whereas customization models lack explicit viewpoint control, making them challenging to unify. Motivated by these gaps, we introduce a novel task, multi-view customization, which aims to jointly achieve multi-view camera pose control and customization. Due to the scarcity of training data in customization, existing multi-view generation models, which inherently rely on large-scale datasets, struggle to generalize to diverse prompts. To address this, we propose MVCustom, a novel diffusion-based framework explicitly designed to achieve both multi-view consistency and customization fidelity. In the training stage, MVCustom learns the subject's identity and geometry using a feature-field representation, incorporating the text-to-video diffusion backbone enhanced with dense spatio-temporal attention, which leverages temporal coherence for multi-view consistency. In the inference stage, we introduce two novel techniques: depth-aware feature rendering explicitly enforces geometric consistency, and consistent-aware latent completion ensures accurate perspective alignment of the customized subject and surrounding backgrounds. Extensive experiments demonstrate that MVCustom achieves the most balanced and consistent competitive performance across multi-view consistency, customization fidelity, demonstrating effective solution of multi-objective generation task.

This paper presents a generation-based debiasing framework for object detection. Prior debiasing methods are often limited by the representation diversity of samples, while naive generative augmentation often preserves the biases it aims to solve. Moreover, our analysis reveals that simply generating more data for rare classes is suboptimal due to two core issues: i) instance frequency is an incomplete proxy for the true data needs of a model, and ii) current layout-to-image synthesis lacks the fidelity and control to generate high-quality, complex scenes. To overcome this, we introduce the representation score (RS) to diagnose representational gaps beyond mere frequency, guiding the creation of new, unbiased layouts. To ensure high-quality synthesis, we replace ambiguous text prompts with a precise visual blueprint and employ a generative alignment strategy, which fosters communication between the detector and generator. Our method significantly narrows the performance gap for underrepresented object groups, e.g., improving large/rare instances by 4.4/3.6 mAP over the baseline, and surpassing prior L2I synthesis models by 15.9 mAP for layout accuracy in generated images.

Hypergraph network data, which capture multi-way interactions among entities, have become increasingly prevalent in the big data era, spanning fields such as social science, medical research, and biology. Generating synthetic hyperlinks with attributes from an observed hypergraph has broad applications in data augmentation, simulation, and advancing the understanding of real-world complex systems. This task, however, poses unique challenges due to special properties of hypergraphs, including discreteness, hyperlink sparsity, and the mixed data types of hyperlinks and their attributes, rendering many existing generative models unsuitable. In this paper, we introduce ReLaSH (REconstructing joint LAtent Spaces for Hypergraphs with attributes), a general generative framework for producing realistic synthetic hypergraph data with hyperlink attributes via training a likelihood-based joint embedding model and reconstructing the joint latent space. Given a hypergraph dataset, ReLaSH first embeds the hyperlinks and their attributes into a joint latent space by training a likelihood-based model, and then reconstructs this joint latent space using a distribution-free generator. The generation task is completed by first sampling embeddings from the distribution-free generator and then decoding them into hyperlinks and attributes through the trained likelihood-based model. Compared with existing generative models, ReLaSH explicitly accounts for the unique structure of hypergraphs and jointly models hyperlinks and their attributes. Moreover, the likelihood-based embedding model provides efficiency and interpretability relative to deep black-box architectures, while the distribution-free generator in the joint latent space ensures flexibility. We theoretically demonstrate consistency and generalizability of ReLaSH. Empirical results on a range of real-world datasets from diverse domains demonstrate the strong performance of ReLaSH, underscoring its broad utility and effectiveness in practical applications.

Neural Controlled Differential Equations (Neural CDEs) provide a principled framework for modelling irregular time series in continuous time. Their number of function evaluations (NFEs) acts as a natural analogue of depth in discrete neural networks and is typically controlled indirectly via solver tolerances. However, tightening tolerances increases numerical precision without necessarily improving expressiveness. We propose a simple alternative: scaling the integration time horizon to increase NFEs and thereby "deepen" the model. Since enlarging the interval can cause uncontrolled growth in standard vector fields, we introduce a Negative Feedback (NF) mechanism that ensures provable stability without limiting flexibility. We further establish general risk bounds for Neural CDEs and quantify discretization error using Gaussian process theory, improving robustness to integration and interpolation error. On four public benchmarks, our method, **DeNOTS**, outperforms existing approaches—including Neural RDEs and state space models—by up to $20$%. DeNOTS combines expressiveness, stability, and robustness for reliable continuous-time modelling.

