Daily Papers

Long-horizon video editing agents receive final-product feedback only after many interdependent decisions. Yet editing quality is subjective, admits multiple valid solutions, and is not meaningfully calibrated across heterogeneous requests, making a global scalar objective both ambiguous and temporally uninformative. Our key observation is that fixing the request, materials, and production constraints converts this subjective objective into an ordinal comparison among directly comparable alternatives. We introduce Group-Relative Preference Backpropagation (GRPB), which transforms same-task rankings into zero-sum advantages and redistributes them as bounded credit over semantic editing segments. A lagged allocator and guarded transmission prevent current judgments or unreliable estimates from directly shaping the same rollout group. We manually construct a project-disjoint, horizon-stratified suite of realistic editing tasks for training and controlled evaluation. Across matched baselines, credit interventions, external benchmarking, and blinded human evaluation, GRPB improves both editing behavior and rendered products. The resulting 9B Crayotter model surpasses several proprietary systems on AgenticVBench, supporting task-local preference reduction as a practical approach to learning from subjective, delayed outcomes. Code and all supporting materials are publicly available at https://github.com/idwts/Crayotter.

Group Relative Policy Optimization (GRPO) is a prominent reinforcement learning algorithm for post-training Large Language Models (LLMs). It is commonly believed that GRPO necessitates a large group size to ensure stable training via precise statistical estimation, which incurs substantial computational overhead. In this work, we challenge this assumption by reframing GRPO as a form of contrastive learning, which reveals a fundamental connection to Direct Preference Optimization (DPO). Motivated by DPO's empirical success, we investigate the minimal two-rollout case (2-GRPO), a configuration previously deemed infeasible. We provide a rigorous theoretical analysis to validate 2-GRPO and demonstrate empirically that it achieves performance on par with 16-GRPO, despite using only 1/8 of the rollouts and reducing training time by over 70%.

Recent advances in large language models (LLMs) highlight the importance of post training techniques for improving reasoning and mathematical ability. Group Relative Policy Optimization (GRPO) has shown promise in this domain by combining group relative advantage estimation, PPO style clipping, and KL regularization. However, its complexity raises the question of whether all components are necessary for fostering reasoning behaviors. We conduct a systematic analysis of GRPO and identify two key findings: (1) incorporating negative feedback is essential training solely on actions above a baseline limits learning; and (2) PPO style constraints, such as policy ratio clipping, are not required to improve mathematical reasoning or performance. Building on these insights, we propose REINFORCE with Group Relative Advantage (RGRA), a simplified variant that retains group relative advantage estimation but removes PPO style clipping and policy ratio terms. Experiments across standard mathematical benchmarks indicate that RGRA has the potential to achieve stronger performance than GRPO. Our results suggest that simpler REINFORCE based approaches can effectively enhance reasoning in LLMs, offering a more transparent and efficient alternative to GRPO.

Group Relative Policy Optimization (GRPO) has become a standard reinforcement learning method for post-training language models. Recent work shows that GRPO can reduce the base model's reasoning capacity and underperform it in Pass@k when k is large, indicating reduced coverage of reasoning paths. We find that this reduction is associated with GRPO concentrating on responses that the base model already generates with high probability. We trace this concentration to two mechanisms in the GRPO update. At the response level, high-probability responses dominate the group gradient through repeated occurrence. At the token level, GRPO's importance ratio scales gradients, further reinforcing tokens that become more likely under the current policy. We propose ReCo, a reweighting method that addresses both effects. Response contributions are normalized by their expected occurrence within the rollout group, and the token-level importance ratio is replaced with a variance-based ratio that gives larger update scale to non-saturated decision points where alternative token choices remain plausible. Across Qwen2.5-Math-1.5B/7B and Llama-3.1-8B-Instruct on five mathematical reasoning benchmarks, ReCo improves Pass@k for large values of k and is comparable to GRPO for small values of k.

Generative Reward Models (GRMs) have attracted considerable research interest in reward modeling due to their interpretability, inference-time scalability, and potential for refinement through reinforcement learning (RL). However, widely used pairwise GRMs create a computational bottleneck when integrated with RL algorithms such as Group Relative Policy Optimization (GRPO). This bottleneck arises from two factors: (i) the O(n^2) time complexity of pairwise comparisons required to obtain relative scores, and (ii) the computational overhead of repeated sampling or additional chain-of-thought (CoT) reasoning to improve performance. To address the first factor, we propose Intergroup Relative Preference Optimization (IRPO), a novel RL framework that incorporates the well-established Bradley-Terry model into GRPO. By generating a pointwise score for each response, IRPO enables efficient evaluation of arbitrarily many candidates during RL training while preserving interpretability and fine-grained reward signals. Experimental results demonstrate that IRPO achieves state-of-the-art (SOTA) performance among pointwise GRMs across multiple benchmarks, with performance comparable to that of current leading pairwise GRMs. Furthermore, we show that IRPO significantly outperforms pairwise GRMs in post-training evaluations.

Large language models are increasingly aligned to human preferences via reward modeling, but user preference data are sensitive and often cannot be centralized. Federated learning keeps such data local while learning a shared initial reward model, which is later personalized for each client through local fine-tuning. Because users often assign opposite labels to the same pair of responses, existing federated methods address preference heterogeneity by clustering similar clients and training one reward model per group, assuming that each group requires its own initialization. We show that this assumption is unnecessary. Under balanced preference groups, a single FedAvg model, despite starting at nearly random accuracy, surpasses reward models trained separately for each ground-truth group after only a few local optimization steps. We attribute this phenomenon to the flatness of the shared initialization: averaging across all clients learns richer shared representations that distinguish responses while canceling conflicting preference directions, leaving the model near a decision boundary that can be rapidly adapted. Group imbalance breaks this effect as the cancellation becomes asymmetric and leaves minority clients too far from the boundary to recover. Motivated by this observation, we propose FedGD (Federated Learning with Group Debiasing), which discovers latent preference groups during federated training and learns a single reward model using group-debiased client sampling. By counteracting the effect of group imbalance, FedGD learns an initialization that remains highly adaptable, enabling effective personalization without prior knowledge of the underlying groups.

Reinforcement mid-training lets language models learn internal thoughts from unlabeled text, but efficient token-level credit assignment remains challenging. Existing group-relative methods require costly repeated generation. Learned critics offer single-rollout feedback, but accurate return prediction alone does not ensure reliable policy updates. Our analysis shows how training--inference mismatch and PPO clipping prevent a common offset in advantage estimates from cancelling out, introducing additional update drift. We propose , a twin-critic method that calibrates token-level advantages from a single generated trajectory. After warmup and held-out qualification, the critics provide two advantage estimates, combined using action-dependent weights learned through a conditional-moment saddle-point objective. This objective brings the average advantage at each prefix toward zero, while a signal-retention constraint prevents the correction from erasing the learning signal. Sharing information across text positions avoids repeated sampling of each prefix. Theoretically, we characterize optimal mixing under the signal-retention constraint and establish an upper bound on residual mean-induced drift. Experiments show that, compared with the state-of-the-art critic-free method, improves mean benchmark performance by 7.8\% and reduces mean training-step time by up to 63.4\%.

Reinforcement learning has become a cornerstone for enhancing the reasoning capabilities of Large Language Models, where group-based approaches such as GRPO have emerged as efficient paradigms that optimize policies by leveraging intra-group performance differences. However, these methods typically rely on absolute numerical rewards, introducing intrinsic limitations. In verifiable tasks, identical group evaluations often result in sparse supervision, while in open-ended scenarios, the score range instability of reward models undermines advantage estimation based on group means. To address these limitations, we propose Reinforcement Learning with Relative Rewards (RLRR), a framework that shifts reward shaping from absolute scoring to relative ranking. Complementing this framework, we introduce the Ranking Reward Model, a listwise preference model tailored for group-based optimization to directly generate relative rankings. By transforming raw evaluations into robust relative signals, RLRR effectively mitigates signal sparsity and reward instability. Experimental results demonstrate that RLRR yields consistent performance improvements over standard group-based baselines across reasoning benchmarks and open-ended generation tasks.

Group-relative policy optimization methods train language models by generating multiple rollouts per prompt and normalizing rewards with a shared mean reward baseline. In resource-constrained settings where the rollout budget is small, accuracy often degrades. We find that noise in the shared baseline induces advantage sign flips, where some rollouts receive an incorrect advantage sign, and the update direction is reversed. To address this, we propose Median-Centered Group Relative Policy Optimization (MC-GRPO), a simple and effective solution for small-rollout training. Our main idea is to replace the mean baseline with a median baseline: the median is far less sensitive to outlier rewards than the mean, mitigating the sign flips under small rollout size (G). We generate one additional rollout for median reference (G+1), and compute advantages by using the group median. With an odd-sized group, exactly one completion is the median and receives zero advantage, we exclude this pivot rollout from backpropagation so the number of gradient-contributing samples per prompt remains G, preserving the core update cost of standard G-rollout training. Across various GRPO-family methods and a wide range of models and scales, this median-centered training consistently improves stability and final accuracy in the low-rollout regime, reducing the gap between G=2 and G=8 to within 1%. Code is available at https://github.com/lotusroot-kim/MC-GRPO

We address the problem of performing backpropagation for computation graphs involving 3D transformation groups SO(3), SE(3), and Sim(3). 3D transformation groups are widely used in 3D vision and robotics, but they do not form vector spaces and instead lie on smooth manifolds. The standard backpropagation approach, which embeds 3D transformations in Euclidean spaces, suffers from numerical difficulties. We introduce a new library, which exploits the group structure of 3D transformations and performs backpropagation in the tangent spaces of manifolds. We show that our approach is numerically more stable, easier to implement, and beneficial to a diverse set of tasks. Our plug-and-play PyTorch library is available at https://github.com/princeton-vl/lietorch.

Group Relative Policy Optimization (GRPO) was introduced and used recently for promoting reasoning in LLMs under verifiable (binary) rewards. We show that the mean + variance calibration of these rewards induces a weighted contrastive loss in which the contrastive samples are synthetic data drawn from the previous policy. While GRPO was originally paired with clipping to keep updates near the old policy, we analyze variants that differ in reward normalization (mean-only vs mean + variance) and in how they regularize updates using KL divergence: either penalizing divergence from the previous model (mirror), penalizing divergence from a fixed reference model π_{ref}, or combining both forms of regularization. For each, the optimal policy π_n admits an explicit form in terms of the binary reward and the first and second order statistics of the reward under π_{n-1}, as well as the policies π_{n-1} and π_{ref}. Iterating results in a sequence {π_n} whose probability of success (PoS) obeys a simple recurrence that converges to a fixed point determined by the reference PoS and the regularization strength. We further show that this fixed point exceeds the reference, demonstrating that GRPO amplifies the policy's probability of success.

Recent advances in reasoning with large language models (LLMs) have shown the effectiveness of Monte Carlo Tree Search (MCTS) for generating high-quality intermediate trajectories, particularly in math and symbolic domains. Inspired by this, we explore how MCTS-derived trajectories, traditionally used for training value or reward models, can be repurposed to improve policy optimization in preference-based reinforcement learning (RL). Specifically, we focus on Group Relative Policy Optimization (GRPO), a recent algorithm that enables preference-consistent policy learning without value networks. We propose a staged GRPO training paradigm where completions are derived from partially revealed MCTS rollouts, introducing a novel tree-structured setting for advantage estimation. This leads to a rich class of prefix-conditioned reward signals, which we analyze theoretically and empirically. Our initial results indicate that while structured advantage estimation can stabilize updates and better reflect compositional reasoning quality, challenges such as advantage saturation and reward signal collapse remain. We propose heuristic and statistical solutions to mitigate these issues and discuss open challenges for learning under staged or tree-like reward structures.

Group Relative Policy Optimization (GRPO) enhances policy learning by computing gradients from relative comparisons among candidate outputs that share a common input prefix. Despite its effectiveness, GRPO introduces substantial computational overhead when processing long shared prefixes, which must be redundantly encoded for each group member. This inefficiency becomes a major scalability bottleneck in long-context learning scenarios. We propose Prefix Grouper, an efficient GRPO training algorithm that eliminates redundant prefix computation via a Shared-Prefix Forward strategy. In particular, by restructuring self-attention into two parts, our method enables the shared prefix to be encoded only once, while preserving full differentiability and compatibility with end-to-end training. We provide both theoretical and empirical evidence that Prefix Grouper is training-equivalent to standard GRPO: it yields identical forward outputs and backward gradients, ensuring that the optimization dynamics and final policy performance remain unchanged. Empirically, our experiments confirm that Prefix Grouper achieves consistent results while significantly reducing the computational cost of training, particularly in long-prefix scenarios. The proposed method is fully plug-and-play: it is compatible with existing GRPO-based architectures and can be seamlessly integrated into current training pipelines as a drop-in replacement, requiring no structural modifications and only minimal changes to input construction and attention computation. Prefix Grouper enables the use of larger group sizes under the same computational budget, thereby improving the scalability of GRPO to more complex tasks and larger models. Code is now available at https://github.com/johncaged/PrefixGrouper

Group relative policy optimization (GRPO), a core methodological component of DeepSeekMath and DeepSeek-R1, has emerged as a cornerstone for scaling reasoning capabilities of large language models. Despite its widespread adoption and the proliferation of follow-up works, the theoretical properties of GRPO remain less studied. This paper provides a unified framework to understand GRPO through the lens of classical U-statistics. We demonstrate that the GRPO policy gradient is inherently a U-statistic, allowing us to characterize its mean squared error (MSE), derive the finite-sample error bound and asymptotic distribution of the suboptimality gap for its learned policy. Our findings reveal that GRPO is asymptotically equivalent to an oracle policy gradient algorithm -- one with access to a value function that quantifies the goodness of its learning policy at each training iteration -- and achieves asymptotically optimal performance within a broad class of policy gradient algorithms. Furthermore, we establish a universal scaling law that offers principled guidance for selecting the optimal group size. Empirical experiments further validate our theoretical findings, demonstrating that the optimal group size is universal, and verify the oracle property of GRPO.

Reinforcement learning (RL) has demonstrated significant success in enhancing reasoning capabilities in large language models (LLMs). One of the most widely used RL methods is Group Relative Policy Optimization (GRPO)~Shao-2024-Deepseekmath, known for its memory efficiency and success in training DeepSeek-R1~Guo-2025-Deepseek. However, GRPO stalls when all sampled responses in a group are incorrect -- referred to as an all-negative-sample group -- as it fails to update the policy, hindering learning progress. The contributions of this paper are two-fold. First, we propose a simple yet effective framework that introduces response diversity within all-negative-sample groups in GRPO using AI feedback. We also provide a theoretical analysis, via a stylized model, showing how this diversification improves learning dynamics. Second, we empirically validate our approach, showing the improved performance across various model sizes (7B, 14B, 32B) in both offline and online learning settings with 10 benchmarks, including base and distilled variants. Our findings highlight that learning from all-negative-sample groups is not only feasible but beneficial, advancing recent insights from Xiong-2025-Minimalist.

Group Relative Policy Optimization (GRPO) has emerged as the de facto Reinforcement Learning (RL) objective driving recent advancements in Multimodal Large Language Models. However, extending this success to open-source multimodal generalist models remains heavily constrained by two primary challenges: the extreme variance in reward topologies across diverse visual tasks, and the inherent difficulty of balancing fine-grained perception with multi-step reasoning capabilities. To address these issues, we introduce Gaussian GRPO (G^2RPO), a novel RL training objective that replaces standard linear scaling with non-linear distributional matching. By mathematically forcing the advantage distribution of any given task to strictly converge to a standard normal distribution, N(0,1), G^2RPO theoretically ensures inter-task gradient equity, mitigates vulnerabilities to heavy-tail outliers, and offers symmetric update for positive and negative rewards. Leveraging the enhanced training stability provided by G^2RPO, we introduce two task-level shaping mechanisms to seamlessly balance perception and reasoning. First, response length shaping dynamically elicits extended reasoning chains for complex queries while enforce direct outputs to bolster visual grounding. Second, entropy shaping tightly bounds the model's exploration zone, effectively preventing both entropy collapse and entropy explosion. Integrating these methodologies, we present OpenVLThinkerV2, a highly robust, general-purpose multimodal model. Extensive evaluations across 18 diverse benchmarks demonstrate its superior performance over strong open-source and leading proprietary frontier models.

