Daily Papers

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.

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.

We propose Delta L Normalization, a simple yet effective loss aggregation method tailored to the characteristic of dynamic generation lengths in Reinforcement Learning with Verifiable Rewards (RLVR). Recently, RLVR has demonstrated strong potential in improving the reasoning capabilities of large language models (LLMs), but a major challenge lies in the large variability of response lengths during training, which leads to high gradient variance and unstable optimization. Although previous methods such as GRPO, DAPO, and Dr. GRPO introduce different loss normalization terms to address this issue, they either produce biased estimates or still suffer from high gradient variance. By analyzing the effect of varying lengths on policy loss both theoretically and empirically, we reformulate the problem as finding a minimum-variance unbiased estimator. Our proposed Delta L Normalization not only provides an unbiased estimate of the true policy loss but also minimizes gradient variance in theory. Extensive experiments show that it consistently achieves superior results across different model sizes, maximum lengths, and tasks. Our code will be made public at https://github.com/zerolllin/Delta-L-Normalization.

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.

State-of-the-art reasoning models utilize long chain-of-thought (CoT) to solve increasingly complex problems using more test-time computation. In this work, we explore a long CoT setting where the model makes up to K successive attempts at solving a problem, in which each attempt is allowed to build on earlier ones after the model receives a hard verifier feedback. This motivates RL methods that can harness per-attempt rewards by carefully weighting individual attempts. We study optimizing the Verification@K reward (the model succeeds by the K-th attempt) and show that naively weighing the attempts by their pass/fail results in biased gradients. We introduce Calibrated Attempt-Level (CAL) GRPO by devising a weighing strategy to obtain unbiased gradients while maintaining small variance. Our theory reveals how incorporating per-attempt rewards influence the training and the eventual Verification@K performance. Experiments, baselines, and ablations on synthetic and real data corroborate our theory and the benefits of CAL-GRPO over vanilla GRPO as well as naive weighting.

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.

Recently, GRPO-based reinforcement learning has shown remarkable progress in optimizing flow-matching models, effectively improving their alignment with task-specific rewards. Within these frameworks, the policy update relies on importance-ratio clipping to constrain overconfident positive and negative gradients. However, in practice, we observe a systematic shift in the importance-ratio distribution-its mean falls below 1 and its variance differs substantially across timesteps. This left-shifted and inconsistent distribution prevents positive-advantage samples from entering the clipped region, causing the mechanism to fail in constraining overconfident positive updates. As a result, the policy model inevitably enters an implicit over-optimization stage-while the proxy reward continues to increase, essential metrics such as image quality and text-prompt alignment deteriorate sharply, ultimately making the learned policy impractical for real-world use. To address this issue, we introduce GRPO-Guard, a simple yet effective enhancement to existing GRPO frameworks. Our method incorporates ratio normalization, which restores a balanced and step-consistent importance ratio, ensuring that PPO clipping properly constrains harmful updates across denoising timesteps. In addition, a gradient reweighting strategy equalizes policy gradients over noise conditions, preventing excessive updates from particular timestep regions. Together, these designs act as a regulated clipping mechanism, stabilizing optimization and substantially mitigating implicit over-optimization without relying on heavy KL regularization. Extensive experiments on multiple diffusion backbones (e.g., SD3.5M, Flux.1-dev) and diverse proxy tasks demonstrate that GRPO-Guard significantly reduces over-optimization while maintaining or even improving generation quality.

Partial correlations quantify linear association between two variables adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is specified from log ratios of variables, so unless we try to "open" the data via a normalization, this implies changes in the definition and interpretation of partial correlations. In the present work, we elucidate how results derived by Aitchison (1986) lead to a natural definition of partial correlation that has a number of advantages over current measures of association. For this, we show that the residuals of log-ratios between a variable with a reference, when adjusting for all remaining variables including the reference, are reference-independent. Since the reference itself can be controlled for, correlations between residuals are defined for the variables directly without the necessity to recur to ratios except when specifying which variables are partialled out. Thus, perhaps surprisingly, partial correlations do not have the problems commonly found with measures of pairwise association on compositional data. They are well-defined between two variables, are properly scaled, and allow for negative association. By design, they are subcompositionally incoherent, but they share this property with conventional partial correlations (where results change when adjusting for the influence of fewer variables). We discuss the equivalence with normalization-based approaches whenever the normalizing variables are controlled for. We also discuss the partial variances and correlations we obtain from a previously studied data set of Roman glass cups.