Training long-context language models to capture long-range dependencies requires specialized data construction. Current approaches, such as generic text concatenation or heuristic-based variants, frequently fail to guarantee genuine long-range dependencies. We propose \textbf{EntropyLong}, a novel data construction method that leverages predictive uncertainty to verify dependency quality. Our approach identifies high-entropy positions in documents, retrieves semantically relevant contexts from large corpora, and verifies their utility by assessing whether they reduce prediction entropy. This \textit{model-in-the-loop verification} ensures each dependency represents measurable information gain rather than spurious correlation. We construct training samples with long-range dependencies by combining original documents with these verified contextual supplements. Using FineWeb-Edu and Cosmopedia, we generate a dataset of 128K-length sequences with verified dependencies. Models trained on this data demonstrate significant improvements on RULER benchmarks, particularly in tasks requiring distant information. Following instruction fine-tuning, our models also achieve substantial gains on LongBench-v2, demonstrating enhanced long-context understanding. Extensive ablation studies further validate the necessity and effectiveness of entropy-based verification for long-context training.

We present DuPO, a dual learning-based preference optimization framework that generates annotation-free feedback via the generalized duality. DuPO addresses two key limitations: Reinforcement Learning with Verifiable Rewards (RLVR)’s reliance on costly labels and applicability restricted to verifiable tasks, and traditional dual learning’s restriction to strictly dual task pairs (e.g., translation and back-translation). Specifically, DuPO decomposes a primal task’s input into known and unknown components, then constructs its dual task to reconstruct the unknown part using the primal output and known information (e.g., reversing math solutions to recover hidden variables), broadening applicability to non-invertible tasks. The quality of this reconstruction serves as a self-supervised reward to optimize the primal task, synergizing with LLMs’ ability to instantiate both tasks via a single model. Empirically, DuPO achieves substantial gains across diverse tasks: it enhances the average translation quality by 2.1 COMET over 756 directions, boosts the mathematical reasoning accuracy by an average of 6.2 points on three challenge benchmarks, and enhances performance by 9.3 points as an inference-time reranker (trading computation for accuracy). These results position DuPO as a scalable, general, and annotation-free paradigm for LLM optimization.

This work investigates descriptive captions as an additional source of supervision for biological multimodal foundation models. Images and captions can be viewed as complementary samples from the latent morphospace of a species, each capturing certain biological traits. Incorporating captions during training encourages alignment with this shared latent structure, emphasizing potentially diagnostic characters while suppressing spurious correlations. The main challenge, however, lies in obtaining faithful, instance-specific captions at scale. This requirement has limited the utilization of natural language supervision in organismal biology compared with many other scientific domains. We complement this gap by generating synthetic captions with multimodal large language models (MLLMs), guided by Wikipedia-derived visual information and taxon-tailored format examples. These domain-specific contexts help reduce hallucination and yield accurate, instance-based descriptive captions. Using these captions, we train BioCAP (i.e., BioCLIP with Captions), a biological foundation model that captures rich semantics and achieves strong performance in species classification and text-image retrieval. These results demonstrate the value of descriptive captions beyond labels in bridging biological images with multimodal foundation models

Probabilistic programming offers a powerful framework for modeling uncertainty, yet statistical model discovery in this domain entails navigating an immense search space under strict domain‐specific constraints. When small language models are tasked with generating probabilistic programs, they frequently produce outputs that suffer from both syntactic, and semantic errors, such as flawed inference constructs. Motivated by probabilistic programmers’ domain expertise and debugging strategies, we introduce RefineStat, a language model–driven framework that enforces semantic constraints ensuring synthesized programs contain valid distributions, well‐formed parameters, and then applies diagnostic‐aware refinement by resampling prior or likelihood components whenever reliability checks fail. We evaluate RefineStat on multiple probabilistic-programming code-generation tasks using smaller language models (SLMs) and find that it produces programs that are both syntactically sound and statistically reliable, often matching or surpassing those from closed-source large language models (e.g., OpenAI o3).

Formal models are essential to specifying large, complex computer systems and verifying their correctness, but are notoriously expensive to write and maintain. Recent advances in generative AI show promise in generating certain forms of specifications. However, existing work mostly targets small code, not complete systems. It is unclear whether AI can deal with realistic system artifacts, as this requires abstracting their complex behavioral properties into formal models. We present SysMoBench, a benchmark that evaluates AI's ability to formally model large, complex systems. We focus on concurrent and distributed systems, which are keystones of today's critical computing infrastructures, encompassing operating systems and cloud infrastructure. We use TLA+, the de facto specification language for concurrent and distributed systems, though the benchmark can be extended to other specification languages. We address the primary challenge of evaluating AI-generated models by automating metrics like syntactic and runtime correctness, conformance to system code, and invariant correctness. SysMoBench currently includes eleven diverse system artifacts: the Raft implementation of Etcd and Redis, the leader election of ZooKeeper, the Spinlock, Mutex and Ringbuffer in Asterinas OS, etc., with more being added. SysMoBench enables us to understand the capabilities and limitations of today's LLMs and agents, putting tools in this area on a firm footing and opening up promising new research directions.

