ICLR 2026 Papers

Reinforcement learning (RL) has become a cornerstone for enhancing the reasoning capabilities of large language models (LLMs), with recent innovations such as Group Relative Policy Optimization (GRPO) demonstrating exceptional effectiveness. In this study, we identify a critical yet underexplored issue in RL training: low-probability tokens disproportionately influence model updates due to their large gradient magnitudes. This dominance hinders the effective learning of high-probability tokens, whose gradients are essential for LLMs' performance but are substantially suppressed. To mitigate this interference, we propose two novel methods: Advantage Reweighting and Low-Probability Token Isolation (Lopti), both of which effectively attenuate gradients from low-probability tokens while emphasizing parameter updates driven by high-probability tokens. Our approaches promote balanced updates across tokens with varying probabilities, thereby enhancing the efficiency of RL training. Experimental results demonstrate that they substantially improve the performance of GRPO-trained LLMs, achieving up to a 46.2% improvement in K&K Logic Puzzle reasoning tasks.

Online alignment (e.g., GRPO) is generally more performant than offline alignment (e.g., DPO)---but why? Drawing on prospect theory from behavioral economics, we propose a human-centric explanation. We prove that online on-policy sampling better approximates the human-perceived distribution of what the model can produce, and PPO/GRPO-style clipping---originally introduced to just stabilize training---recovers a perceptual bias in how humans perceive probability. In this sense, PPO/GRPO act as perceptual losses already. Our theory further suggests that the online/offline dichotomy is itself incidental to maximizing human utility, since we can achieve the same effect by selectively training on any data in a manner that mimics human perception, rather than restricting ourselves to online on-policy data. Doing so would allow us to post-train more quickly, cheaply, and flexibly without sacrificing performance. To this end, we propose a design pattern that explicitly incorporates perceptual distortions of probability into objectives like DPO/KTO/GRPO, creating $\textit{humanline variants}$ of them. Surprisingly, we find that these humanline variants, even when trained with offline off-policy data, can match the performance of their online counterparts on both verifiable and unverifiable tasks.

Quality-Diversity (QD) algorithms have shown remarkable success in discovering diverse, high-performing solutions, but rely heavily on hand-crafted behavioral descriptors that constrain exploration to predefined notions of diversity. Leveraging the equivalence between policies and occupancy measures, we present a theoretically grounded approach to automatically generate behavioral descriptors by embedding the occupancy measures of policies in Markov Decision Processes. Our method, AutoQD, leverages random Fourier features to approximate the Maximum Mean Discrepancy (MMD) between policy occupancy measures, creating embeddings whose distances reflect meaningful behavioral differences. A low-dimensional projection of these embeddings that captures the most behaviorally significant dimensions can then be used as behavioral descriptors for CMA-MAE, a state of the art blackbox QD method, to discover diverse policies. We prove that our embeddings converge to true MMD distances between occupancy measures as the number of sampled trajectories and embedding dimensions increase. Through experiments in multiple continuous control tasks we demonstrate AutoQD's ability in discovering diverse policies without predefined behavioral descriptors, presenting a well-motivated alternative to prior methods in unsupervised Reinforcement Learning and QD optimization. Our approach opens new possibilities for open-ended learning and automated behavior discovery in sequential decision making settings without requiring domain-specific knowledge.

Practical guidance on training Large Language Models (LLMs) to leverage Code Interpreter across diverse tasks remains lacking. We present R1-Code-Interpreter, an extension of a text-only LLM trained via multi-turn supervised fine-tuning (SFT) and reinforcement learning (RL) to autonomously generate multiple code queries during step-by-step reasoning. Unlike prior RL + tool-use efforts focused on narrow domains such as math or retrieval, we curate 144 diverse reasoning and planning tasks and show that training a general-purpose Code Interpreter across them presents significant challenges due to task heterogeneity and scarcity of effective samples. To address this, we introduce a multi-stage curriculum learning approach that partitions training samples by measured improvement potential. The RL training prioritizes samples with higher potential and gradually shifts to lower-potential ones, increasing the average RL gains from merely +3.4\% to +9.3\% across Qwen-2.5 models (3/7/14B). Our final model, R1-CI-14B, improves average accuracy on the 37 test tasks from 44.1\% to 72.4\%, outperforming text-only GPT-4o (58.6\%) and GPT-4o with Code Interpreter (70.9\%). Notably, R1-CI-14B also exhibits emergent self-checking behavior through code generation.