Reinforcement Learning (RL) has proven to be an effective post-training strategy for enhancing reasoning in vision-language models (VLMs). Group Relative Policy Optimization (GRPO) is a recent prominent method that encourages models to generate complete reasoning traces before answering, leading to increased token usage and computational cost. Inspired by the human-like thinking process-where people skip reasoning for easy questions but think carefully when needed-we explore how to enable VLMs to first decide when reasoning is necessary. To realize this, we propose TON, a two-stage training strategy: (i) a supervised fine-tuning (SFT) stage with a simple yet effective 'thought dropout' operation, where reasoning traces are randomly replaced with empty thoughts. This introduces a think-or-not format that serves as a cold start for selective reasoning; (ii) a GRPO stage that enables the model to freely explore when to think or not, while maximizing task-aware outcome rewards. Experimental results show that TON can reduce the completion length by up to 90% compared to vanilla GRPO, without sacrificing performance or even improving it. Further evaluations across diverse vision-language tasks-covering a range of reasoning difficulties under both 3B and 7B models-consistently reveal that the model progressively learns to bypass unnecessary reasoning steps as training advances. These findings shed light on the path toward human-like reasoning patterns in reinforcement learning approaches. Our code is available at https://github.com/kokolerk/TON.

Reinforcement learning (RL) has emerged as an effective approach for enhancing the reasoning capabilities of large language models (LLMs), especially in scenarios where supervised fine-tuning (SFT) falls short due to limited chain-of-thought (CoT) data. Among RL-based post-training methods, group relative advantage estimation, as exemplified by Group Relative Policy Optimization (GRPO), has attracted considerable attention for eliminating the dependency on the value model, thereby simplifying training compared to traditional approaches like Proximal Policy Optimization (PPO). However, we observe that exsiting group relative advantage estimation method still suffers from training inefficiencies, particularly when the estimated advantage approaches zero. To address this limitation, we propose Advantage-Augmented Policy Optimization (AAPO), a novel RL algorithm that optimizes the cross-entropy (CE) loss using advantages enhanced through a momentum-based estimation scheme. This approach effectively mitigates the inefficiencies associated with group relative advantage estimation. Experimental results on multiple mathematical reasoning benchmarks demonstrate the superior performance of AAPO.

Group Relative Policy Optimization (GRPO) is widely used for critic-free Large Language Model (LLM) post-training, but its KL regularization is usually implemented as a local loss-side token penalty. We show that this misses the policy-gradient signal induced by autoregressive KL regularization. Unlike standard KL-regularized Reinforcement Learning (RL) objectives, GRPO's group normalization induces a non-linear prompt-level utility; for binary verifier rewards, this utility is 2arcsinsqrt p. As a result, reward and KL cannot be fused before normalization without changing the implicit objective. We derive the on-policy gradient of GRPO-style objectives with token-wise f-divergence regularization. The reward term recovers the standardized GRPO advantage, while the regularizer term includes a causal future-regularization return-to-go omitted by local KL losses. For reverse KL, this yields a simple future KL correction: add a reverse cumulative sum of per-token log ratios after advantage construction. The resulting method, Future-KL Regularized Policy Optimization (FRPO), requires no critic or extra model passes. On mathematical reasoning tasks, FRPO improves pass@16 in our main large-model setting while maintaining higher entropy and lower policy drift than conventional loss-side KL baselines.

Large Language Models (LLMs) have shown promise in solving complex mathematical problems, yet they still fall short of producing accurate and consistent solutions. Reinforcement Learning (RL) is a framework for aligning these models with task-specific rewards, improving overall quality and reliability. Group Relative Policy Optimization (GRPO) is an efficient, value-function-free alternative to Proximal Policy Optimization (PPO) that leverages group-relative reward normalization. We introduce Iterative Group Relative Policy Optimization (iGRPO), a two-stage extension of GRPO that adds dynamic self-conditioning through model-generated drafts. In Stage 1, iGRPO samples multiple exploratory drafts and selects the highest-reward draft using the same scalar reward signal used for optimization. In Stage 2, it appends this best draft to the original prompt and applies a GRPO-style update on draft-conditioned refinements, training the policy to improve beyond its strongest prior attempt. Under matched rollout budgets, iGRPO consistently outperforms GRPO across base models (e.g., Nemotron-H-8B-Base-8K and DeepSeek-R1 Distilled), validating its effectiveness on diverse reasoning benchmarks. Moreover, applying iGRPO to OpenReasoning-Nemotron-7B trained on AceReason-Math achieves new state-of-the-art results of 85.62\% and 79.64\% on AIME24 and AIME25, respectively. Ablations further show that the refinement wrapper generalizes beyond GRPO variants, benefits from a generative judge, and alters learning dynamics by delaying entropy collapse. These results underscore the potential of iterative, self-feedback-based RL for advancing verifiable mathematical reasoning.

Recent works have demonstrated the effectiveness of reinforcement learning (RL)-based post-training in enhancing the reasoning capabilities of large language models (LLMs). In particular, Group Relative Policy Optimization (GRPO) has shown impressive success by employing a PPO-style reinforcement algorithm with group-based normalized rewards. However, the application of GRPO to Video Large Language Models (Video LLMs) has been less studied. In this paper, we explore GRPO for video LLMs and identify two primary issues that impede its effective learning: (1) reliance on safeguards, and (2) the vanishing advantage problem. To mitigate these challenges, we propose DeepVideo-R1, a video large language model trained with our proposed Reg-GRPO (Regressive GRPO) and difficulty-aware data augmentation strategy. Reg-GRPO reformulates the GRPO objective as a regression task, directly predicting the advantage in GRPO. This design eliminates the need for safeguards like clipping and min functions, thereby facilitating more direct policy guidance by aligning the model with the advantage values. We also design the difficulty-aware data augmentation strategy that dynamically augments training samples at solvable difficulty levels, fostering diverse and informative reward signals. Our comprehensive experiments show that DeepVideo-R1 significantly improves video reasoning performance across multiple video reasoning benchmarks.

Group Relative Policy Optimization (GRPO) is one of the most widely adopted RLVR algorithms for post-training large language models on reasoning tasks. We first show that GRPO admits an equivalent discriminative reformulation, in which policy optimization maximizes the expected score gap between verified positive and negative rollouts. This reformulation reveals two objective-level limitations: likelihood-misaligned surrogate scores, in which clipped ratio-based scores are optimized rather than the sequence likelihoods that govern generation, and score-insensitive credit assignment, in which rollout-level credit does not reflect the current score gaps between positive and negative rollouts. To address these limitations, we propose ConSPO, a Contrastive Sequence-level Policy Optimization method that uses length-normalized sequence log-probabilities as rollout scores and contrasts verified positive rollouts against negative distractors within the same group. ConSPO optimizes a group-wise InfoNCE-style objective to adaptively strengthen updates for poorly separated positives and high-scoring negatives, together with a curriculum-scheduled margin that preserves separation pressure as training progresses. Experiments across diverse settings show that ConSPO outperforms strong baselines on challenging reasoning benchmarks. Code will be released upon paper acceptance.

Recent advances in reinforcement learning (RL) have significantly enhanced the agentic capabilities of large language models (LLMs). In long-term and multi-turn agent tasks, existing approaches driven solely by outcome rewards often suffer from the problem of sparse supervision. To address the challenge, we propose Tree-based Group Relative Policy Optimization (Tree-GRPO), a grouped agent RL method based on tree search, where each tree node represents the complete agent interaction step. By sharing common prefixes, the tree search sampling increases the number of rollouts achievable within a fixed budget of tokens or tool calls. Moreover, we find that the tree-structured trajectory naturally allows the construction of step-wise process supervised signals even using only the outcome reward. Based on this, Tree-GRPO estimates the grouped relative advantages both on intra-tree and inter-tree levels. Through theoretical analysis, we demonstrate that the objective of intra-tree level group relative policy optimization is equivalent to that of step-level direct preference learning. Experiments across 11 datasets and 3 types of QA tasks demonstrate the superiority of the proposed tree-based RL over the chain-based RL method.

Group Relative Policy Optimization (GRPO) assigns a single scalar advantage to all tokens in a completion. For structured generations with explicit segments and objectives, this couples unrelated reward signals across segments, leading to objective interference and misattributed credit. We propose Blockwise Advantage Estimation, a family of GRPO-compatible methods that assigns each objective its own advantage and applies it only to the tokens in the corresponding text block, reducing reliance on hand-designed scalar rewards and scaling naturally to additional objectives. A key challenge is estimating advantages for later blocks whose rewards are conditioned on sampled prefixes; standard unbiased approaches require expensive nested rollouts from intermediate states. Concretely, we introduce an Outcome-Conditioned Baseline that approximates intermediate state values using only within-group statistics by stratifying samples according to a prefix-derived intermediate outcome. On math tasks with uncertainty estimation, our method mitigates reward interference, is competitive with a state-of-the-art reward-designed approach, and preserves test-time gains from confidence-weighted ensembling. More broadly, it provides a modular recipe for optimizing sequential objectives in structured generations without additional rollouts.

Adapting large language models (LLMs) for specific tasks usually involves fine-tuning through reinforcement learning with human feedback (RLHF) on preference data. While these data often come from diverse labelers' groups (e.g., different demographics, ethnicities, company teams, etc.), traditional RLHF approaches adopt a "one-size-fits-all" approach, i.e., they indiscriminately assume and optimize a single preference model, thus not being robust to unique characteristics and needs of the various groups. To address this limitation, we propose a novel Group Robust Preference Optimization (GRPO) method to align LLMs to individual groups' preferences robustly. Our approach builds upon reward-free direct preference optimization methods, but unlike previous approaches, it seeks a robust policy which maximizes the worst-case group performance. To achieve this, GRPO adaptively and sequentially weights the importance of different groups, prioritizing groups with worse cumulative loss. We theoretically study the feasibility of GRPO and analyze its convergence for the log-linear policy class. By fine-tuning LLMs with GRPO using diverse group-based global opinion data, we significantly improved performance for the worst-performing groups, reduced loss imbalances across groups, and improved probability accuracies compared to non-robust baselines.

While Group Relative Policy Optimization (GRPO) offers a powerful framework for LLM post-training, its effectiveness in open-ended domains like Machine Translation hinges on accurate intra-group ranking. We identify that standard Scalar Quality Metrics (SQM) fall short in this context; by evaluating candidates in isolation, they lack the comparative context necessary to distinguish fine-grained linguistic nuances. To address this, we introduce the Group Quality Metric (GQM) paradigm and instantiate it via the Group Relative Reward Model (GRRM). Unlike traditional independent scorers, GRRM processes the entire candidate group jointly, leveraging comparative analysis to rigorously resolve relative quality and adaptive granularity. Empirical evaluations confirm that GRRM achieves competitive ranking accuracy among all baselines. Building on this foundation, we integrate GRRM into the GRPO training loop to optimize the translation policy. Experimental results demonstrate that our framework not only improves general translation quality but also unlocks reasoning capabilities comparable to state-of-the-art reasoning models. We release codes, datasets, and model checkpoints at https://github.com/NJUNLP/GRRM.

We propose Fuzzy Group Relative Policy Reward (FGRPR), a novel framework that integrates Group Relative Policy Optimization (GRPO) with a fuzzy reward function to enhance learning efficiency. Unlike the conventional binary 0/1 accuracy reward, our fuzzy reward model provides nuanced incentives, encouraging more precise outputs. Experimental results demonstrate that GRPO with a standard 0/1 accuracy reward underperforms compared to supervised fine-tuning (SFT). In contrast, FGRPR, applied to Qwen2.5-VL(3B and 7B), surpasses all baseline models, including GPT4o, LLaMA2(90B), and SFT, across five in-domain datasets. On an out-of-domain dataset, FGRPR achieves performance comparable to SFT but excels when target values are larger, as its fuzzy reward function assigns higher rewards to closer approximations. This approach is broadly applicable to tasks where the precision of the answer is critical. Code and data: https://github.com/yeyimilk/CrowdVLM-R1

We revisit Group Relative Policy Optimization (GRPO) in both on-policy and off-policy optimization regimes. Our motivation comes from recent work on off-policy Proximal Policy Optimization (PPO), which improves training stability, sampling efficiency, and memory usage. In addition, a recent analysis of GRPO suggests that estimating the advantage function with off-policy samples could be beneficial. Building on these observations, we adapt GRPO to the off-policy setting. We show that both on-policy and off-policy GRPO objectives yield an improvement in the reward. This result motivates the use of clipped surrogate objectives in the off-policy version of GRPO. We then compare the empirical performance of reinforcement learning with verifiable rewards in post-training using both GRPO variants. Our results show that off-policy GRPO either significantly outperforms or performs on par with its on-policy counterpart.

Reinforcement Learning from Verifier Rewards (RLVR) has emerged as a widely used approach for post-training large language models on reasoning tasks, with group-based methods such as GRPO and its variants gaining broad adoption. These methods rely on group-relative advantage estimation to avoid learned critics, yet its theoretical properties remain poorly understood. In this work, we uncover a fundamental issue of group-based RL: the group-relative advantage estimator is inherently biased relative to the true (expected) advantage. We provide the first theoretical analysis showing that it systematically underestimates advantages for hard prompts and overestimates them for easy prompts, leading to imbalanced exploration and exploitation. To address this issue, we propose History-Aware Adaptive Difficulty Weighting (HA-DW), an adaptive reweighting scheme that adjusts advantage estimates based on an evolving difficulty anchor and training dynamics. Both theoretical analysis and experiments on five mathematical reasoning benchmarks demonstrate that HA-DW consistently improves performance when integrated into GRPO and its variants. Our results suggest that correcting biased advantage estimation is critical for robust and efficient RLVR training.

Recent progress in multimodal large language models has led to strong performance on reasoning tasks, but these improvements largely rely on high-quality annotated data or teacher-model distillation, both of which are costly and difficult to scale. To address this, we propose an unsupervised self-evolution training framework for multimodal reasoning that achieves stable performance improvements without using human-annotated answers or external reward models. For each input, we sample multiple reasoning trajectories and jointly model their within group structure. We use the Actor's self-consistency signal as a training prior, and introduce a bounded Judge based modulation to continuously reweight trajectories of different quality. We further model the modulated scores as a group level distribution and convert absolute scores into relative advantages within each group, enabling more robust policy updates. Trained with Group Relative Policy Optimization (GRPO) on unlabeled data, our method consistently improves reasoning performance and generalization on five mathematical reasoning benchmarks, offering a scalable path toward self-evolving multimodal models. The code are available at https://github.com/OPPO-Mente-Lab/LLM-Self-Judge.

Large Language Models (LLMs) have made remarkable progress in enhancing step-by-step reasoning through reinforcement learning. However, the Group Relative Policy Optimization (GRPO) algorithm, which relies on sparse reward rules, often encounters the issue of identical rewards within groups, leading to the advantage collapse problem. Existing works typically address this challenge from two perspectives: enforcing model reflection to enhance response diversity, and introducing internal feedback to augment the training signal (advantage). In this work, we begin by analyzing the limitations of model reflection and investigating the policy entropy of responses at the fine-grained sample level. Based on our experimental findings, we propose the EDGE-GRPO algorithm, which adopts Entropy-Driven Advantage and Guided Error Correction to effectively mitigate the problem of advantage collapse. Extensive experiments on several main reasoning benchmarks demonstrate the effectiveness and superiority of our approach. It is available at https://github.com/ZhangXJ199/EDGE-GRPO.