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.

Recent advancements in reasoning language models have been driven by Reinforcement Learning (RL) fine-tuning. Most often, these rely on the Group Relative Policy Optimization (GRPO) algorithm or modifications thereof to steer the models to produce Chain-of-Thought (CoT) traces. The final answer can only be verified, and the reward assigned, after the CoT trace is complete, making it a delayed reward problem. GRPO and its modifications correspond to Monte Carlo methods in standard RL, which are known to suffer from high variance. A possible solution to this problem is the redistribution of rewards through credit assignment, where segments of the CoT trace that are important for arriving at the desirable solution are emphasized by assigning a higher reward. While Monte Carlo sampling can be used to provide an unbiased estimate of intermediate state values, its computational overhead makes it unsuitable for train-time credit assignment in long contexts at high granularity. We introduce RREDCoT (Reward REDistribution for Chain of Thoughts), which utilizes the model itself to approximate the optimal reward redistribution without additional generation. We investigate the advantages of our method compared to MC sampling and several attribution methods. We further analyze several aspects relevant to the construction of the redistribution such as segmentation of CoT traces and state value estimation.

Training large language models to reason efficiently is a critical challenge. While integrating length-penalizing rewards into Group Relative Policy Optimization (GRPO) aims to reduce verbosity, it frequently triggers reward collapse, severely degrading reasoning capabilities. Through a systematic evaluation of various reward configurations, we identify the root mechanism: GRPO's group normalization creates divergent advantages when incorrect answers receive continuous length penalties. Consequently, methods penalizing the length of incorrect answers are structurally prone to collapse under sustained optimization. Furthermore, restricting penalties exclusively to correct answers avoids this primary failure, but leaves the model susceptible to a stochastic collapse driven by response over-compression. To robustly prevent both failure modes, we propose ACOER (Adaptive Correct-Only Efficiency Reward). ACOER eliminates the structural penalty loop by isolating brevity bonuses to correct completions and prevents stochastic compression via dynamic budget normalization and control-loop penalty adjustments. Evaluated across diverse mathematical reasoning benchmarks, ACOER improves overall accuracy compared to the base model while reducing token generation by over 60%, establishing a fundamentally stable approach for efficiency-aware optimization.

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.

We investigate a narrow but common failure mode of GRPO-style reinforcement learning in the context of sparse verifiable rewards: early updates contain more responses with negative advantages than those with positive advantages, while response-level length normalization ties the magnitude of the update to the length of the output. We propose Hysteretic Policy Optimization (HPO), a minimal modification of GRPO that reduces the weight of negative-advantage updates and replaces per-response length normalization with mean-length normalization. We further introduce Adaptive HPO (A-HPO), which sets the hysteretic weight based on batch-level advantage-sign statistics, thereby removing the need for tuning a fixed hysteretic weight. In our TeleLogs and Countdown experiments, A-HPO improves the reward per update compared to GRPO, with the largest gains in early sparse reward regimes. On TeleLogs, A-HPO achieves a final reward of 0.84, outperforming SAPO by 5%, GSPO by 11%, and GRPO by 15%, while maintaining a comparable response-length. On Countdown, A-HPO achieves the largest gains in initial and most difficult configurations across 1.5B-7B models. Ablation studies on the hysteretic weight show that the gains of A-HPO come from better balancing the contributions of positive and negative advantages compared to positive-only or fully symmetric updates.