Temporal point processes (TPPs) are a fundamental tool for modeling event sequences in continuous time, but most existing approaches rely on autoregressive parameterizations that are limited by their sequential sampling. Recent non-autoregressive, diffusion-style models mitigate these issues by jointly interpolating between noise and data through event insertions and deletions in a discrete Markov chain. In this work, we generalize this perspective and introduce an Edit Flow process for TPPs that transports noise to data via insert, delete, and substitute edit operations. By learning the instantaneous edit rates within a continuous-time Markov chain framework, we attain a flexible and efficient model that effectively reduces the total number of necessary edit operations during generation. Empirical results demonstrate the generative flexibility of our unconditionally trained model in a wide range of unconditional and conditional generation tasks on benchmark TPPs.

Clustering is a hard discrete optimization problem. Nonconvex approaches such as low-rank semidefinite programming (SDP) have recently demonstrated promising statistical and local algorithmic guarantees for cluster recovery. Due to the combinatorial structure of the $K$-means clustering problem, current relaxation algorithms struggle to balance their constraint feasibility and objective optimality, presenting tremendous challenges in computing the second-order critical points with rigorous guarantees. In this paper, we provide a new formulation of the $K$-means problem as a smooth unconstrained optimization over a submanifold and characterize its Riemannian structures to allow it to be solved using a second-order cubic-regularized Riemannian Newton algorithm. By factorizing the $K$-means manifold into a product manifold, we show how each Newton subproblem can be solved in linear time. Our numerical experiments show that the proposed method converges significantly faster than the state-of-the-art first-order nonnegative low-rank factorization method, while achieving similarly optimal statistical accuracy.

Dataset distillation aims to find a small synthetic training set, such that training on the synthetic data achieves similar performance to training on a larger training dataset. Early methods solve this by interpreting the distillation problem as a bi-level optimization problem. On the other hand, disentangled methods bypass pixel-space optimization by matching data distributions and using generative techniques, leading to better computational complexity in terms of size of both training and distilled datasets. We demonstrate that by using latent spaces, the empirically successful disentangled methods can be reformulated as an optimal quantization problem, where a finite set of points is found to approximate the underlying probability measure. In particular, we link disentangled dataset distillation methods to the classical problem of optimal quantization, and are the first to demonstrate consistency of distilled datasets for diffusion-based generative priors. We propose Dataset Distillation by Optimal Quantization (DDOQ), based on clustering in the latent space of latent diffusion models. Compared to a similar clustering method D4M, we achieve better performance and inter-model generalization on the ImageNet-1K dataset using the same model and with trivial additional computation, achieving SOTA performance in higher image-per-class settings. Using the distilled noise initializations in a stronger diffusion transformer model, we obtain competitive or SOTA distillation performance on ImageNet-1K and its subsets, outperforming recent diffusion guidance methods.

Linear bandits have become a cornerstone of online learning and sequential decision-making, providing solid theoretical foundations for balancing exploration and exploitation. Within this domain, matrix sketching serves as a critical component for achieving computational efficiency, especially when confronting high-dimensional problem instances. The sketch-based approaches reduce per-round complexity from $\Omega(d^2)$ to $O(dl)$, where $d$ is the dimension and $l<d$ is the sketch size. However, this computational efficiency comes with a fundamental pitfall: when the streaming matrix exhibits heavy spectral tails, such algorithms can incur vacuous *linear regret*. In this paper, we revisit the regret bounds and algorithmic design for sketch-based linear bandits. Our analysis reveals that inappropriate sketch sizes can lead to substantial spectral error, severely undermining regret guarantees. To overcome this issue, we propose Dyadic Block Sketching, a novel multi-scale matrix sketching approach that dynamically adjusts the sketch size during the learning process. We apply this technique to linear bandits and demonstrate that the new algorithm achieves *sublinear regret* bounds without requiring prior knowledge of the streaming matrix properties. It establishes a general framework for efficient sketch-based linear bandits, which can be integrated with any matrix sketching method that provides covariance guarantees. Comprehensive experimental evaluation demonstrates the superior utility-efficiency trade-off achieved by our approach.

Decision-focused learning (DFL) is an increasingly popular paradigm for training predictive models whose outputs are used in decision-making tasks. Instead of merely optimizing for predictive accuracy, DFL trains models to directly minimize the loss associated with downstream decisions. However, existing studies focus solely on scenarios where a fixed batch of data is available and the objective function does not change over time. We instead investigate DFL in dynamic environments where the objective function and data distribution evolve over time. This setting is challenging for online learning because the objective function has zero or undefined gradients---which prevents the use of standard first-order optimization methods---and is generally non-convex. To address these difficulties, we (i) regularize the objective to make it differentiable and (ii) use perturbation techniques along with a near-optimal oracle to overcome non-convexity. Combining those techniques yields two original online algorithms tailored for DFL, for which we establish respectively static and dynamic regret bounds. These are the first provable guarantees for the online decision-focused problem. Finally, we showcase the effectiveness of our algorithms on a knapsack experiment, where they outperform two standard benchmarks.

Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and others. Among the existing OT approaches, of considerable interest are adversarial minimax solvers based on semi-dual formulations of OT problems. While promising, these methods lack theoretical investigation from a statistical learning perspective. Our work fills this gap by establishing upper bounds on the generalization error of an approximate OT map recovered by the minimax quadratic OT solver. Importantly, the bounds we derive depend solely on some standard statistical and mathematical properties of the considered functional classes (neural nets). While our analysis focuses on the quadratic OT, we believe that similar bounds could be derived for general OT case, paving the promising direction for future research. Our experimental illustrations are available online https://github.com/milenagazdieva/StatOT.

Unified multimodal Large Language Models (LLMs) that can both understand and generate visual content hold immense potential. However, existing open-source models often suffer from a performance trade-off between these capabilities. We present Manzano, a simple and scalable unified framework that substantially reduces this tension by coupling a hybrid image tokenizer with a well-curated training recipe. A single shared vision encoder feeds two lightweight adapters that produce continuous embeddings for image-to-text understanding and discrete tokens for text-to-image generation within a common semantic space. A unified autoregressive LLM predicts high-level semantics in the form of text and image tokens, with an auxiliary diffusion decoder subsequently translating the image tokens into pixels. The architecture, together with a unified training recipe over understanding and generation data, enables scalable joint learning of both capabilities. Manzano achieves state-of-the-art results among unified models, and is competitive with specialist models, particularly on text-rich evaluation. Our studies show minimal task conflicts and consistent gains from scaling model size, validating our design choice of a hybrid tokenizer.

Recent findings reveal that token embeddings of Large Language Models (LLMs) exhibit strong hyperbolicity. This insight motivates leveraging LLMs for scientific taxonomy tasks, where maintaining and expanding hierarchical knowledge structures is critical. Although potential, generally-trained LLMs face challenges in directly handling domain-specific taxonomies, including computational cost and hallucination. Meanwhile, Small Language Models (SLMs) provide a more economical alternative if empowered with proper knowledge transfer. In this work, we introduce SS-Mono (Structure-Semantic Monotonization), a novel pipeline that combines local taxonomy augmentation from LLMs, self-supervised fine-tuning of SLMs with geometric constraints, and LLM calibration. Our approach enables efficient and accurate taxonomy expansion across root, leaf, and intermediate nodes. Extensive experiments on both leaf and non-leaf expansion benchmarks demonstrate that a fine-tuned SLM (e.g., DistilBERT-base-110M) consistently outperforms frozen LLMs (e.g., GPT-4o, Gemma-2-9B) and domain-specific baselines. These findings highlight the promise of lightweight yet effective models for structured knowledge enrichment in scientific domains.

Large vision–language models (VLMs) deliver state-of-the-art results on a wide range of multimodal tasks, yet they remain prone to visual hallucinations, producing content that is not grounded in the input image. Despite progress with visual supervision, reinforcement learning, and post-hoc attention reshaping, the representational origins of hallucinations remain unclear. Our study reveals that successful grounding emerges when adjacent visual tokens exhibit coherent alignment, while hallucinations arise when key vectors scatter isotropically, weakening cross-modal attention and blurring object boundaries. Building on this insight, we propose Depth and Spatial aware Cache Refinement (DSCR), a lightweight and training-free method that augments the Transformer's key-value (KV) cache with depth cues and 2D spatial proximity. DSCR clusters vectors within objects and separates those across surfaces, guiding attention toward relevant regions without any fine-tuning. Comprehensive evaluations show that DSCR consistently reduces hallucinations, delivering up to 23\% accuracy gains across MME, POPE, RePOPE, CHAIR, and a new depth-sensitive benchmark. Our findings highlight KV-coherence as a core factor behind hallucinations and demonstrate a practical, model-agnostic solution for enhancing VLM reliability.

Neural networks applied to sequential decision-making tasks typically rely on latent representations of environment states. While environment dynamics dictate how semantic states evolve, the corresponding latent transitions are usually left implicit, leaving room for misalignment between the two. We propose to model latent dynamics explicitly by drawing an analogy between Markov decision process (MDP) trajectories and ordinary differential equation (ODE) flows: in both cases, the current state fully determines its successors. Building on this view, we introduce a neural ODE–based regularization method that enforces latent embeddings to follow consistent ODE flows, thereby aligning representation learning with environment dynamics. Although broadly applicable to deep learning agents, we demonstrate its effectiveness in reinforcement learning by integrating it into Actor–Critic algorithms, where it yields major performance gains across various standard Atari benchmarks for A2C as well as gridworld environments for PPO.