Group-relative reinforcement learning (RL) relies on reward variation among sampled responses to estimate informative relative advantages. As language models become increasingly capable, existing training data can become reward-saturated: all sampled responses to the same problem might receive equally high rewards, where the group-relative learning signals vanish and leave previously useful data obsolete. In this work, we investigate whether useful learning signals can be recovered from such saturated data. We study interventions at four levels of group-policy RL pipelines---data, rollout, reward, and advantage---and conduct extensive RL training on saturated reasoning data only. While standard GRPO on saturated data would almost always yield near-0 advantages and near-noise signals, diverse interventions successfully recycle and repurpose such data: among the proposed strategies, interventions at rollout generation are consistently most effective: nudging the policy to generate ``high-quality'', incorrect solutions introduces rollouts with poor rewards into saturated groups as negative samples, which turns out to improve GRPO by 6.4% to 9.0% across Qwen3-1.7B and 4B. Other interventions such as increasing rollout temperature or adding auxiliary rewards can also restore non-zero advantages, but yield less consistent gains. Further analyses show that effective negative rollouts require informative negative trajectories, that the method remains effective alongside unsaturated data, and that it supports iterative recycling of newly saturated examples. While increasingly stronger LLMs would render more data as saturated, our results demonstrate that don't waste your saturated data: with the right strategies they can be recycled into useful RL training signals in an increasingly data-scarce world.

Group-Relative Policy Optimization (GRPO) is a key technique for training large reasoning models, yet it suffers from a critical vulnerability: the Think-Answer Mismatch, where noisy reward signals corrupt the learning process. This problem is most severe in unbalanced response groups, paradoxically degrading the signal precisely when it should be most informative. To address this challenge, we propose Stable Group-Relative Policy Optimization (S-GRPO), a principled enhancement that derives optimal, noise-aware advantage weights to stabilize training. Our comprehensive experiments on mathematical reasoning benchmarks demonstrate S-GRPO's effectiveness and robustness. On various models, S-GRPO significantly outperforms DR. GRPO, achieving performance gains of +2.5% on Qwen-Math-7B-Base, +2.2% on Llama-3.2-3B-Base, and +2.4% on Qwen-Math-1.5B-Instruct. Most critically, while standard GRPO fails to learn under 20% synthetic reward noise, S-GRPO maintains stable learning progress. These results highlight S-GRPO's potential for more robust and effective training of large-scale reasoning models. \footnote{Code and data are available at: https://github.com/shenpeijun0212/S-GRPO

In the field of large language models (LLMs), aligning models with the diverse preferences of users is a critical challenge. Direct Preference Optimization (DPO) has played a key role in this area. It works by using pairs of preferences derived from the same prompts, and it functions without needing an additional reward model. However, DPO does not fully reflect the complex nature of human learning, which often involves understanding contrasting responses to not only identical but also similar questions. To overcome this shortfall, we propose Relative Preference Optimization (RPO). RPO is designed to discern between more and less preferred responses derived from both identical and related prompts. It introduces a contrastive weighting mechanism, enabling the tuning of LLMs using a broader range of preference data, including both paired and unpaired sets. This approach expands the learning capabilities of the model, allowing it to leverage insights from a more varied set of prompts. Through empirical tests, including dialogue and summarization tasks, and evaluations using the AlpacaEval2.0 leaderboard, RPO has demonstrated a superior ability to align LLMs with user preferences and to improve their adaptability during the training process. Our code can be viewed at https://github.com/yinyueqin/relative-preference-optimization

Large language models are typically post-trained using supervised fine-tuning (SFT) and reinforcement learning (RL), yet effectively unifying efficient knowledge injection with robust generalization remains challenging. In this work, we provide a training-dynamics analysis showing that SFT can be interpreted as a special case of policy gradient optimization with an extremely sparse implicit reward and unstable inverse-probability weighting, which together lead to single-path dependency, entropy collapse, and gradient explosion. Motivated by this diagnosis, we propose Group Fine-Tuning (GFT), a unified post-training framework that addresses these intrinsic limitations through two mechanisms: Group Advantage Learning, which constructs diverse response groups and derives normalized contrastive supervision to alleviate reward sparsity, and Dynamic Coefficient Rectification, which adaptively bounds inverse-probability weights to stabilize optimization while preserving efficient knowledge injection. Experiments demonstrate that GFT consistently surpasses SFT-based methods and yields policies that integrate more smoothly with subsequent RL training.

Reinforcement learning has been widely applied to enhance the reasoning capabilities of large language models. Extending the inference limits of smaller models has become a prominent research focus. However, algorithms such as Group Relative Policy Optimization (GRPO) suffer from a clear drawback: the upper bound of a model's rollout responses is entirely determined by the model itself, preventing the acquisition of knowledge from samples that are either all incorrect or all correct. In this paper, we introduce Group Contrastive Policy Optimization (GCPO), a method that incorporates external standard reference answers. When the model cannot solve a problem, the reference answer supplies the correct response, steering the model toward an unequivocally accurate update direction. This approach offers two main advantages: (1) it improves training efficiency by fully utilizing every sample; (2) it enables the model to emulate the problem solving strategy of the reference answer during training, thereby enhancing generalization in reasoning. GCPO achieves outstanding results across multiple benchmark datasets, yielding substantial improvements over the baseline model. Our code is available at: https://github.com/AchoWu/GCPO.

Backpropagation (BP), a foundational algorithm for training artificial neural networks, predominates in contemporary deep learning. Although highly successful, it is often considered biologically implausible. A significant limitation arises from the need for precise symmetry between connections in the backward and forward pathways to backpropagate gradient signals accurately, which is not observed in biological brains. Researchers have proposed several algorithms to alleviate this symmetry constraint, such as feedback alignment and direct feedback alignment. However, their divergence from backpropagation dynamics presents challenges, particularly in deeper networks and convolutional layers. Here we introduce the Product Feedback Alignment (PFA) algorithm. Our findings demonstrate that PFA closely approximates BP and achieves comparable performance in deep convolutional networks while avoiding explicit weight symmetry. Our results offer a novel solution to the longstanding weight symmetry problem, leading to more biologically plausible learning in deep convolutional networks compared to earlier methods.

Recent studies have demonstrated that Reinforcement Learning (RL), notably Group Relative Policy Optimization (GRPO), can intrinsically elicit and enhance the reasoning capabilities of Vision-Language Models (VLMs). However, despite the promise, the underlying mechanisms that drive the effectiveness of RL models as well as their limitations remain underexplored. In this paper, we highlight a fundamental behavioral distinction between RL and base models, where the former engages in deeper yet narrow reasoning, while base models, despite less refined along individual path, exhibit broader and more diverse thinking patterns. Through further analysis of training dynamics, we show that GRPO is prone to diversity collapse, causing models to prematurely converge to a limited subset of reasoning strategies while discarding the majority of potential alternatives, leading to local optima and poor scalability. To address this, we propose Multi-Group Policy Optimization (MUPO), a simple yet effective approach designed to incentivize divergent thinking across multiple solutions, and demonstrate its effectiveness on established benchmarks. Project page: https://xytian1008.github.io/MUPO/

Recent advancements in reinforcement learning, particularly through Group Relative Policy Optimization (GRPO), have significantly improved multimodal large language models for complex reasoning tasks. However, two critical limitations persist: 1) they often produce unfocused, verbose reasoning chains that obscure salient spatiotemporal cues and 2) binary rewarding fails to account for partially correct answers, resulting in high reward variance and inefficient learning. In this paper, we propose TW-GRPO, a novel framework that enhances visual reasoning with focused thinking and dense reward granularity. Specifically, we employs a token weighting mechanism that prioritizes tokens with high informational density (estimated by intra-group variance), suppressing redundant tokens like generic reasoning prefixes. Furthermore, we reformulate RL training by shifting from single-choice to multi-choice QA tasks, where soft rewards enable finer-grained gradient estimation by distinguishing partial correctness. Additionally, we propose question-answer inversion, a data augmentation strategy to generate diverse multi-choice samples from existing benchmarks. Experiments demonstrate state-of-the-art performance on several video reasoning and general understanding benchmarks. Notably, TW-GRPO achieves 50.4\% accuracy on CLEVRER (18.8\% improvement over Video-R1) and 65.8\% on MMVU. Our codes are available at https://github.com/longmalongma/TW-GRPO.

Benefiting from pre-trained text-to-image (T2I) diffusion models, real-world image super-resolution (Real-ISR) methods can synthesize rich and realistic details. However, due to the inherent stochasticity of T2I models, different noise inputs often lead to outputs with varying perceptual quality. Although this randomness is sometimes seen as a limitation, it also introduces a wider perceptual quality range, which can be exploited to improve Real-ISR performance. To this end, we introduce Direct Perceptual Preference Optimization for Real-ISR (DP^2O-SR), a framework that aligns generative models with perceptual preferences without requiring costly human annotations. We construct a hybrid reward signal by combining full-reference and no-reference image quality assessment (IQA) models trained on large-scale human preference datasets. This reward encourages both structural fidelity and natural appearance. To better utilize perceptual diversity, we move beyond the standard best-vs-worst selection and construct multiple preference pairs from outputs of the same model. Our analysis reveals that the optimal selection ratio depends on model capacity: smaller models benefit from broader coverage, while larger models respond better to stronger contrast in supervision. Furthermore, we propose hierarchical preference optimization, which adaptively weights training pairs based on intra-group reward gaps and inter-group diversity, enabling more efficient and stable learning. Extensive experiments across both diffusion- and flow-based T2I backbones demonstrate that DP^2O-SR significantly improves perceptual quality and generalizes well to real-world benchmarks.

Group Relative Policy Optimisation (GRPO) enhances large language models by estimating advantages across a group of sampled trajectories. However, mapping these trajectory-level advantages to policy updates requires aggregating token-level probabilities within each sequence. Relying on a fixed aggregation mechanism for this step fundamentally limits the algorithm's adaptability. Empirically, we observe a critical trade-off: certain fixed aggregations frequently suffer from training collapse, while others fail to yield satisfactory performance. To resolve this, we propose HölderPO, a generalised policy optimisation framework unifying token-level probability aggregation via the Hölder mean. By explicitly modulating the parameter p, our framework provides continuous control over the trade-off between gradient concentration and variance bounds. Theoretically, we prove that a larger p concentrates the gradient to amplify sparse learning signals, whereas a smaller p strictly bounds gradient variance. Because no static configuration can universally resolve this concentration-stability trade-off, we instantiate the framework with a dynamic annealing algorithm that progressively schedules p across the training lifecycle. Extensive evaluations demonstrate superior stability and convergence over existing baselines. Specifically, our approach achieves a state-of-the-art average accuracy of 54.9% across multiple mathematical benchmarks, yielding a substantial 7.2% relative gain over standard GRPO and secures an exceptional 93.8% success rate on ALFWorld.

Group-based reinforcement learning methods such as GRPO for large language models avoid training a critic by sampling multiple responses for each prompt. A reliable critic could instead estimate token-level advantages from one response, but standard critic-based training recipes are often unstable. We study this instability and develop **Best Practice Critic Optimization (BPCO)**, a recipe that combines DPPO, value predictions bounded to the reward range, Monte Carlo value targets, unnormalized policy advantages, and length-adaptive generalized advantage estimation. Because the critic is used only during training, BPCO can also condition it on reward-defining information, such as a reference answer or grading rubric, that is hidden from the policy. Controlled experiments isolate the effect of each design choice. Across mathematical reasoning tasks with models ranging from 1.5B parameters to 30B-A3B mixtures of experts, BPCO improves a strong critic-based baseline consistently, and matches or exceeds a group-based baseline while sampling one response per prompt. The same recipe also improves learning with rubric-based rewards. These results show that a carefully designed critic provides a reliable alternative to group-relative advantage estimation. Code is available at https://github.com/QPHutu/golden_critic.

Recent advances of reasoning models, exemplified by OpenAI's o1 and DeepSeek's R1, highlight the significant potential of Reinforcement Learning (RL) to enhance the reasoning capabilities of Large Language Models (LLMs). However, replicating these advancements across diverse domains remains challenging due to limited methodological transparency. In this work, we present two-Staged history-Resampling Policy Optimization (SRPO), which successfully surpasses the performance of DeepSeek-R1-Zero-32B on the AIME24 and LiveCodeBench benchmarks. SRPO achieves this using the same base model as DeepSeek (i.e. Qwen2.5-32B) and relies solely on RL, without prior Supervised Fine-Tuning (SFT). Building upon Group Relative Policy Optimization (GRPO), we introduce two key methodological innovations: (1) a two-stage cross-domain training paradigm designed to balance the development of mathematical reasoning and coding proficiency, and (2) History Resampling (HR), a technique to address ineffective samples. Our comprehensive experiments validate the effectiveness of our approach, dedicating to offer valuable insights into scaling LLM reasoning capabilities across diverse tasks.

The evolution of Large Language Models (LLMs) has catalyzed a paradigm shift from superficial instruction following to rigorous long-horizon reasoning. While Group Relative Policy Optimization (GRPO) has emerged as a pivotal mechanism for eliciting such post-training reasoning capabilities due to its exceptional performance, it remains plagued by significant training instability and poor sample efficiency. We theoretically identify the root cause of these issues as the lack of distinctiveness within on-policy rollouts: for routine queries, highly homogeneous samples induce destructive gradient conflicts; whereas for hard queries, the scarcity of valid positive samples results in ineffective optimization. To bridge this gap, we propose Distinctiveness-aware Group Relative Policy Optimization (DaGRPO). DaGRPO incorporates two core mechanisms: (1) Sequence-level Gradient Rectification, which utilizes fine-grained scoring to dynamically mask sample pairs with low distinctiveness, thereby eradicating gradient conflicts at the source; and (2) Off-policy Data Augmentation, which introduces high-quality anchors to recover training signals for challenging tasks. Extensive experiments across 9 mathematical reasoning and out-of-distribution (OOD) generalization benchmarks demonstrate that DaGRPO significantly surpasses existing SFT, GRPO, and hybrid baselines, achieving new state-of-the-art performance (e.g., a +4.7% average accuracy gain on math benchmarks). Furthermore, in-depth analysis confirms that DaGRPO effectively mitigates gradient explosion and accelerates the emergence of long-chain reasoning capabilities.

Reinforcement Learning has become a standard paradigm for aligning Large Language Models with human intent and task requirements. While Group Relative Policy Optimization offers an efficient, value-model-free alternative to Proximal Policy Optimization, adapting it to real-world multi-reward settings remains challenging. Standard scalarization practices, such as Reward Combination and Advantage Combination, suffer from significant drawbacks: Reward Combination frequently generates advantages with excessively large squared magnitudes that lead to training instability, while Advantage Combination relies on static hyperparameters and ignores cross-objective correlations. To address these limitations, we propose Dynamic Variance-adaptive Advantage Optimization (DVAO), which dynamically adjusts combination weights based on the empirical reward variance of each objective within a rollout group, effectively up-weighting objectives with a stronger learning signal while suppressing noisy ones. We mathematically prove that DVAO maintains bounded advantage magnitudes for stable training and introduces a self-adaptive cross-objective regularization mechanism. Extensive experiments on mathematical reasoning and tool-use benchmarks using Qwen3 and Qwen2.5 models demonstrate that DVAO significantly outperforms baseline methods, achieving a superior multi-objective Pareto frontier and robust training stability.

Multimodal Large Language Models (MLLMs) have gained significant traction for their ability to process diverse input data types and generate coherent, contextually relevant outputs across various applications. While supervised fine-tuning (SFT) has been the predominant approach to enhance MLLM capabilities in task-specific optimization, it often falls short in fostering crucial generalized reasoning abilities. Although reinforcement learning (RL) holds great promise in overcoming these limitations, it encounters two significant challenges: (1) its generalized capacities in multimodal tasks remain largely unexplored, and (2) its training constraints, including the constant Kullback-Leibler divergence or the clamp strategy, often result in suboptimal bottlenecks. To address these challenges, we propose OThink-MR1, an advanced MLLM equipped with profound comprehension and reasoning capabilities across multimodal tasks. Specifically, we introduce Group Relative Policy Optimization with a dynamic Kullback-Leibler strategy (GRPO-D), which markedly enhances reinforcement learning (RL) performance. For Qwen2-VL-2B-Instruct, GRPO-D achieves a relative improvement of more than 5.72% over SFT and more than 13.59% over GRPO in same-task evaluation on two adapted datasets. Furthermore, GRPO-D demonstrates remarkable cross-task generalization capabilities, with an average relative improvement of more than 61.63% over SFT in cross-task evaluation. These results highlight that the MLLM trained with GRPO-D on one multimodal task can be effectively transferred to another task, underscoring the superior generalized reasoning capabilities of our proposed OThink-MR1 model.