We introduce Purrception, a variational flow matching approach for vector-quantized image generation that provides explicit categorical supervision while maintaining continuous transport dynamics. Our method adapts Variational Flow Matching to vector-quantized latents by learning categorical posteriors over codebook indices while computing velocity fields in the continuous embedding space. This combines the geometric awareness of continuous methods with the discrete supervision of categorical approaches, enabling uncertainty quantification over plausible codes and temperature-controlled generation. We evaluate Purrception on ImageNet-1k $256 \times 256$ generation. Training converges faster than both continuous flow matching and discrete flow matching baselines while achieving competitive FID scores with state-of-the-art models. This demonstrates that Variational Flow Matching can effectively bridge continuous transport and discrete supervision for improved training efficiency in image generation.

Test-time adaptation (TTA) of Vision-Language Models (VLMs) has emerged as a technique for tackling distribution shifts during the test time. Recent research indicates that the test-time adaptation is intrinsically linked to the model's training history. However, existing TTA methods, such as Test-time Prompt Tuning, often design adaptation strategies in isolation from the models' training characteristics, which degrade their performance. This paper argues that the flatness acquired via sharpness-aware training is an efficient clue for the test-time adaptation of VLMs. Built on this insight, this paper proposes a novel Flatness-Guided Adaptation framework (FGA) for VLMs to cohesively unify training and test-time procedures. Its core idea is to leverage the alignment between the training minimum and test loss flat regions to guide the adaptation process. Specifically, our FGA consists of a prompt-tuning stage and a test-time adaptation stage. In the tuning stage, a Sharpness-Aware Prompt Tuning method is utilized to identify the training flat minimum, offering a geometric clue of flatness for subsequent adaptation. In the test stage, a Sharpness-based Test Sample Selection approach is proposed to ensure the alignment of flat minima between the training and each augmented test sample's loss landscape. In comparison to existing TTA methods, our FGA avoids the expensive prompt parameter updates during test time, and substantially reduces the computation overhead. Extensive experiments on both domain generalization and cross-dataset benchmarks demonstrate that our FGA achieves superior performance over prevalent TTA methods. Notably, FGA even surpasses SOTA performance by 4.55\% on ImageNet-A, when using a ViT-B/16 image encoder. Our code will be available soon.

Chain-of-Thought (CoT) reasoning has proven effective in enhancing large language models by encouraging step-by-step intermediate reasoning, and recent advances have extended this paradigm to Multimodal Large Language Models (MLLMs). In the medical domain, where diagnostic decisions depend on nuanced visual cues and sequential reasoning, CoT aligns naturally with clinical thinking processes. However, Current benchmarks for medical image understanding generally focus on the final answer while ignoring the reasoning path. An opaque process lacks reliable bases for judgment, making it difficult to assist doctors in diagnosis. To address this gap, we introduce a new M3CoTBench benchmark specifically designed to evaluate the correctness, efficiency, impact, and consistency of CoT reasoning in medical image understanding. M3CoTBench features (1) a diverse, multi-level difficulty dataset covering 24 examination types, (2) 13 varying-difficulty tasks, (3) a suite of CoT-specific evaluation metrics (correctness, efficiency, impact, and consistency) tailored to clinical reasoning, and (4) a performance analysis of multiple MLLMs. M3CoTBench systematically evaluates CoT reasoning across diverse medical imaging tasks, revealing current limitations of MLLMs in generating reliable and clinically interpretable reasoning, and aims to foster the development of transparent, trustworthy, and diagnostically accurate AI systems for healthcare.

Visual autoregressive (VAR) models generate images through next-scale prediction, naturally achieving coarse-to-fine, fast, high-fidelity synthesis mirroring human perception. In practice, this hierarchy can drift at inference time, as limited capacity and accumulated error cause the model to deviate from its coarse-to-fine nature. We revisit this limitation from an information-theoretic perspective and deduce that ensuring each scale to contribute high-frequency content not explained by earlier scales mitigates the train–inference discrepancy. With this insight, we propose Scaled Spatial Guidance (SSG), a training-free, inference-time guidance that steers generation toward the intended hierarchy while maintaining global coherence. SSG emphasizes target high-frequency signals, defined as the semantic residual, isolated from a coarser prior. To obtain this prior, we leverage a principled frequency-domain procedure, Discrete Spatial Enhancement (DSE), devised to sharpen and better isolate the semantic residual through frequency-aware construction. SSG applies broadly across VAR models leveraging discrete visual tokens, regardless of tokenization design or conditioning modality. Experiments demonstrate SSG yields consistent gains in fidelity and diversity while preserving low latency, revealing untapped efficiency in coarse-to-fine image generation.