Imitation learning for manipulation has a well-known data scarcity problem. Unlike natural language and 2D computer vision, there is no Internet-scale corpus of data for dexterous manipulation. One appealing option is egocentric human video, a passively scalable data source. However, existing large-scale datasets such as Ego4D do not have native hand pose annotations and do not focus on object manipulation. To this end, we use Apple Vision Pro to collect EgoDex: the largest and most diverse dataset of dexterous human manipulation to date. EgoDex has 829 hours of egocentric video with paired 3D hand and finger tracking data collected at the time of recording, where multiple calibrated cameras and on-device SLAM can be used to precisely track the pose of every joint of each hand. The dataset covers a wide range of diverse manipulation behaviors with everyday household objects in 194 different tabletop tasks ranging from tying shoelaces to folding laundry. Furthermore, we train and systematically evaluate imitation learning policies for hand trajectory prediction on the dataset, introducing metrics and benchmarks for measuring progress in this increasingly important area. By releasing this large-scale dataset, we hope to push the frontier of robotics, computer vision, and foundation models. EgoDex is publicly available for download.

Inferring ground truth from noisy, crowdsourced labels is a fundamental challenge in machine learning. For decades, the dominant paradigm has relied on dataset-specific parameter estimation, a non-scalable method that fails to transfer knowledge. Recent efforts toward universal aggregation models do not account for the structural and behavioral complexities of human-annotated crowdsourcing, resulting in poor real-world performance. To address this gap, we introduce CrowdFM, a foundation model for crowdsourced label aggregation. At its core, CrowdFM is a bipartite graph neural network that is pre-trained on a vast, domain-randomized synthetic dataset. By leveraging a size-invariant initialization and attention-based message passing, it learns universal principles of collective intelligence and generalizes to new, unseen datasets. Extensive experiments on 22 real-world benchmarks show that our single, fixed model consistently matches or surpasses bespoke, per-dataset methods in both accuracy and efficiency. Furthermore, the representations learned by CrowdFM readily support diverse downstream applications, such as worker assessment and task assignment. Code and pre-trained models will be made publicly available upon acceptance.

Evaluating the faithfulness of attribution methods remains an open challenge. Standard metrics such as Insertion and Deletion Scores rely on heuristic input perturbations (e.g., zeroing pixels), which often push samples out of the data distribution (OOD). This can distort model behavior and lead to unreliable evaluations. We propose FUD, a novel evaluation framework that reconstructs masked regions using score-based diffusion models to produce in-distribution, semantically coherent inputs. This distribution-aware approach avoids the common pitfalls of existing Attribution Evaluation Methods (AEMs) and yields assessments that more accurately reflect attribution faithfulness. Experiments across models show that FUD produces significantly different—and more reliable—judgments than prior approaches. Our implementation is available at: https://anonymous.4open.science/r/FUD-CCD5/

Large Vision-Language Models (LVLMs), such as GPT-4o and LLaVA, have recently witnessed remarkable advancements and are increasingly being deployed in real-world applications. However, inheriting the sensitivity of visual neural networks, LVLMs remain vulnerable to adversarial attacks, which can result in erroneous or malicious outputs. While existing efforts utilize adversarial fine-tuning to enhance robustness, they often suffer from significant performance degradation on clean inputs. In this paper, we propose AdPO, a novel adversarial defense strategy for LVLMs based on preference optimization. For the first time, we reframe adversarial training as a preference optimization problem, aiming to enhance the model’s preference for generating normal outputs on clean inputs while rejecting the potential misleading outputs for adversarial examples. Notably, AdPO achieves this by solely modifying the image encoder, e.g., CLIP ViT, resulting in superior clean and adversarial performance in a variety of downstream tasks. Due to the computational cost of training large language models, we show that training on smaller LVLMs and transferring to larger ones achieves state-of-the-art performance with efficiency comparable to previous methods. Our comprehensive experiments confirm the effectiveness of the proposed AdPO which highlights the potential of preference-based learning in adversarially robust multimodal systems.

Post-training quantization (PTQ) is an attractive approach for compressing diffusion models to speed up the sampling process and reduce the memory footprint. Most existing PTQ methods uniformly sample data from various time steps in the denoising process to construct a calibration set for quantization and consider calibration samples equally important during quantization process. However, treating all calibration samples equally may not be optimal. One notable property in the denoising process of diffusion models is low-frequency features are primarily recovered in early stages, while high-frequency features are recovered in later stages of the denoising process. However, none of previous works on quantization for diffusion models consider this property to enhance the effectiveness of quantized models. In this paper, we propose a novel meta-learning approach for PTQ of diffusion models that jointly optimizes the contributions of calibration samples and the weighting of frequency components at each time step for quantizing noise estimation networks. Specifically, our approach automatically learns to assign optimal weights to calibration samples while selectively focusing on mimicking specific frequency components of data generated by the full-precision noise estimation network at each denoising time step. Extensive experiments on CIFAR-10, LSUN-Bedrooms, FFHQ, and ImageNet datasets demonstrate that our approach consistently outperforms state-of-the-art PTQ methods for diffusion models.