While reinforcement learning methods such as Group Relative Preference Optimization (GRPO) have significantly enhanced Large Language Models, adapting them to diffusion models remains challenging. In particular, GRPO demands a stochastic policy, yet the most cost-effective diffusion samplers are based on deterministic ODEs. Recent work addresses this issue by using inefficient SDE-based samplers to induce stochasticity, but this reliance on model-agnostic Gaussian noise leads to slow convergence. To resolve this conflict, we propose Direct Group Preference Optimization (DGPO), a new online RL algorithm that dispenses with the policy-gradient framework entirely. DGPO learns directly from group-level preferences, which utilize relative information of samples within groups. This design eliminates the need for inefficient stochastic policies, unlocking the use of efficient deterministic ODE samplers and faster training. Extensive results show that DGPO trains around 20 times faster than existing state-of-the-art methods and achieves superior performance on both in-domain and out-of-domain reward metrics. Code is available at https://github.com/Luo-Yihong/DGPO.

Many applications of large language models (LLMs), ranging from chatbots to creative writing, require nuanced subjective judgments that can differ significantly across different groups. Existing alignment algorithms can be expensive to align for each group, requiring prohibitive amounts of group-specific preference data and computation for real-world use cases. We introduce Group Preference Optimization (GPO), an alignment framework that steers language models to preferences of individual groups in a few-shot manner. In GPO, we augment the base LLM with an independent transformer module trained to predict the preferences of a group for the LLM generations. For few-shot learning, we parameterize this module as an in-context autoregressive transformer and train it via meta-learning on several groups. We empirically validate the efficacy of GPO through rigorous evaluations using LLMs with varied sizes on three human opinion adaptation tasks. These tasks involve adapting to the preferences of US demographic groups, global countries, and individual users. Our results demonstrate that GPO not only aligns models more accurately but also requires fewer group-specific preferences, and less training and inference computing resources, outperforming existing strategies such as in-context steering and fine-tuning methods.

Group Relative Policy Optimization (GRPO) is widely used to train reasoning language models, where it computes advantages by centering and normalizing rewards across rollouts of the same prompt. For multiple rewards, GRPO sums the reward components and normalizes the total reward by its within-group standard deviation. The corresponding variance equals the sum of all pairwise reward covariances. For a fixed centered reward, larger aggregate covariance produces smaller advantages, and vice versa, allowing update magnitudes to adapt to reward dependence. However, correlated rewards with large scales can dominate this normalization and suppress signals from smaller-scale rewards. We propose Correlation-Normalized GRPO (CorrGRPO), which normalizes pairwise covariances into Pearson correlation coefficients. CorrGRPO keeps the centered total reward unchanged while balancing the influence of differently scaled rewards on the correlation-based normalization. This allows advantage magnitudes to adapt to reward correlations without the normalization being dominated by large-scale reward components. We compare CorrGRPO with GRPO and other variants on code generation, tool calling, and agent security, using models ranging from 0.5B to 8B parameters. These tasks all involve multiple rewards that can improve together or present tradeoffs. Results show improvements across three domains, including code generation, tool calling, and agent security. Our code is available at https://github.com/HKUST-KnowComp/CorrGRPO.

Warning: This paper contains several toxic and offensive statements. Modern large language models (LLMs) are typically aligned through large-scale post-training to ensure fair and reliable behavior. In this work, we investigate how easily such guardrails can be broken by Group Relative Policy Optimization (GRPO). We show that one-shot GRPO training on a single biased example is sufficient to induce systematic bias, with stereotype-driven reasoning generalizing across attributes, categories, and benchmarks. We further find that models differ in their susceptibility based on the initial likelihood of producing biased outputs. Our results reveal a critical vulnerability in post-training: alignment can be overridden by a single example.

The recent success and openness of DeepSeek-R1 have brought widespread attention to Group Relative Policy Optimization (GRPO) as a reinforcement learning method for large reasoning models (LRMs). In this work, we analyze the GRPO objective under a binary reward setting and reveal an inherent limitation of question-level difficulty bias. We also identify a connection between GRPO and traditional discriminative methods in supervised learning. Motivated by these insights, we introduce a new Discriminative Constrained Optimization (DisCO) framework for reinforcing LRMs, grounded in the principle of discriminative learning. The main differences between DisCO and GRPO and its recent variants are: (1) it replaces the group relative objective with a discriminative objective defined by a scoring function; (2) it abandons clipping-based surrogates in favor of non-clipping RL surrogate objectives used as scoring functions; (3) it employs a simple yet effective constrained optimization approach to enforce the KL divergence constraint, ensuring stable training. As a result, DisCO offers notable advantages over GRPO and its variants: (i) it completely eliminates difficulty bias by adopting discriminative objectives; (ii) it addresses the entropy instability in GRPO and its variants through the use of non-clipping scoring functions and a constrained optimization approach; (iii) it allows the incorporation of advanced discriminative learning techniques to address data imbalance, where a significant number of questions have more negative than positive generated answers during training. Our experiments on enhancing the mathematical reasoning capabilities of SFT-finetuned models show that DisCO significantly outperforms GRPO and its improved variants such as DAPO, achieving average gains of 7\% over GRPO and 6\% over DAPO across six benchmark tasks for an 1.5B model.

Training robust and generalizable reward models for human visual preferences is essential for aligning text-to-image and text-to-video generative models with human intent. However, current reward models often fail to generalize, and supervised fine-tuning leads to memorization, demanding complex annotation pipelines. While reinforcement learning (RL), specifically Group Relative Policy Optimization (GRPO), improves generalization, we uncover a key failure mode: a significant drop in reasoning accuracy occurs when a model's reasoning trace contradicts that of an independent, frozen vision-language model ("listener") evaluating the same output. To address this, we introduce a listener-augmented GRPO framework. Here, the listener re-evaluates the reasoner's chain-of-thought to provide a dense, calibrated confidence score, shaping the RL reward signal. This encourages the reasoner not only to answer correctly, but to produce explanations that are persuasive to an independent model. Our listener-shaped reward scheme achieves best accuracy on the ImageReward benchmark (67.4%), significantly improves out-of-distribution (OOD) performance on a large-scale human preference dataset (1.2M votes, up to +6% over naive reasoner), and reduces reasoning contradictions compared to strong GRPO and SFT baselines. These results demonstrate that listener-based rewards provide a scalable, data-efficient path to aligning vision-language models with nuanced human preferences. We will release our reasoning model here: https://huggingface.co/alexgambashidze/qwen2.5vl_image_preference_reasoner.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an important paradigm for unlocking reasoning capabilities in large language models, exemplified by the success of OpenAI o1 and DeepSeek-R1. Currently, Group Relative Policy Optimization (GRPO) stands as the dominant algorithm in this domain due to its stable training and critic-free efficiency. However, we argue that GRPO suffers from a structural limitation: it imposes a uniform, static trust region constraint across all samples. This design implicitly assumes signal homogeneity, a premise misaligned with the heterogeneous nature of outcome-driven learning, where advantage magnitudes and variances fluctuate significantly. Consequently, static constraints fail to fully exploit high-quality signals while insufficiently suppressing noise, often precipitating rapid entropy collapse. To address this, we propose Elastic Trust Regions (ETR), a dynamic mechanism that aligns optimization constraints with signal quality. ETR constructs a signal-aware landscape through dual-level elasticity: at the micro level, it scales clipping boundaries based on advantage magnitude to accelerate learning from high-confidence paths; at the macro level, it leverages group variance to implicitly allocate larger update budgets to tasks in the optimal learning zone. Extensive experiments on AIME and MATH benchmarks demonstrate that ETR consistently outperforms GRPO, achieving superior accuracy while effectively mitigating policy entropy degradation to ensure sustained exploration.

Mitigating social bias in Large Language Models (LLMs) presents a distinct alignment challenge: unlike verifiable tasks, bias lacks a single ground truth, creating a high-variance, subjective reward landscape. Previous preference-based fine-tuning methods have major trade-offs: Direct Preference Optimization (DPO) is limited by the lack of exploration inherent in offline training, while Proximal Policy Optimization (PPO) can lead to training instability due to potentially unreliable critic estimates. In this paper, we propose BiasGRPO, a framework using Group Relative Policy Optimization (GRPO) to stabilize alignment by normalizing rewards across a group of sampled completions. By substituting the value function with a group-relative baseline, our approach reduces instability while maintaining the exploration benefits of online training. We find that BiasGRPO outperforms DPO and PPO across multiple benchmarks, indicating its effectiveness. To adapt GRPO, we synthetically extend a dataset spanning multiple domains and contexts. We also create and release a custom bias reward model that effectively guides generation while being highly compute-efficient and avoiding knowledge degradation, providing a valuable resource that can be seamlessly integrated into multi-objective RLHF pipelines.

In this paper, we introduce a Group Relative Policy Optimization (GRPO)-based method for training Speech-Aware Large Language Models (SALLMs) on open-format speech understanding tasks, such as Spoken Question Answering and Automatic Speech Translation. SALLMs have proven highly effective for speech understanding tasks. GRPO has recently gained traction for its efficiency in training LLMs, and prior work has explored its application to SALLMs, primarily in multiple-choice tasks. Building on this, we focus on open-format tasks that better reflect the generative abilities of the models. Our approach leverages GRPO with BLEU as the reward signal to optimize SALLMs, and we demonstrate empirically that it surpasses standard SFT across several key metrics. Finally, we explore the potential of incorporating off-policy samples within GRPO for these tasks, highlighting avenues for further improvement and further research.

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training large language models (LLMs). While Group Relative Policy Optimization (GRPO) is widely adopted, it suffers from sparse reward signals and loses gradients entirely when all responses within a group receive identical rewards. On-policy distillation (OPD) offers a natural remedy by providing dense, token-level supervision from a teacher model. However, naively combining GRPO with OPD leads to degraded performance, due to three underlying causes: not all samples benefit from distillation; fitting too quickly to the teacher undermines the exploratory capacity of RL; and OPD's advantages are asymmetric, suppressing most tokens. To address these challenges, we propose RSTG (Recovering Learning Signals via Adaptive Teacher Guidance), which applies distillation selectively and precisely where it matters most. At the sample level, OPD is restricted to negative zero-variance prompts with each sample weighted by the teacher's confidence score. At the token level, distillation targets only tokens with high student entropy or large teacher-student divergence. We further augment training with SFT on correct trajectories generated by the teacher model, injecting positive gradient signals where RL yields none. Experiments demonstrate that RSTG substantially outperforms naive GRPO+OPD by +4.02% on math and +3.05% on code.

Vision encoders for retrieval are typically trained with class-label supervision: each training pair reduces to a scalar that uniformly pushes the embedding apart or pulls it together, as if every visual attribute either differed or matched. A multimodal large language model (MLLM), shown the same pair, can articulate those attributes and use them to predict whether the images share a class. We propose SAGA, a framework that turns this language-grounded, attribute-aware perception into a training signal for the encoder itself. Specifically, we use Group Relative Policy Optimization (GRPO) to reward the MLLM for correct predictions on the vision encoder's tokens. Since correct predictions require those tokens to expose the specific attributes that differ or match between the pair, the gradient pushes the encoder to encode them, replacing the uniform pair-level scalar with attribute-resolved supervision. An auxiliary attention-distillation loss anchors the encoder's embedding to tokens the MLLM attended to, and a standard metric-learning loss shapes the embedding geometry for nearest-neighbour retrieval. The MLLM is frozen throughout and discarded at inference, matching the deployment cost of a metric-learning baseline. SAGA improves Recall@1 by 3 to 6 points over state-of-the-art baselines on CUB-200-2011, Cars-196, FGVC-Aircraft, and iNaturalist Aves on zero-shot image retrieval.

Reinforcement learning (RL) with group-relative advantages has become the de facto standard for post-training language model reasoners. However, when optimizing multiple reward objectives, existing methods typically scalarize the reward vector with a fixed weighted sum before group-wise standardization. We show that this design leads to two fundamental problems: rollouts with distinct reward profiles can receive identical advantages, and all objectives are optimized with fixed relative weights regardless of their current level of saturation. As a result, training continues to allocate gradient budget to already-solved objectives instead of focusing on those with greater remaining headroom. We introduce Saturation Aware Advantage Reweighting for Multi-Reward Policy Optimization (SA-MRPO), which standardizes each reward objective independently and adaptively discounts its contribution according to a batch-level estimate of objective saturation. This dynamically reallocates optimization effort toward under-optimized objectives while empirically maintaining performance on those that are already well satisfied. We further show that saturation-aware reweighting can reverse the sign of an update, rather than merely rescale its magnitude. Across mathematical reasoning with two- and three-objective reward combinations, SA-MRPO improves the harder correctness objective over GDPO in 12 of 15 benchmark comparisons, with gains of up to 5% on AIME24. On adaptive reasoning it improves accuracy on all five benchmarks, by 3.8% on average and up to 9.2 % on AMC23, and on coding benchmarks it improves pass rate by up to 2.3%, while in all settings maintaining the easier objectives near their already satisfied levels.

This paper studies post-training large language models (LLMs) using preference feedback from a powerful oracle to help a model iteratively improve over itself. The typical approach for post-training LLMs involves Reinforcement Learning from Human Feedback (RLHF), which traditionally separates reward learning and subsequent policy optimization. However, such a reward maximization approach is limited by the nature of "point-wise" rewards (such as Bradley-Terry model), which fails to express complex intransitive or cyclic preference relations. While advances on RLHF show reward learning and policy optimization can be merged into a single contrastive objective for stability, they yet still remain tethered to the reward maximization framework. Recently, a new wave of research sidesteps the reward maximization presumptions in favor of directly optimizing over "pair-wise" or general preferences. In this paper, we introduce Direct Nash Optimization (DNO), a provable and scalable algorithm that marries the simplicity and stability of contrastive learning with theoretical generality from optimizing general preferences. Because DNO is a batched on-policy algorithm using a regression-based objective, its implementation is straightforward and efficient. Moreover, DNO enjoys monotonic improvement across iterations that help it improve even over a strong teacher (such as GPT-4). In our experiments, a resulting 7B parameter Orca-2.5 model aligned by DNO achieves the state-of-the-art win-rate against GPT-4-Turbo of 33% on AlpacaEval 2.0 (even after controlling for response length), an absolute gain of 26% (7% to 33%) over the initializing model. It outperforms models with far more parameters, including Mistral Large, Self-Rewarding LM (70B parameters), and older versions of GPT-4.

Reinforcement Learning with Verifiable Rewards (RLVR) has advanced the reasoning capabilities of Large Language Models (LLMs) by leveraging direct outcome verification instead of learned reward models. Building on this paradigm, Group Relative Policy Optimization (GRPO) eliminates the need for critic models but suffers from indiscriminate credit assignment for intermediate steps, which limits its ability to identify effective reasoning strategies and incurs overthinking. In this work, we introduce a model-free and verifiable process supervision via probing the model's belief in the correct answer throughout its reasoning trajectory. By segmenting the generation into discrete steps and tracking the conditional probability of the correct answer appended at each segment boundary, we efficiently compute interpretable segment-wise progress measurements to refine GRPO's trajectory-level feedback. This approach enables more targeted and sample-efficient policy updates, while avoiding the need for intermediate supervision derived from costly Monte Carlo rollouts or auxiliary models. Experiments on mathematical and general-domain benchmarks show consistent gains over GRPO across diverse models: up to 2.6-point accuracy improvements and 13.7% reasoning-length reductions on math tasks, and up to 2.4 points and 4% on general-domain tasks, demonstrating strong generalization.

Group Relative Policy Optimization (GRPO) has demonstrated great utilization in post-training of Large Language Models (LLMs). In GRPO, prompts are answered by the model and, through reinforcement learning, preferred completions are learnt. Owing to the small communication volume, GRPO is inherently suitable for decentralised training as the prompts can be concurrently answered by multiple nodes and then exchanged in the forms of strings. In this work, we present the first adversarial attack in decentralised GRPO. We demonstrate that malicious parties can poison such systems by injecting arbitrary malicious tokens in benign models in both out-of-context and in-context attacks. Using empirical examples of math and coding tasks, we show that adversarial attacks can easily poison the benign nodes, polluting their local LLM post-training, achieving attack success rates up to 100% in as few as 50 iterations. We propose two ways to defend against these attacks, depending on whether all users train the same model or different models. We show that these defenses can achieve stop rates of up to 100%, making the attack impossible.