We propose Sci2Pol-Bench and Sci2Pol-Corpus, the first benchmark and training dataset for evaluating and fine-tuning large language models (LLMs) on policy brief generation from a scientific paper. We build Sci2Pol-Bench on a five-stage taxonomy to mirror the human writing process: (i) Autocompletion, (ii) Understanding, (iii) Summarization, (iv) Generation, and (v) Verification. It features 18 tasks in multiple-choice and open-ended formats. Specifically, for the Generation stage, we show that BERTScore and ROUGE scores fail to capture the quality of brief writing, and introduce a new LLM-based evaluation metric aligned with expert judgement. Using this benchmark, we evaluate 13 leading open-source and commercial LLMs to uncover key limitations. To improve LLM performance on brief writing, we curate the Sci2Pol-Corpus for fine-tuning. We start by linking each cited scientific paper to its corresponding policy document, drawn from 5.6 million policy records. This produces 140,000 candidate pairs. We then employ an LLM-as-a-judge to filter high-quality examples, followed by in-context polishing using three expert-written samples as references. This process yields a final set of 639 new pairs. Finally, we fine-tune three models on Sci2Pol-Corpus: LLaMA-3.1-8B, Gemma-12B, and Gemma-27B. Fine-tuning leads to consistent performance improvements across Sci2Pol-Bench. Notably, after fine-tuning, Gemma-27B surpasses the much larger GPT-4o and DeepSeek-V3 (671B). These demonstrate the effectiveness of our corpus in bridging the gap between science and policy.

Matrix denoising is a crucial component in machine learning, offering valuable insights into the behavior of learning algorithms (Bishop and Nasrabadi, 2006). This paper focuses on the rectangular matrix denoising problem, which involves estimating the left and right singular vectors of a rank-one matrix that is corrupted by additive noise. Traditional algorithms for this problem often exhibit high computational complexity, leading to the widespread use of gradient descent (GD)-based estimation methods with a quadratic cost function. However, the learning dynamics of these GD-based methods, particularly the analytical solutions that describe their exact trajectories, have been largely overlooked in existing literature. To fill this gap, we investigate the learning dynamics in detail, providing convergence proofs and asymptotic analysis. By leveraging tools from large random matrix theory, we derive a closed-form solution for the learning dynamics, characterized by the inner products of the estimates and the ground truth vectors. We rigorously prove the almost sure convergence of these dynamics as the signal dimensions tend to infinity. Additionally, we analyze the asymptotic behavior of the learning dynamics in the large-time limit, which aligns with the well-known Baik-Ben Arous-Péchée phase transition phenomenon n (Baik et al., 2005). Experimental results support our theoretical findings, demonstrating that when the signal-to-noise ratio (SNR) surpasses a critical threshold, learning converges rapidly from an initial value close to the stationary point. In contrast, estimation becomes infeasible when the ratio of the inner products between the initial left and right vectors and their corresponding ground truth vectors reaches a specific value, which depends on both the SNR and the data dimensions.

Reinforcement Learning (RL) has proven highly effective for autoregressive language models, but adapting these methods to diffusion large language models (dLLMs) presents fundamental challenges. The core difficulty lies in likelihood approximation: while autoregressive models naturally provide token-level conditional probabilities essential for token-level RL objectives (e.g., GRPO), dLLMs generate sequences through iterative non-autoregressive denoising steps that lack this factorization. To address this fundamental mismatch, we propose ELBO-based Sequence-level Policy Optimization (ESPO), a principled RL framework that treats entire sequence generation as a single action and uses the ELBO as a tractable sequence-level likelihood proxy. Our method incorporates per-token normalization of importance ratios and robust KL-divergence estimation to ensure stable large-scale training. Extensive experiments on mathematical reasoning, coding, and planning tasks demonstrate that ESPO significantly outperforms token-level baselines, achieving dramatic improvements of 20-40 points on the Countdown task, while maintaining consistent gains on math and coding benchmarks. Our approach establishes sequence-level optimization as a principled and empirically effective paradigm for RL in dLLMs.