Language models are increasingly trained against several verifiable rewards at once, such as the correctness and the format of a tool call, or the individual constraints of a complex instruction. Reward-decoupled normalization (GDPO) normalizes each reward separately so that different reward combinations keep distinct advantages, but it still spreads every reward's advantage evenly over the whole response, although each verifier checks only a few positions. We propose MRTPO, which assigns the advantage of each reward to the tokens relevant to it, using the information its verifier checks, without auxiliary models or token-level annotations. For each reward, the policy replays its own response with and without that reward's verifier information, and the per-token Jensen-Shannon distance between the two next-token distributions measures each token's relevance and reassigns the advantage. On text-to-SQL, multi-constraint instruction following and tool calling, MRTPO converges faster and achieves better performance than the compared methods.

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.

Dense per-step supervision is an appealing remedy for sparse-reward, long-horizon LLM agents: reward the agent for predicting its next observation, and memory should follow. We show that under group-normalized RL (GRPO), this recipe does not merely fail -- it destroys the policy. Across Qwen3-1.7B/4B/8B on ALFWorld, a potential-based prediction reward drives every run into a degenerate absorbing state (prediction accuracy -> 1.0, task success -> 0,episode length pinned at the horizon): the "dark room" pathology, built automatically by the optimizer. A single-factor ablation localizes the cause -- removing only GRPO's std normalization turns the same reward from catastrophic (0%) into baseline parity -- and a two-line proposition explains why: in all-fail groups the z-scored advantage is invariant to the shaping coefficient, so bounded rewards become unbounded pressure and annealing cannot help. Our central insight generalizes this: what z-scoring amplifies is a dense signal's within-group variance while all-fail groups dominate, so signals whose variance decays by mastery are structurally amplifier-safe.This variance-profile criterion retrodicts our collapses, carries preregistered predictions for arms that had not yet run, and is consistent with published reward-channel successes (a compatibility check, not an independent test). Finally, a controlled signal-delivery matrix (identical signal, varying only the consumption mechanism) shows the reward channel is at best neutral while the auxiliary-loss channel gains ~20 points -- and a shuffled-gold placebo matches the true-gold arm, so the gap survives without correct labels. Endpoints are single-seed; seed replication and group-size controls are preregistered and in progress.

Recent advancements in flow-matching have enabled high-quality text-to-image generation. However, the deterministic nature of flow-matching models makes them poorly suited for reinforcement learning, a key tool for improving image quality and human alignment. Prior work has introduced stochasticity by perturbing latents with random noise, but such perturbations are inefficient and unstable. We propose Smart-GRPO, the first method to optimize noise perturbations for reinforcement learning in flow-matching models. Smart-GRPO employs an iterative search strategy that decodes candidate perturbations, evaluates them with a reward function, and refines the noise distribution toward higher-reward regions. Experiments demonstrate that Smart-GRPO improves both reward optimization and visual quality compared to baseline methods. Our results suggest a practical path toward reinforcement learning in flow-matching frameworks, bridging the gap between efficient training and human-aligned generation.

Normalizing flows, a popular class of deep generative models, often fail to represent extreme phenomena observed in real-world processes. In particular, existing normalizing flow architectures struggle to model multivariate extremes, characterized by heavy-tailed marginal distributions and asymmetric tail dependence among variables. In light of this shortcoming, we propose COMET (COpula Multivariate ExTreme) Flows, which decompose the process of modeling a joint distribution into two parts: (i) modeling its marginal distributions, and (ii) modeling its copula distribution. COMET Flows capture heavy-tailed marginal distributions by combining a parametric tail belief at extreme quantiles of the marginals with an empirical kernel density function at mid-quantiles. In addition, COMET Flows capture asymmetric tail dependence among multivariate extremes by viewing such dependence as inducing a low-dimensional manifold structure in feature space. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of COMET Flows in capturing both heavy-tailed marginals and asymmetric tail dependence compared to other state-of-the-art baseline architectures. All code is available on GitHub at https://github.com/andrewmcdonald27/COMETFlows.