Graph neural networks (GNNs) have achieved remarkable success across a wide range of applications, such as recommendation, drug discovery, and question answering. Behind the success of GNNs lies the backpropagation (BP) algorithm, which is the de facto standard for training deep neural networks (NNs). However, despite its effectiveness, BP imposes several constraints, which are not only biologically implausible, but also limit the scalability, parallelism, and flexibility in learning NNs. Examples of such constraints include storage of neural activities computed in the forward pass for use in the subsequent backward pass, and the dependence of parameter updates on non-local signals. To address these limitations, the forward-forward algorithm (FF) was recently proposed as an alternative to BP in the image classification domain, which trains NNs by performing two forward passes over positive and negative data. Inspired by this advance, we propose ForwardGNN in this work, a new forward learning procedure for GNNs, which avoids the constraints imposed by BP via an effective layer-wise local forward training. ForwardGNN extends the original FF to deal with graph data and GNNs, and makes it possible to operate without generating negative inputs (hence no longer forward-forward). Further, ForwardGNN enables each layer to learn from both the bottom-up and top-down signals without relying on the backpropagation of errors. Extensive experiments on real-world datasets show the effectiveness and generality of the proposed forward graph learning framework. We release our code at https://github.com/facebookresearch/forwardgnn.

This paper investigates large language model (LLM) abstention learning, specifically using ternary reward, which incentivize truthfulness in large language models. This paper extends that idea by moving from a ternary reward to a Trajectory-Informed advantage reweighting, dynamically re-weights the abstention reward during Group Relative Policy Optimization (GRPO) training. The objective of this work focuses on abstention learning instead of improving truthfulness, serving as an exploration into hallucination reduction. The novelty of this paper lies in methodological innovation, advantage re-weighting, and benchmark selection. Leveraging GRPO's multiple trajectories as a natural abstention signal, this method uses a reward signal to explore knowledge boundaries and encourage consistency. By demonstrating that trajectories can be used as a confidence indicator of the policy relative to the query, they are then used to dynamically calculate the abstention advantage. AbstentionBench is used as the evaluation benchmark, as this work aims to contribute to the field of abstention learning. All datasets on the benchmark were tested against this method and various baselines. Empirical results demonstrate that TIAR achieves state-of-the-art abstention F1 scores across five of six evaluation categories, outperforming the static ternary baseline on 17 of 31 benchmark datasets while fully preserving baseline accuracy.

Group Relative Policy Optimization (GRPO) is widely used for reinforcement learning with verifiable rewards, but it often suffers from advantage collapse: when all rollouts in a group receive the same reward, the group yields zero relative advantage and thus no learning signal. For example, if a question is too hard for the reasoner, all sampled rollouts can be incorrect and receive zero reward. Recent work addresses this issue by adding hints or auxiliary scaffolds to such hard questions so that the reasoner produces mixed outcomes and recovers a non-zero update. However, existing hints are usually fixed rather than adapted to the current reasoner, and a hint that creates learning signal under the hinted input does not necessarily improve the no-hint policy used at test time. To this end, we propose Hint Learning for Reinforcement Learning (HiLL), a framework that jointly trains a hinter policy and a reasoner policy during RL. For each hard question, the hinter generates hints online conditioned on the current reasoner's incorrect rollout, allowing hint generation to adapt to the reasoner's evolving errors. We further introduce hint reliance, which measures how strongly correct hinted trajectories depend on the hint. We derive a transferability result showing that lower hint reliance implies stronger transfer from hinted success to no-hint success, and we use this result to define a transfer-weighted reward for training the hinter. Therefore, HiLL favors hints that not only recover informative GRPO groups, but also produce signals that are more likely to improve the original no-hint policy. Experiments across multiple benchmarks show that HiLL consistently outperforms GRPO and prior hint-based baselines, demonstrating the value of adaptive and transfer-aware hint learning for RL. The code is available at https://github.com/Andree-9/HiLL.

Despite being the workhorse of deep learning, the backpropagation algorithm is no panacea. It enforces sequential layer updates, thus preventing efficient parallelization of the training process. Furthermore, its biological plausibility is being challenged. Alternative schemes have been devised; yet, under the constraint of synaptic asymmetry, none have scaled to modern deep learning tasks and architectures. Here, we challenge this perspective, and study the applicability of Direct Feedback Alignment to neural view synthesis, recommender systems, geometric learning, and natural language processing. In contrast with previous studies limited to computer vision tasks, our findings show that it successfully trains a large range of state-of-the-art deep learning architectures, with performance close to fine-tuned backpropagation. At variance with common beliefs, our work supports that challenging tasks can be tackled in the absence of weight transport.

Group Relative Policy Optimization (GRPO) has demonstrated remarkable success in aligning text-to-image (T2I) flow models with human preferences. However, we have identified that the learning loop of current flow-based GRPO is fundamentally decoupled from the learner's current capability, suffering from critical blind spots at both prompt selection and advantage estimation: (i) Existing methods sample prompts randomly, overlooking the substantial impact of data selection on reinforcement learning (RL) efficacy--a factor proven crucial in GRPO for large language models; (ii) They evaluate sample quality solely relying on intra-group statistics, lacking a global perspective to accurately measure true policy improvement. To address these issues, we propose Adaptive GRPO (AdaGRPO), a novel capability-aware RL algorithm tailored for flow models. Specifically, AdaGRPO consists of two principal components: (i) Online Curriculum Filtering Strategy: Dynamically tracks the model's proficiency and adaptively selects prompts that best match its current learning boundary; (ii) Cross-Level Advantage Fusion: Synergistically integrates fine-grained intra-group advantages with macro-level global advantages, providing a comprehensive and unbiased policy evaluation. As a lightweight, plug-and-play module, AdaGRPO can be seamlessly integrated with existing frameworks such as Flow-GRPO, DanceGRPO, and Flow-CPS. Extensive experiments demonstrate that AdaGRPO consistently drives performance gains while significantly stabilizes GRPO training for flow models.

Speech Recognition has seen a dramatic shift towards adopting Large Language Models (LLMs). This shift is partly driven by good scalability properties demonstrated by LLMs, ability to leverage large amounts of labelled, unlabelled speech and text data, streaming capabilities with auto-regressive framework and multi-tasking with instruction following characteristics of LLMs. However, simple next-token prediction objective, typically employed with LLMs, have certain limitations in performance and challenges with hallucinations. In this paper, we propose application of Group Relative Policy Optimization (GRPO) to enable reinforcement learning from human feedback for automatic speech recognition (ASR). We design simple rule based reward functions to guide the policy updates. We demonstrate significant improvements in word error rate (upto 18.4% relative), reduction in hallucinations, increased robustness on out-of-domain datasets and effectiveness in domain adaptation.

As language models become increasingly capable, users expect them to provide not only accurate responses but also behaviors aligned with diverse human preferences across a variety of scenarios. To achieve this, Reinforcement learning (RL) pipelines have begun incorporating multiple rewards, each capturing a distinct preference, to guide models toward these desired behaviors. However, recent work has defaulted to apply Group Relative Policy Optimization (GRPO) under multi-reward setting without examining its suitability. In this paper, we demonstrate that directly applying GRPO to normalize distinct rollout reward combinations causes them to collapse into identical advantage values, reducing the resolution of the training signal and resulting in suboptimal convergence and, in some cases, early training failure. We then introduce Group reward-Decoupled Normalization Policy Optimization (GDPO), a new policy optimization method to resolve these issues by decoupling the normalization of individual rewards, more faithfully preserving their relative differences and enabling more accurate multi-reward optimization, along with substantially improved training stability. We compare GDPO with GRPO across three tasks: tool calling, math reasoning, and coding reasoning, evaluating both correctness metrics (accuracy, bug ratio) and constraint adherence metrics (format, length). Across all settings, GDPO consistently outperforms GRPO, demonstrating its effectiveness and generalizability for multi-reward reinforcement learning optimization.

DeepSeek-R1-Zero has shown that reinforcement learning (RL) at scale can directly enhance the reasoning capabilities of LLMs without supervised fine-tuning. In this work, we critically examine R1-Zero-like training by analyzing its two core components: base models and RL. We investigate a wide range of base models, including DeepSeek-V3-Base, to understand how pretraining characteristics influence RL performance. Our analysis reveals that DeepSeek-V3-Base already exhibit ''Aha moment'', while Qwen2.5 base models demonstrate strong reasoning capabilities even without prompt templates, suggesting potential pretraining biases. Additionally, we identify an optimization bias in Group Relative Policy Optimization (GRPO), which artificially increases response length (especially for incorrect outputs) during training. To address this, we introduce Dr. GRPO, an unbiased optimization method that improves token efficiency while maintaining reasoning performance. Leveraging these insights, we present a minimalist R1-Zero recipe that achieves 43.3% accuracy on AIME 2024 with a 7B base model, establishing a new state-of-the-art. Our code is available at https://github.com/sail-sg/understand-r1-zero.

Visual reward models are essential for evaluating and improving visual generation models, yet existing approaches typically map task conditions and candidate outputs directly to scalar rewards, leaving implicit what should be evaluated for each individual case. We introduce Think Before You Score, a paradigm that explicitly determines what matters for each case before judging how well the candidate performs. Following this principle, we propose the Thinking Reward Model (TRM), which formulates case-adaptive rubrics, performs rubric-guided assessment, and produces fine-grained pointwise rewards. We further observe that conventional pairwise preference optimization can induce score polarization, and introduce Pairwise Dual-Group Relative Policy Optimization (PD-GRPO), which leverages pairwise supervision to improve reward discrimination while preserving fine-grained pointwise scoring. Extensive experiments on image generation and editing reward-modeling benchmarks demonstrate that TRM achieves state-of-the-art performance among open-source reward models while remaining highly competitive with proprietary alternatives. Moreover, using TRM as a reward for reinforcement learning consistently improves diverse visual generation models, demonstrating that its fine-grained, case-adaptive rewards translate into effective optimization signals for visual generation.

Group Relative Policy Optimization (GRPO) has been shown to be an effective algorithm when an accurate reward model is available. However, such a highly reliable reward model is not available in many real-world tasks. In this paper, we particularly focus on multi-objective settings, in which we identify that GRPO is vulnerable to reward hacking, optimizing only one of the objectives at the cost of the others. To address this issue, we propose MO-GRPO, an extension of GRPO with a simple normalization method to reweight the reward functions automatically according to the variances of their values. We first show analytically that MO-GRPO ensures that all reward functions contribute evenly to the loss function while preserving the order of preferences, eliminating the need for manual tuning of the reward functions' scales. Then, we evaluate MO-GRPO experimentally in four domains: (i) the multi-armed bandits problem, (ii) simulated control task (Mo-Gymnasium), (iii) machine translation tasks on the WMT benchmark (En-Ja, En-Zh), and (iv) instruction following task. MO-GRPO achieves stable learning by evenly distributing correlations among the components of rewards, outperforming GRPO, showing MO-GRPO to be a promising algorithm for multi-objective reinforcement learning problems.

Following the success of Group Relative Policy Optimization (GRPO) in foundation LLMs, an increasing number of works have sought to adapt GRPO to Visual Large Language Models (VLLMs) for visual perception tasks (e.g., detection and segmentation). However, much of this line of research rests on a long-standing yet unexamined assumption: training paradigms developed for language reasoning can be transferred seamlessly to visual perception. Our experiments show that this assumption is not valid, revealing intrinsic differences between reasoning-oriented and perception-oriented settings. Using reasoning segmentation as a representative case, we surface two overlooked factors: (i) the need for a broader output space, and (ii) the importance of fine-grained, stable rewards. Building on these observations, we propose Dr.~Seg, a simple, plug-and-play GRPO-based framework consisting of a Look-to-Confirm mechanism and a Distribution-Ranked Reward module, requiring no architectural modifications and integrating seamlessly with existing GRPO-based VLLMs. Extensive experiments demonstrate that Dr.~Seg improves performance in complex visual scenarios while maintaining strong generalization. Code, models, and datasets are available at https://github.com/eVI-group-SCU/Dr-Seg.

Recent advancements underscore the significant role of Reinforcement Learning (RL) in enhancing the Chain-of-Thought (CoT) reasoning capabilities of large language models (LLMs). Two prominent RL algorithms, Direct Preference Optimization (DPO) and Group Relative Policy Optimization (GRPO), are central to these developments, showcasing different pros and cons. Autoregressive image generation, also interpretable as a sequential CoT reasoning process, presents unique challenges distinct from LLM-based CoT reasoning. These encompass ensuring text-image consistency, improving image aesthetic quality, and designing sophisticated reward models, rather than relying on simpler rule-based rewards. While recent efforts have extended RL to this domain, these explorations typically lack an in-depth analysis of the domain-specific challenges and the characteristics of different RL strategies. To bridge this gap, we provide the first comprehensive investigation of the GRPO and DPO algorithms in autoregressive image generation, evaluating their in-domain performance and out-of-domain generalization, while scrutinizing the impact of different reward models on their respective capabilities. Our findings reveal that GRPO and DPO exhibit distinct advantages, and crucially, that reward models possessing stronger intrinsic generalization capabilities potentially enhance the generalization potential of the applied RL algorithms. Furthermore, we systematically explore three prevalent scaling strategies to enhance both their in-domain and out-of-domain proficiency, deriving unique insights into efficiently scaling performance for each paradigm. We hope our study paves a new path for inspiring future work on developing more effective RL algorithms to achieve robust CoT reasoning in the realm of autoregressive image generation. Code is released at https://github.com/ZiyuGuo99/Image-Generation-CoT

Large reasoning models (LRMs) aim to solve diverse and complex problems through structured reasoning. Recent advances in group-based policy optimization methods have shown promise in enabling stable advantage estimation without reliance on process-level annotations. However, these methods rely on advantage gaps induced by high-quality samples within the same batch, which makes the training process fragile and inefficient when intra-group advantages collapse under challenging tasks. To address these problems, we propose a reinforcement learning mechanism named \textbf{R^3} that along three directions: (1) a cross-context \underline{\textbf{R}eplay} strategy that maintains the intra-group advantage by recalling valuable examples from historical trajectories of the same query, (2) an in-context self-\underline{\textbf{R}eflection} mechanism enabling models to refine outputs by leveraging past failures, and (3) a structural entropy \underline{\textbf{R}anking reward}, which assigns relative rewards to truncated or failed samples by ranking responses based on token-level entropy patterns, capturing both local exploration and global stability. We implement our method on Deepseek-R1-Distill-Qwen-1.5B and train it on the DeepscaleR-40k in the math domain. Experiments demonstrate our method achieves SoTA performance on several math benchmarks, representing significant improvements and fewer reasoning tokens over the base models. Code and model will be released.

Reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving reasoning language models on tasks such as mathematics, coding, and scientific question answering. However, widely used group-relative objectives, such as GRPO, summarize each sampled group with scalar statistics and therefore discard fine-grained relational information among candidate responses. This weakens credit assignment under sparse outcome rewards, especially when multiple generated solutions differ only subtly in reasoning quality. We propose LamPO, a Lambda-Style Policy Optimization method that replaces scalar group advantages with a Pairwise Decomposed Advantage. LamPO aggregates pairwise reward gaps within each response group and modulates each comparison by a confidence-aware weight computed from sequence log-probability differences, while retaining the critic-free and clipped-update structure of PPO-style optimization. When reference solutions are available, we further add a lightweight ROUGE-L-based dense auxiliary reward to reduce reward sparsity. Experiments on AIME24, AIME25, MATH-500, and GPQA-Diamond with Qwen3-1.7B, Qwen3-4B, and Phi-4-mini show that LamPO consistently improves over GRPO and recent RLVR variants, with more stable training dynamics and better sample efficiency.

Backpropagation (BP) is the most successful and widely used algorithm in deep learning. However, the computations required by BP are challenging to reconcile with known neurobiology. This difficulty has stimulated interest in more biologically plausible alternatives to BP. One such algorithm is the inference learning algorithm (IL). IL has close connections to neurobiological models of cortical function and has achieved equal performance to BP on supervised learning and auto-associative tasks. In contrast to BP, however, the mathematical foundations of IL are not well-understood. Here, we develop a novel theoretical framework for IL. Our main result is that IL closely approximates an optimization method known as implicit stochastic gradient descent (implicit SGD), which is distinct from the explicit SGD implemented by BP. Our results further show how the standard implementation of IL can be altered to better approximate implicit SGD. Our novel implementation considerably improves the stability of IL across learning rates, which is consistent with our theory, as a key property of implicit SGD is its stability. We provide extensive simulation results that further support our theoretical interpretations and also demonstrate IL achieves quicker convergence when trained with small mini-batches while matching the performance of BP for large mini-batches.

Fine-tuning pretrained large models to downstream tasks is an important problem, which however suffers from huge memory overhead due to large-scale parameters. This work strives to reduce memory overhead in fine-tuning from perspectives of activation function and layer normalization. To this end, we propose the Approximate Backpropagation (Approx-BP) theory, which provides the theoretical feasibility of decoupling the forward and backward passes. We apply our Approx-BP theory to backpropagation training and derive memory-efficient alternatives of GELU and SiLU activation functions, which use derivative functions of ReLUs in the backward pass while keeping their forward pass unchanged. In addition, we introduce a Memory-Sharing Backpropagation strategy, which enables the activation memory to be shared by two adjacent layers, thereby removing activation memory usage redundancy. Our method neither induces extra computation nor reduces training efficiency. We conduct extensive experiments with pretrained vision and language models, and the results demonstrate that our proposal can reduce up to sim30% of the peak memory usage. Our code is released at https://github.com/yyyyychen/LowMemoryBP.

Reinforcement learning (RL) for code agents often uses executable tests to provide binary rewards. With these rewards, Group Relative Policy Optimization (GRPO) assigns identical advantages to test-passing trajectories within each rollout group, overlooking differences in implementation quality and adherence to task requirements. This leaves the policy without a learning signal that favors clean, targeted implementations over those containing unnecessary or out-of-scope changes. We introduce GAGAR, a framework for quality-aware credit redistribution in code agent RL. Built on dynamic sampling that retains groups containing both passing and failing trajectories, GAGAR places all trajectories from each group in a shared workspace, where an SFT-trained agentic grader jointly inspects them and ranks the test-passing candidates. Based on this ranking, we downweight lower-ranked trajectories and proportionally rescale the advantages of all test-passing trajectories to restore their original sum. This sum-preserving redistribution retains the relative weights established by quality-based downweighting while shifting credit toward higher-quality implementations. We evaluate GAGAR at industrial scale using pre-RL SFT checkpoints of MiMo-V2.6-Flash (310B total parameters) and MiMo-V2.6-Pro (1.02T total parameters). Controlled code-only Flash experiments show improved code agent performance, reduced trajectory-length growth, and more stable training. We further apply GAGAR in large-scale mixed-task RL with both Flash and Pro. Our results support combining test-based verification with groupwise agentic grading to improve the quality and stability of code agent RL.

RLVR has enhanced the reasoning capabilities of Large Language Models (LLMs) across various tasks. However, GRPO, a representative RLVR algorithm, suffers from a critical limitation: when all responses within a group are either entirely correct or entirely incorrect, the model fails to learn from these homogeneous responses. This is particularly problematic for homogeneously incorrect groups, where GRPO's advantage function yields a value of zero, leading to null gradients and the loss of valuable learning signals. To overcome this issue, we propose NGRPO (Negative-enhanced Group Relative Policy Optimization), an algorithm designed to convert homogeneous errors into robust learning signals. First, NGRPO introduces Advantage Calibration. This mechanism hypothesizes the existence of a virtual maximum-reward sample during advantage calculation, thereby altering the mean and variance of rewards within a group and ensuring that the advantages for homogeneously incorrect samples are no longer zero. Second, NGRPO employs Asymmetric Clipping, which relaxes the update magnitude for positive samples while imposing stricter constraints on that of negative samples. This serves to stabilize the exploration pressure introduced by the advantage calibration. Our experiments on Qwen2.5-Math-7B demonstrate that NGRPO significantly outperforms baselines such as PPO, GRPO, DAPO, and PSR-NSR on mathematical benchmarks including MATH500, AMC23, and AIME2025. These results validate NGRPO's ability to learn from homogeneous errors, leading to stable and substantial improvements in mathematical reasoning. Our code is available at https://github.com/nangongrui-ngr/NGRPO.

The development of largely human-annotated benchmarks has driven the success of deep neural networks in various NLP tasks. To enhance the effectiveness of existing benchmarks, collecting new additional input-output pairs is often too costly and challenging, particularly considering their marginal impact on improving the current model accuracy. Instead, additional or complementary annotations on the existing input texts in the benchmarks can be preferable as an efficient way to pay the additional human cost. In this paper, we investigate task-specific preferences between pairs of input texts as a new alternative way for such auxiliary data annotation. From 'pair-wise' comparisons with respect to the task, the auxiliary preference learning enables the model to learn an additional informative training signal that cannot be captured with 'instance-wise' task labels. To this end, we propose a novel multi-task learning framework, called prefer-to-classify (P2C), which can enjoy the cooperative effect of learning both the given classification task and the auxiliary preferences. Here, we provide three different ways to collect preference signals in practice: (a) implicitly extracting from annotation records (for free, but often unavailable), (b) collecting explicitly from crowd workers (high paid), or (c) pre-trained large language models such as GPT-3 (low paid). Given existing classification NLP benchmarks, we demonstrate that the proposed auxiliary preference learning via P2C on them is effective in improving text classifiers. Our codes are publicly available.

Recent advances in large language models (LLMs) have demonstrated remarkable capabilities across diverse domains, particularly in mathematical reasoning, amid which geometry problem solving remains a challenging area where auxiliary construction plays a enssential role. Existing approaches either achieve suboptimal performance or rely on massive LLMs (e.g., GPT-4o), incurring massive computational costs. We posit that reinforcement learning with verifiable reward (e.g., GRPO) offers a promising direction for training smaller models that effectively combine auxiliary construction with robust geometric reasoning. However, directly applying GRPO to geometric reasoning presents fundamental limitations due to its dependence on unconditional rewards, which leads to indiscriminate and counterproductive auxiliary constructions. To address these challenges, we propose Group Contrastive Policy Optimization (GCPO), a novel reinforcement learning framework featuring two key innovations: (1) Group Contrastive Masking, which adaptively provides positive or negative reward signals for auxiliary construction based on contextual utility, and a (2) length reward that promotes longer reasoning chains. Building on GCPO, we develop GeometryZero, a family of affordable-size geometric reasoning models that judiciously determine when to employ auxiliary construction. Our extensive empirical evaluation across popular geometric benchmarks (Geometry3K, MathVista) demonstrates that GeometryZero models consistently outperform baselines (e.g. GRPO), achieving an average improvement of 4.29% across all benchmarks.

Group-advantage-based reinforcement learning methods, such as GRPO and DAPO, have demonstrated strong performance across diverse domains, including mathematical reasoning and text-to-image generation. However, their reliance on sample-level rewards introduces a key limitation as uniform credit assignment across all tokens fails to capture fine-grained, token-level contributions. To address this issue, we propose Guidance Contrastive Policy Optimization (GCPO), a novel algorithm that enables per-token credit assignment by contrasting model predictions under positive and negative prompts. Rather than uniformly broadcasting sample-level advantages, GCPO assigns token-level advantages proportional to the difference between these contrastive predictions, allowing more precise and informative learning signals. Empirically, we find that GCPO emphasizes semantically relevant regions such as visual areas aligned with textual prompts in text-to-image generation, and critical keywords within reasoning traces for chain-of-thought tasks. Through extensive experiments, GCPO consistently outperforms GRPO and DAPO baselines on both text-to-image generation and chain-of-thought reasoning benchmarks, demonstrating its effectiveness as a general and scalable optimization strategy for discrete policy learning.

Group Relative Policy Optimization (GRPO) has proven effective in RLVR by using outcome-based rewards. While fine-grained dense rewards can theoretically improve performance, we reveal that under practical sampling budgets, Monte Carlo estimation yields high-variance and sign-inconsistent advantages for early reasoning tokens, paradoxically underperforming outcome-only GRPO. We propose Skip-Connected Optimization (SKPO), which decomposes reasoning into upstream and downstream phases: upstream receives dense rewards from downstream Monte Carlo sampling with single-stream optimization; downstream maintains group-relative optimization, where a skip connection concatenates the upstream segment with the original problem, enabling the model to leverage helpful upstream reasoning while preserving the freedom to bypass flawed reasoning through direct problem access. Experiments demonstrate improvements of 3.91% and 6.17% relative gains over the strongest baselines on Qwen2.5-Math-7B and Llama-3.2-3B respectively across mathematical benchmarks and out-of-domain tasks including general reasoning and code generation. Further analysis reveals an implicit advantage: SKPO generates trajectories with higher intermediate-step quality even when matched for final correctness.

RLHF has emerged as a predominant approach for aligning artificial intelligence systems with human preferences, demonstrating exceptional and measurable efficacy in instruction following tasks; however, it exhibits insufficient compliance capabilities when confronted with complex multi-instruction tasks. Conventional approaches rely heavily on human annotation or more sophisticated large language models, thereby introducing substantial resource expenditure or potential bias concerns. Meanwhile, alternative synthetic methods that augment standard preference datasets often compromise the model's semantic quality. Our research identifies a critical oversight in existing techniques, which predominantly focus on comparing responses while neglecting valuable latent signals embedded within prompt inputs, and which only focus on preference disparities at the intra-sample level, while neglecting to account for the inter-sample level preference differentials that exist among preference data. To leverage these previously neglected indicators, we propose a novel Multi-level Aware Preference Learning (MAPL) framework, capable of enhancing multi-instruction capabilities. Specifically, for any given response in original preference data pairs, we construct varied prompts with a preference relation under different conditions, in order to learn intra-sample level preference disparities. Furthermore, for any given original preference pair, we synthesize multi-instruction preference pairs to capture preference discrepancies at the inter-sample level. Building on the two datasets constructed above, we consequently devise two sophisticated training objective functions. Subsequently, our framework integrates seamlessly into both Reward Modeling and Direct Preference Optimization paradigms. Through rigorous evaluation across multiple benchmarks, we empirically validate the efficacy of our framework.

Recent advances in reinforcement learning (RL) have significantly enhanced the reasoning capabilities of large language models (LLMs). Group Relative Policy Optimization (GRPO), a lightweight variant of Proximal Policy Optimization (PPO), improves efficiency but suffers from limited exploration and training instability, limiting its effectiveness on complex reasoning tasks. To address these challenges, we introduce EFRame, an Exploration-Filter-Replay framework that augments GRPO across three dimensions: additional rollouts enable deeper and more targeted exploration, online filtering removes low-quality samples to stabilize gradients and accelerate training, and experience replay amplifies rare yet informative trajectories for stable convergence. This unified framework establishes a principled training cycle that balances exploration, efficiency, and stability. Experiments on diverse reasoning benchmarks demonstrate that EFRame achieves consistent gains, including a 37.9\% relative improvement on Geometry3K over GRPO. EFRame further supports fine-grained sample categorization and precise entropy control, highlighting it as a robust solution for advancing deeper reasoning in LLMs. Our code is available at https://github.com/597358816/EFRame.

Policy-based optimizations are widely adopted today for the training and alignment of language models, where one of the most recent and effective approaches is Group-relative Policy Optimization (GRPO). In this paper, we reveals and analyze two major limitations of GRPO: (i) tokens frequently appear in completions with both positive and negative rewards, leading to conflicting gradient updates that can reduce their output probability, even though can be essential for maintaining proper structure; (ii) negatively rewarded completions may penalize confident responses and shift model decisions toward unlikely tokens, progressively flattening the output distribution and degrading learning. To address these issues and provide a more stable and effective policy optimization strategy, we introduce GTPO (Group-relative Trajectory-based Policy Optimization), which identifies conflict tokens, tokens appearing in the same position across completions with opposite rewards, protects them by skipping negative updates, while amplifying positive ones. To further prevent policy collapse, GTPO filters out completions whose entropy exceeds a provable threshold. Unlike GRPO, GTPO does not rely on KL-divergence regularization, eliminating the need for a reference model during training, while still ensuring greater training stability and improved performance, validated through multiple experiments on GSM8K, MATH and AIME 2024 benchmarks.

We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to 1/2 everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.

Visual generation is dominated by three paradigms: AutoRegressive (AR), diffusion, and Visual AutoRegressive (VAR) models. Unlike AR and diffusion, VARs operate on heterogeneous input structures across their generation steps, which creates severe asynchronous policy conflicts. This issue becomes particularly acute in reinforcement learning (RL) scenarios, leading to unstable training and suboptimal alignment. To resolve this, we propose a novel framework to enhance Group Relative Policy Optimization (GRPO) by explicitly managing these conflicts. Our method integrates three synergistic components: 1) a stabilizing intermediate reward to guide early-stage generation; 2) a dynamic time-step reweighting scheme for precise credit assignment; and 3) a novel mask propagation algorithm, derived from principles of Reward Feedback Learning (ReFL), designed to isolate optimization effects both spatially and temporally. Our approach demonstrates significant improvements in sample quality and objective alignment over the vanilla GRPO baseline, enabling robust and effective optimization for VAR models.

Tool-integrated (TI) reinforcement learning (RL) enables large language models (LLMs) to perform multi-step reasoning by interacting with external tools such as search engines and retrievers. Group Relative Policy Optimization (GRPO), exemplified by the recent Search-R1, offers fast convergence and a value-free formulation that makes it appealing for this setting, yet consistently suffers from training collapse. We identify Lazy Likelihood Displacement (LLD), a systematic reduction or stagnation in the likelihood of both correct and incorrect responses, as the core mechanism driving this failure. LLD emerges early and triggers a self-reinforcing LLD Death Spiral, where declining likelihood leads to low-confidence responses, inflating gradients, and ultimately causing collapse. We empirically characterize this process across models on a Search-R1-style, search-integrated question answering task, revealing a consistent three-phase trajectory: early stagnation, steady decay, and accelerated collapse. To address this, we propose a lightweight likelihood-preserving regularization LLDS for GRPO that activates only when a trajectory's likelihood decreases, and regularizes only the tokens responsible. This fine-grained structure mitigates LLD with minimal interference to optimization. Across seven open-domain and multi-hop QA benchmarks, our method stabilizes training, prevents gradient explosion, and yields substantial performance improvements, including +37.8% gains on Qwen2.5-3B and +32.0% gains on Qwen2.5-7B. Our results establish LLD as a fundamental bottleneck in GRPO-based TIRL and provide a practical path toward stable, scalable training of tool-integrated LLM.

Large language models (LLMs) achieve remarkable performance in code generation tasks. However, a significant performance disparity persists between popular programming languages (e.g., Python, C++) and others. To address this capability gap, we leverage the code translation task to train LLMs, thereby facilitating the transfer of coding proficiency across diverse programming languages. Moreover, we introduce OORL for training, a novel reinforcement learning (RL) framework that integrates on-policy and off-policy strategies. Within OORL, on-policy RL is applied during code translation, guided by a rule-based reward signal derived from unit tests. Complementing this coarse-grained rule-based reward, we propose Group Equivalent Preference Optimization (GEPO), a novel preference optimization method. Specifically, GEPO trains the LLM using intermediate representations (IRs) groups. LLMs can be guided to discern IRs equivalent to the source code from inequivalent ones, while also utilizing signals about the mutual equivalence between IRs within the group. This process allows LLMs to capture nuanced aspects of code functionality. By employing OORL for training with code translation tasks, LLMs improve their recognition of code functionality and their understanding of the relationships between code implemented in different languages. Extensive experiments demonstrate that our OORL for LLMs training with code translation tasks achieves significant performance improvements on code benchmarks across multiple programming languages.

When deploying a single predictor across multiple subpopulations, we propose a fundamentally different approach: interpreting group fairness as a bargaining problem among subpopulations. This game-theoretic perspective reveals that existing robust optimization methods such as minimizing worst-group loss or regret correspond to classical bargaining solutions and embody different fairness principles. We propose relative improvement, the ratio of actual risk reduction to potential reduction from a baseline predictor, which recovers the Kalai-Smorodinsky solution. Unlike absolute-scale methods that may not be comparable when groups have different potential predictability, relative improvement provides axiomatic justification including scale invariance and individual monotonicity. We establish finite-sample convergence guarantees under mild conditions.

Fairness, especially group fairness, is an important consideration in the context of machine learning systems. The most commonly adopted group fairness-enhancing techniques are in-processing methods that rely on a mixture of a fairness objective (e.g., demographic parity) and a task-specific objective (e.g., cross-entropy) during the training process. However, when data arrives in an online fashion -- one instance at a time -- optimizing such fairness objectives poses several challenges. In particular, group fairness objectives are defined using expectations of predictions across different demographic groups. In the online setting, where the algorithm has access to a single instance at a time, estimating the group fairness objective requires additional storage and significantly more computation (e.g., forward/backward passes) than the task-specific objective at every time step. In this paper, we propose Aranyani, an ensemble of oblique decision trees, to make fair decisions in online settings. The hierarchical tree structure of Aranyani enables parameter isolation and allows us to efficiently compute the fairness gradients using aggregate statistics of previous decisions, eliminating the need for additional storage and forward/backward passes. We also present an efficient framework to train Aranyani and theoretically analyze several of its properties. We conduct empirical evaluations on 5 publicly available benchmarks (including vision and language datasets) to show that Aranyani achieves a better accuracy-fairness trade-off compared to baseline approaches.

Group Relative Policy Optimization (GRPO) has proven to be an effective tool for post-training language models (LMs). However, AI systems are increasingly expressed as modular programs that mix together multiple LM calls with distinct prompt templates and other tools, and it is not clear how best to leverage GRPO to improve these systems. We begin to address this challenge by defining mmGRPO, a simple multi-module generalization of GRPO that groups LM calls by module across rollouts and handles variable-length and interrupted trajectories. We find that mmGRPO, composed with automatic prompt optimization, improves accuracy by 11% on average across classification, many-hop search, and privacy-preserving delegation tasks against the post-trained LM, and by 5% against prompt optimization on its own. We open-source mmGRPO in DSPy as the dspy.GRPO optimizer.

Off-policy reinforcement learning (RL) for large language models (LLMs) is attracting growing interest, driven by practical constraints in real-world applications, the complexity of LLM-RL infrastructure, and the need for further innovations of RL methodologies. While classic REINFORCE and its modern variants like Group Relative Policy Optimization (GRPO) are typically regarded as on-policy algorithms with limited tolerance of off-policyness, we present in this work a first-principles derivation for group-relative REINFORCE without assuming a specific training data distribution, showing that it admits a native off-policy interpretation. This perspective yields two general principles for adapting REINFORCE to off-policy settings: regularizing policy updates, and actively shaping the data distribution. Our analysis demystifies some myths about the roles of importance sampling and clipping in GRPO, unifies and reinterprets two recent algorithms -- Online Policy Mirror Descent (OPMD) and Asymmetric REINFORCE (AsymRE) -- as regularized forms of the REINFORCE loss, and offers theoretical justification for seemingly heuristic data-weighting strategies. Our findings lead to actionable insights that are validated with extensive empirical studies, and open up new opportunities for principled algorithm design in off-policy RL for LLMs. Source code for this work is available at https://github.com/modelscope/Trinity-RFT/tree/main/examples/rec_gsm8k.

Group Relative Policy Optimization (GRPO) has recently emerged as a practical recipe for aligning large language models with verifiable objectives. However, under sparse terminal rewards, GRPO often stalls because rollouts within a group frequently receive identical rewards, causing relative advantages to collapse and updates to vanish. We propose self-hint aligned GRPO with privileged supervision (SAGE), an on-policy reinforcement learning framework that injects privileged hints during training to reshape the rollout distribution under the same terminal verifier reward. For each prompt x, the model samples a compact hint h (e.g., a plan or decomposition) and then generates a solution τ conditioned on (x,h). Crucially, the task reward R(x,τ) is unchanged; hints only increase within-group outcome diversity under finite sampling, preventing GRPO advantages from collapsing under sparse rewards. At test time, we set h=varnothing and deploy the no-hint policy without any privileged information. Moreover, sampling diverse self-hints serves as an adaptive curriculum that tracks the learner's bottlenecks more effectively than fixed hints from an initial policy or a stronger external model. Experiments over 6 benchmarks with 3 LLMs show that SAGE consistently outperforms GRPO, on average +2.0 on Llama-3.2-3B-Instruct, +1.2 on Qwen2.5-7B-Instruct and +1.3 on Qwen3-4B-Instruct. The code is available at https://github.com/BaohaoLiao/SAGE.

Biomolecular generators are often adapted with reward feedback to improve task-specific utility, but pushing utility alone can concentrate generation on a narrow family of candidates. Maintaining diversity is difficult because sample diversity is a set-level property. We introduce Supergroup Relative Policy Optimization (SGRPO), a flexible GRPO-style framework that directly constructs rewards from set-level diversity. For each condition, SGRPO samples a supergroup of candidate sets, compares their diversity under the same condition, and redistributes the group diversity reward to individual rollouts through leave-one-out diversity contributions before combining it with rollout-level utility. This design decouples SGRPO from a particular generator, utility reward, or diversity metric, and allows instantiation with different GRPO-style approaches. We evaluate SGRPO on de novo small-molecule design, pocket-based small-molecule design, and de novo protein design, instantiating it with both GRPO and Coupled-GRPO across autoregressive and discrete diffusion generators. Across decoding sweeps, SGRPO expands the utility-diversity Pareto frontier and achieves the best frontier-level metrics relative to pretrained generators, GRPO, and memory-assisted GRPO when applicable. Our analyses further show that direct set-level diversity rewards remain effective with small groups and help preserve broader generation-distribution coverage during post-training. The code is available at https://github.com/IDEA-XL/SGRPO.

Training stability remains a critical bottleneck for Group Relative Policy Optimization (GRPO), often manifesting as a trade-off between reasoning plasticity and general capability retention. We identify a root cause as the geometric conflict between plasticity and stability gradients, which leads to destructive interference. Crucially, we argue that deterministic projection methods are suboptimal for GRPO as they overlook the intrinsic stochasticity of group-based gradient estimates. To address this, we propose Probabilistic Conflict Resolution (PCR), a Bayesian framework that models gradients as random variables. PCR dynamically arbitrates conflicts via an uncertainty-aware ``soft projection'' mechanism, optimizing the signal-to-noise ratio. Extensive experiments demonstrate that PCR significantly smooths the training trajectory and achieves superior performance in various reasoning tasks.

Reinforcement learning is emerging as a primary driver for improving language model reasoning capabilities. A fundamental question is whether current reinforcement learning algorithms -- such as Group Relative Policy Optimization (GRPO), the de facto standard algorithm used to improve language model reasoning -- merely sharpen the base model's distribution around problems it can already solve. We investigate this question in the context of formal theorem proving, which has access to a perfect verifier. We identify a degenerate rank bias in GRPO in which highly probable trajectories are reinforced and rare ones are neglected. This results in distribution sharpening: the model can solve some problems with fewer samples, but underperforms simply sampling more solutions from the original model. To overcome GRPO's rank bias we introduce unlikeliness reward, a simple method for explicitly up-weighting rare but correct solutions. We show that unlikeliness reward mitigates rank bias and improves pass@N across a large range of N in both synthetic and real theorem proving settings. We also uncover an unexpected link between rank bias and a seemingly mundane hyperparameter -- the number of updates per batch -- that leads to a second, complementary mitigation. We combine our insights into a revised GRPO training recipe for formal theorem proving, yielding an open pipeline that achieves competitive performance to DeepSeek-Prover-V1.5-RL on the miniF2F-test benchmark. We release our implementation at https://github.com/AndreHe02/rewarding-unlikely-release

Reinforcement learning from verifiable rewards has significantly advanced the reasoning capabilities of large language models. However, Group Relative Policy Optimization (GRPO) typically assigns a uniform, sequence-level advantage to all tokens, thereby overlooking the intrinsic information heterogeneity along reasoning chains. We show that this coarse-grained credit assignment leads to premature entropy collapse and encourages the model to generate redundant, low-quality reasoning paths. Through systematic empirical analysis, we identify Critical Decision Pivots (CDPs): transient high-entropy states where the policy's trajectory is most sensitive to perturbations. These pivots represent the "forks in the road" where effective multi-path exploration is most crucial yet often suppressed by uniform advantage signals. Building on these insights, we propose Entropy-Regulated Policy Optimization (ERPO), which transitions the optimization focus from coarse sequences to fine-grained token dynamics. ERPO introduces three synergistic components: (i) Entropy-aware Gating, which adaptively amplifies exploration at CDPs to facilitate diverse path discovery; (ii) Bucket-based Implicit Normalization, which mitigates difficulty bias by aligning token progress windows; and (iii) Result-anchored Advantage Synthesis, which re-weights token-level signals via outcome-driven anchors. Extensive experiments on competitive mathematical benchmarks demonstrate that ERPO significantly outperforms GRPO. Notably, ERPO not only boosts reasoning accuracy but also yields significantly more concise and robust derivation paths, while achieving performance comparable to large models with orders of magnitude more parameters.

Group Relative Policy Optimization (GRPO) improves language-model reasoning by comparing verified rewards among multiple solution rollouts for each query. However, difficult training queries can yield only incorrect rollouts, leaving GRPO with no reward contrast or learning signal. Prior hint-based methods construct auxiliary hints from solution evidence and use them to re-solve failed queries, recovering learning signal. Yet the resulting trajectories are typically treated as ordinary solution trajectories despite being generated under an assisted condition unavailable at evaluation. We discover hinted reward shift: recovered reward contrast can concentrate policy updates on hinted trajectories, limiting improvement without hints. This also creates a trade-off: increasing hinted trajectories can accelerate early learning but intensify reward shift later. To address this problem, we propose HATCH (Hint-Annealed Self-Teaching), an online single-policy framework that learns from both generating and using its own hints to improve reasoning without assistance. To mitigate hinted reward shift, we introduce online weighting to anneal the contribution of hinted trajectories. However, learning to generate hints can conflict with improving query solving. We therefore use gradient projection to remove the opposing component of hint-generation updates. Together, these designs support self-improvement by enabling the policy to create learning opportunities for itself and turn them into stronger reasoning without hints. We evaluate our method on mathematical reasoning benchmarks and outperform state-of-the-art methods by 1.02 pp on Llama-3.2-1B-Instruct, 2.84 pp on Qwen3-1.7B, and 4.32 pp on Qwen3-8B.

Modeling human preferences is crucial for aligning foundation models with human values. Traditional reward modeling methods, such as the Bradley-Terry (BT) reward model, fall short in expressiveness, particularly in addressing intransitive preferences. Although supervised pair preference models (PairPM) can express general preferences, their implementation is highly ad-hoc and cannot guarantee a consistent preference probability of compared pairs. Additionally, they impose high computational costs due to their quadratic query complexity when comparing multiple responses. In this paper, we introduce preference representation learning, an approach that embeds responses into a latent space to capture intricate preference structures efficiently, achieving linear query complexity. Additionally, we propose preference score-based General Preference Optimization (GPO), which generalizes reward-based reinforcement learning from human feedback. Experimental results show that our General Preference representation model (GPM) outperforms the BT reward model on the RewardBench benchmark with a margin of up to 5.6% and effectively models cyclic preferences where any BT reward model behaves like a random guess. Furthermore, evaluations on downstream tasks such as AlpacaEval2.0 and MT-Bench, following the language model post-training with GPO and our general preference model, reveal substantial performance improvements with margins up to 9.3%. These findings indicate that our method may enhance the alignment of foundation models with nuanced human values. The code is available at https://github.com/general-preference/general-preference-model.

Aligning large language models (LLMs) with human values and safety constraints is challenging, especially when objectives like helpfulness, truthfulness, and avoidance of harm conflict. Reinforcement Learning from Human Feedback (RLHF) has achieved notable success in steering models, but is complex and can be unstable. Recent approaches such as Direct Preference Optimization (DPO) simplify preference-based fine-tuning but may introduce bias or trade-off certain objectives~dpo. In this work, we propose a Group Relative Policy Optimization (GRPO) framework with a multi-label reward regression model to achieve safe and aligned language generation. The GRPO algorithm optimizes a policy by comparing groups of sampled responses, eliminating the need for a separate value critic and improving training efficiency~grpo. We train a reward model to predict multiple alignment scores (e.g., safety, helpfulness, etc.), which are combined into a single reward signal. We provide a theoretical derivation for using this learned multi-aspect reward within GRPO and discuss its advantages and limitations. Empirically, our approach improves all the safety and quality metrics evaluated in language generation tasks on model scales (0.5B, 7B, and 14B parameters), demonstrating a robust balance of objectives. We compare GRPO to PPO-based RLHF and DPO, highlighting that GRPO achieves alignment with significantly lower computational cost and explicit multi-objective handling. \textbf{We will open-source all trained models at https://huggingface.co/hydroxai.

Reinforcement Learning (RL) can directly enhance the reasoning capabilities of large language models without extensive reliance on Supervised Fine-Tuning (SFT). In this work, we revisit the traditional Policy Gradient (PG) mechanism and propose a minimalist RL approach termed Group Policy Gradient (GPG). Unlike conventional methods, GPG directly optimize the original RL objective, thus obviating the need for surrogate loss functions. As illustrated in our paper, by eliminating both the critic and reference models, and avoiding KL divergence constraints, our approach significantly simplifies the training process when compared to Group Relative Policy Optimization (GRPO). Our approach achieves superior performance without relying on auxiliary techniques or adjustments. Extensive experiments demonstrate that our method not only reduces computational costs but also consistently outperforms GRPO across various unimodal and multimodal tasks. Our code is available at https://github.com/AMAP-ML/GPG.

Existing methods for extracting reward signals in Reinforcement Learning typically rely on labeled data and dedicated training splits, a setup that contrasts with how humans learn directly from their environment. In this work, we propose TTRV to enhance vision language understanding by adapting the model on the fly at inference time, without the need for any labeled data. Concretely, we enhance the Group Relative Policy Optimization (GRPO) framework by designing rewards based on the frequency of the base model's output, while inferring on each test sample multiple times. Further, we also propose to control the diversity of the model's output by simultaneously rewarding the model for obtaining low entropy of the output empirical distribution. Our approach delivers consistent gains across both object recognition and visual question answering (VQA), with improvements of up to 52.4% and 29.8%, respectively, and average boosts of 24.6% and 10.0% across 16 datasets.Remarkably, on image recognition, TTRV applied to InternVL 8B surpasses GPT-4o by an average of 2.3% over 8 benchmarks, while remaining highly competitive on VQA, demonstrating that test-time reinforcement learning can match or exceed the strongest proprietary models. Finally, we find many interesting properties of test-time RL for VLMs: for example, even in extremely data-constrained scenarios, where adaptation is performed on a single randomly chosen unlabeled test example, TTRV still yields non-trivial improvements of up to 5.5% in recognition tasks.

Group Relative Policy Optimization (GRPO) has proven highly effective in enhancing the alignment capabilities of Large Language Models (LLMs). However, current adaptations of GRPO for the flow matching-based image generation neglect a foundational conflict between its core principles and the distinct dynamics of the visual synthesis process. This mismatch leads to two key limitations: (i) Uniformly applying a sparse terminal reward across all timesteps impairs temporal credit assignment, ignoring the differing criticality of generation phases from early structure formation to late-stage tuning. (ii) Exclusive reliance on relative, intra-group rewards causes the optimization signal to fade as training converges, leading to the optimization stagnation when reward diversity is entirely depleted. To address these limitations, we propose Value-Anchored Group Policy Optimization (VGPO), a framework that redefines value estimation across both temporal and group dimensions. Specifically, VGPO transforms the sparse terminal reward into dense, process-aware value estimates, enabling precise credit assignment by modeling the expected cumulative reward at each generative stage. Furthermore, VGPO replaces standard group normalization with a novel process enhanced by absolute values to maintain a stable optimization signal even as reward diversity declines. Extensive experiments on three benchmarks demonstrate that VGPO achieves state-of-the-art image quality while simultaneously improving task-specific accuracy, effectively mitigating reward hacking. Project webpage: https://yawen-shao.github.io/VGPO/.

Traditional alignment methods for Large Vision and Language Models (LVLMs) primarily rely on human-curated preference data. Human-generated preference data is costly; machine-generated preference data is limited in quality; and self-supervised preference data often introduces hallucinations. To overcome these limitations, we propose a novel Panel-of-Peers learning framework inspired by collaborative learning among humans. This approach leverages a panel of LVLMs, each evaluating and learning from their collective outputs through an iterative self-improvement process. By simulating a peer review system, our models generate, assess, and refine outputs in response to a curated set of prompts, mimicking a classroom learning environment. We demonstrate that this methodology enhances model performance without requiring extensive human-labeled datasets. Our experiments show significant improvement across multiple benchmarks, demonstrating the potential of peer evaluations as a scalable alternative to self-supervised alignment. Notably, we show that Panel-of-Peers increases the average score on fifteen benchmarks from 48% to 57%

Chinese Semantic Error Correction (CSEC) targets semantic errors in Chinese text, which are typically more subtle and complex than spelling and grammatical errors but remain relatively underexplored. Existing LLM-based approaches face two recurring obstacles in this task: over-correction, and unclear interaction between Chain-of-Thought (CoT) reasoning and self-consistency decoding, such that the benefits brought by CoT cannot be reliably transferred to final corrections. We propose Vote-guided Advantage Allocation for CSEC (VAA-CSEC), a multi-stage framework that combines CoT distillation, Supervised Fine-Tuning (SFT), Reinforcement Learning (RL) and self-consistency decoding. During RL, we design a task-specific reward function that directly aligned with the minimal-editing principle of CSEC. We further introduce Group-Level Relative Policy Optimization (GLPO), which reallocates GRPO advantages according to the margin between individual rollout rewards and the vote-aggregated group reward, aligning the RL training objective with the self-consistency objective used at inference time. Experiments on CSED-C and NaSGEC-Exam show that VAA-CSEC outperforms all LLM-based baselines on CSED-C with an F0.5 of 47.72%, achieves the highest recall of 42.15% among all methods, and establishes a new state of the art of 41.55% F0.5 on NaSGEC-Exam.

Group Relative Policy Optimization (GRPO), a prominent algorithm within the Reinforcement Learning from Verifiable Rewards (RLVR) framework, has achieved strong results in improving the reasoning capabilities of large language models (LLMs). However, GRPO is prone to advantage collapse, a failure mode where homogeneous rewards within a group (e.g., all correct or all incorrect answers) yield near-zero advantages and vanishing gradients. To address this, we introduce the Advantage Collapse Rate (ACR), the first diagnostic metric quantifying the proportion of training batches with ineffective gradients. Across models from 0.5B to 14B parameters on mathematical reasoning benchmarks, we show that ACR strongly predicts training stagnation and final performance. We then propose Adaptive Virtual Sample Policy Optimization (AVSPO), a lightweight extension of GRPO that injects virtual reward samples, guided by real-time ACR monitoring, to enable learning from homogeneous groups without additional model rollouts. AVSPO reduces advantage collapse by 58-63% relative to GRPO and yields consistent accuracy gains of 4-6 percentage points across all model scales, while maintaining generalization on the evaluated out-of-domain task. Code and datasets are available at https://github.com/hexixiang/Advantage-Collapse-Rate.

Learning from preference feedback has emerged as an essential step for improving the generation quality and performance of modern language models (LMs). Despite its widespread use, the way preference-based learning is applied varies wildly, with differing data, learning algorithms, and evaluations used, making disentangling the impact of each aspect difficult. In this work, we identify four core aspects of preference-based learning: preference data, learning algorithm, reward model, and policy training prompts, systematically investigate the impact of these components on downstream model performance, and suggest a recipe for strong learning for preference feedback. Our findings indicate that all aspects are important for performance, with better preference data leading to the largest improvements, followed by the choice of learning algorithm, the use of improved reward models, and finally the use of additional unlabeled prompts for policy training. Notably, PPO outperforms DPO by up to 2.5% in math and 1.2% in general domains. High-quality preference data leads to improvements of up to 8% in instruction following and truthfulness. Despite significant gains of up to 5% in mathematical evaluation when scaling up reward models, we surprisingly observe marginal improvements in other categories. We publicly release the code used for training (https://github.com/hamishivi/EasyLM) and evaluating (https://github.com/allenai/open-instruct) our models, along with the models and datasets themselves (https://huggingface.co/collections/allenai/tulu-v25-suite-66676520fd578080e126f618).

Reinforcement learning with verifiable rewards (RLVR) has become a standard approach for large language models (LLMs) post-training to incentivize reasoning capacity. Among existing recipes, group-based policy gradient is prevalent, which samples a group of responses per prompt and updates the policy via group-relative advantage signals. This work reveals that these optimization strategies share a common geometric structure: each implicitly defines a target distribution on the response simplex and projects toward it via first-order approximation. Building on this insight, we propose Listwise Policy Optimization (LPO) to explicitly conduct the target-projection, which demystifies the implicit target by restricting the proximal RL objective to the response simplex, and then projects the policy via exact divergence minimization. This framework provides (i) monotonic improvement on the listwise objective with bounded, zero-sum, and self-correcting projection gradients, and (ii) flexibility in divergence selection with distinct structural properties through the decoupled projection step. On diverse reasoning tasks and LLM backbones, LPO consistently improves training performance over typical policy gradient baselines under matched targets, while intrinsically preserving optimization stability and response diversity.

With the rapid progress of Multimodal Large Language Models (MLLMs), unified MLLMs that jointly perform image understanding and generation have advanced significantly. However, despite the inherent reasoning capabilities of unified MLLMs for self-reflection and self-refinement, their use in text-to-image generation remains largely underexplored. Meanwhile, existing multimodal reasoning-based image generation methods mostly rely on prompt augmentation or holistic image-text alignment judgments, without fine-grained reflection and refinement of detailed prompt attributes, leading to limited fine-grained control. To address this limitation, we propose FiRe, a Fine-grained Multimodal Reasoning method for enhanced image generation by MLLM. In specific, FiRe performs a fine-grained multi-step reasoning by first decomposing the prompt into key visual requirements and then self-judging their satisfaction in the generated image, followed by localized refinement according to self-generated precise feedback. In addition, to further strengthen the MLLM's multimodal reasoning ability, we introduce FiRe-GRPO, a reinforcement learning method tailored to FiRe. Since standard Group Relative Policy Optimization (GRPO) suffers from sparse, outcome-based rewards in multi-step reasoning, we formulate our reasoning process as a step-level decision-making problem, design step-specific rewards, and compute step-level advantages for granular credit assignment within GRPO. Extensive experiments demonstrate that FiRe consistently outperforms competitive text-to-image baselines, including existing reasoning-based methods, with particularly substantial gains on compositional text-to-image benchmarks.

Group-relative methods for reinforcement learning with verifiable rewards (RLVR) learn from differences in rollout outcomes. Independently sampling complete trajectories is costly and does not explicitly explore the decision space at critical positions. Feedback on a completed trajectory can reveal which earlier choices the policy reconsiders, suggesting where to sample alternative continuations. We introduce Hindsight-Divergence Localization (HDL), which uses hindsight-induced changes in token log-likelihoods to select branch points. HDL generates a small number of complete root trajectories and fills each training group with continuations from the selected positions under the original task context. Each continuation reuses its root prefix and contributes policy updates only through its newly generated suffix, reducing generation cost while focusing additional exploration and learning on decisions after branching. Experiments with three models across math, code, and agent tasks show gains in both rollout efficiency and task performance. Compared with GRPO at matched group sizes and training steps, HDL yields up to a 2.5times reduction in generated tokens and a 1.8times speedup in rollout wall-clock time. Despite this reduced generation budget, HDL improves performance across all three domains, with gains of up to 12.5 points on agent tasks.

While Reinforcement Learning from Human Feedback (RLHF) has become a pivotal paradigm for text-to-image generation, its application to image editing remains largely unexplored. A key bottleneck is the lack of a robust general reward model for all editing tasks. Existing edit reward models usually give overall scores without detailed checks, ignoring different instruction requirements and causing biased rewards. To address this, we argue that the key is to move from a simple scorer to a reasoning verifier. We introduce Edit-R1, a framework that builds a chain-of-thought (CoT) verifier-based reasoning reward model (RRM) and then leverages it for downstream image editing. The Edit-RRM breaks instructions into distinct principles, evaluates the edited image against each principle, and aggregates these checks into an interpretable, fine-grained reward. To build such an RRM, we first apply supervised fine-tuning (SFT) as a ``cold-start'' to generate CoT reward trajectories. Then, we introduce Group Contrastive Preference Optimization (GCPO), a reinforcement learning algorithm that leverages human pairwise preference data to reinforce our pointwise RRM. After building the RRM, we use GRPO to train editing models with this non-differentiable yet powerful reward model. Extensive experiments demonstrate that our Edit-RRM surpasses powerful VLMs such as Seed-1.5-VL and Seed-1.6-VL as an editing-specific reward model, and we observe a clear scaling trend, with performance consistently improving from 3B to 7B parameters. Moreover, Edit-R1 delivers gains to editing models like FLUX.1-kontext, highlighting its effectiveness in enhancing image editing.

The Backpropagation algorithm has often been criticised for its lack of biological realism. In an attempt to find a more biologically plausible alternative, the recently introduced Forward-Forward algorithm replaces the forward and backward passes of Backpropagation with two forward passes. In this work, we show that the internal representations obtained by the Forward-Forward algorithm can organise into category-specific ensembles exhibiting high sparsity -- composed of a low number of active units. This situation is reminiscent of what has been observed in cortical sensory areas, where neuronal ensembles are suggested to serve as the functional building blocks for perception and action. Interestingly, while this sparse pattern does not typically arise in models trained with standard Backpropagation, it can emerge in networks trained with Backpropagation on the same objective proposed for the Forward-Forward algorithm.

We present Direct Reward Fine-Tuning (DRaFT), a simple and effective method for fine-tuning diffusion models to maximize differentiable reward functions, such as scores from human preference models. We first show that it is possible to backpropagate the reward function gradient through the full sampling procedure, and that doing so achieves strong performance on a variety of rewards, outperforming reinforcement learning-based approaches. We then propose more efficient variants of DRaFT: DRaFT-K, which truncates backpropagation to only the last K steps of sampling, and DRaFT-LV, which obtains lower-variance gradient estimates for the case when K=1. We show that our methods work well for a variety of reward functions and can be used to substantially improve the aesthetic quality of images generated by Stable Diffusion 1.4. Finally, we draw connections between our approach and prior work, providing a unifying perspective on the design space of gradient-based fine-tuning algorithms.

Group Relative Policy Optimization (GRPO) has emerged as a powerful framework for preference alignment in text-to-image (T2I) flow models. However, we observe that the standard paradigm where evaluating a group of generated samples against a single condition suffers from insufficient exploration of inter-sample relationships, constraining both alignment efficacy and performance ceilings. To address this sparse single-view evaluation scheme, we propose Multi-View GRPO (MV-GRPO), a novel approach that enhances relationship exploration by augmenting the condition space to create a dense multi-view reward mapping. Specifically, for a group of samples generated from one prompt, MV-GRPO leverages a flexible Condition Enhancer to generate semantically adjacent yet diverse captions. These captions enable multi-view advantage re-estimation, capturing diverse semantic attributes and providing richer optimization signals. By deriving the probability distribution of the original samples conditioned on these new captions, we can incorporate them into the training process without costly sample regeneration. Extensive experiments demonstrate that MV-GRPO achieves superior alignment performance over state-of-the-art methods.

Group Relative Policy Optimization (GRPO) is highly effective for post-training autoregressive (AR) language models, yet its direct application to diffusion large language models (dLLMs) often triggers reward collapse. We identify two sources of incompatibility. First, GRPO relies on importance ratios defined by sequence probabilities, which are intractable in dLLMs and must be estimated (e.g., via ELBO-based or mean-field likelihood proxies), yielding inherently noisy ratios. Second, standard GRPO's formulation is not designed for estimated ratios: its conditional clipping can be anomalously bypassed by model-agnostic estimation noise, producing gradient spikes, while its fixed group-size normalization amplifies gradient-magnitude fluctuations under high-variance ratio estimates. We show these effects form a self-reinforcing instability loop that drives policy drift and further increases ratio variance. To break this loop, we propose StableDRL, a reformulation of GRPO tailored for dLLMs that uses (i) unconditional clipping to suppress outlier-induced spikes and (ii) self-normalization to constrain updates within the convex hull of per-sample gradients. We further extend StableDRL to block-wise diffusion models via a staircase attention mechanism.

Large language models (LLMs) have achieved impressive reasoning performance, with reinforcement learning with verifiable rewards (RLVR) emerging as a standard paradigm for post-training. A representative algorithm, group relative policy optimization (GRPO) (Shao et al., 2024), computes advantages by normalizing outcome rewards within response groups, but suffers from a vanishing advantage issue when all responses in a group receive identical rewards. To address this issue, we propose Adaptive Rollout and Response Reuse Policy Optimization (AR3PO), a sampling efficient RLVR algorithm that introduces two novel techniques: adaptive rollout, which dynamically allocates more responses to difficult prompts while saving computation on easier ones, and response reuse, which leverages previously generated correct responses to provide useful training signals. We compare AR3PO with strong RLVR baselines on multiple representative benchmarks using two different families of base models. Across the 7B and 8B models, AR3PO consistently outperforms GRPO and matches or surpasses DAPO (Yu et al., 2025), reducing rollout cost by up to 4.2x. On the larger 32B model, AR3PO achieves comparable performance to DAPO at similar training steps while maintaining substantially lower rollout cost.

Backpropagation, which uses the chain rule, is the de-facto standard algorithm for optimizing neural networks nowadays. Recently, Hinton (2022) proposed the forward-forward algorithm, a promising alternative that optimizes neural nets layer-by-layer, without propagating gradients throughout the network. Although such an approach has several advantages over back-propagation and shows promising results, the fact that each layer is being trained independently limits the optimization process. Specifically, it prevents the network's layers from collaborating to learn complex and rich features. In this work, we study layer collaboration in the forward-forward algorithm. We show that the current version of the forward-forward algorithm is suboptimal when considering information flow in the network, resulting in a lack of collaboration between layers of the network. We propose an improved version that supports layer collaboration to better utilize the network structure, while not requiring any additional assumptions or computations. We empirically demonstrate the efficacy of the proposed version when considering both information flow and objective metrics. Additionally, we provide a theoretical motivation for the proposed method, inspired by functional entropy theory.

Video quality assessment (VQA) aims to objectively quantify perceptual quality degradation in alignment with human visual perception. Despite recent advances, existing VQA models still suffer from two critical limitations: poor generalization to out-of-distribution (OOD) videos and limited explainability, which restrict their applicability in real-world scenarios. To address these challenges, we propose VQAThinker, a reasoning-based VQA framework that leverages large multimodal models (LMMs) with reinforcement learning to jointly model video quality understanding and scoring, emulating human perceptual decision-making. Specifically, we adopt group relative policy optimization (GRPO), a rule-guided reinforcement learning algorithm that enables reasoning over video quality under score-level supervision, and introduce three VQA-specific rewards: (1) a bell-shaped regression reward that increases rapidly as the prediction error decreases and becomes progressively less sensitive near the ground truth; (2) a pairwise ranking reward that guides the model to correctly determine the relative quality between video pairs; and (3) a temporal consistency reward that encourages the model to prefer temporally coherent videos over their perturbed counterparts. Extensive experiments demonstrate that VQAThinker achieves state-of-the-art performance on both in-domain and OOD VQA benchmarks, showing strong generalization for video quality scoring. Furthermore, evaluations on video quality understanding tasks validate its superiority in distortion attribution and quality description compared to existing explainable VQA models and LMMs. These findings demonstrate that reinforcement learning offers an effective pathway toward building generalizable and explainable VQA models solely with score-level supervision.