Self-Distillation Policy Optimization (SDPO) provides dense token-level credit assignment for reinforcement learning with large language models by leveraging the model's own feedback-conditioned predictions as a self-teacher. Unlike GRPO, however, whose group-relative advantage naturally concentrates learning on a sweet spot of intermediate-difficulty questions, SDPO's KL-based advantage lacks an implicit notion of difficulty awareness. We analyze this gap through the lens of GRPO's advantage normalization. Extending the learnability framework to normalized rewards, we show that normalization absorbs the variance term p(1-p), equalizing leading-order learnability across questions and leaving p(1-p) as the sole residual scaling factor in the per-question gradient. This analysis yields a simple prescription: weight each question's SDPO loss by [p(1-p)]^{1/2}, resulting in SC-SDPO, a scale-consistent variant of SDPO. The proposed weights are obtained as a zero-cost byproduct of on-policy rollouts with batch-adaptive normalization, inducing an implicit curriculum that dynamically tracks the model's evolving competence. Experiments on scientific reasoning and tool-use benchmarks demonstrate that SC-SDPO consistently improves over SDPO, yielding gains of +3.2/+4.3 (mean@16/maj@16) on Qwen3-8B and +1.8/+3.0 on OLMo-3-7B, while preserving stable training dynamics throughout optimization.

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.

Reinforcement learning has become the primary paradigm for aligning large language models (LLMs) on complex reasoning tasks, with group relative policy optimization (GRPO) widely used in large-scale post-training. However, GRPO faces structural limitations in reasoning-heavy settings: sequence-level advantage normalization introduces systematic length bias, penalties for low-quality trajectories are diluted, and the scalar objective discards rich pairwise preference information embedded in within-group reward rankings. As a result, valuable supervision from costly rollouts remains underutilized. We propose AMIR-GRPO, which augments GRPO with an implicit DPO-style contrastive regularizer constructed directly from intra-group reward rankings, requiring no additional annotations. This mechanism amplifies suppression of low-reward trajectories, attenuates response-level length bias, and transforms each rollout group into a denser set of supervision constraints. Across multiple mathematical reasoning benchmarks, AMIR-GRPO consistently outperforms strong GRPO baselines, yields clearer separation between correct and incorrect reasoning chains, and delivers broader coverage gains beyond the subset of instances solved by standard GRPO.

Forecasting an unresolved event requires finding relevant evidence and deciding how strongly it supports each outcome. Yet outcome-based training of Large Language Model (LLM) forecasters often begins with preassembled evidence at a single prediction date, leaving evidence acquisition outside the learning loop. We introduce AlphaBet, an agentic reinforcement learning (RL) framework that trains a single LLM policy to search, reason, and report probabilities across multiple pre-resolution dates. Each dated forecast is scored by a proper scoring rule against the eventual outcome, allowing one resolved event to supervise decisions under different information states. We decompose forecasting regret into an evidence-acquisition gap and a probability-reporting gap, and show that Group Relative Policy Optimization (GRPO)'s standard-deviation normalization can distort the reporting target under multi-class proper scores. On GLM-4.5-Air, AlphaBet reduces the Brier score from 0.731 to 0.626 on Forecast-Dojo and from 0.612 to 0.528 on FutureX. Controlled ablations attribute these gains to multi-date training and show that they come from improvements in both information acquisition and probability reporting. Our empirical results validate that GRPO's std normalization degrades proper-scoring-rule performance while leaving top-outcome accuracy largely unchanged.

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.

Reinforcement learning with verifiable rewards (RLVR) is effective for training large language models on deterministic outcome reasoning tasks. Prior work shows RLVR works with few prompts, but prompt selection is often based only on training-accuracy variance, leading to unstable optimization directions and weaker transfer. We revisit prompt selection from a mechanism-level view and argue that an effective minibatch should provide both (i) a reliable positive anchor and (ii) explicit negative learning signals from rare failures. Based on this principle, we propose positive--negative pairing: at each update, we sample a hard-but-solvable q^{+} and an easy-but-brittle prompt q^{-}(high success rate but not perfect), characterized by low and high empirical success rates under multiple rollouts. We further introduce Weighted GRPO, which reweights binary outcomes at the pair level and uses group-normalized advantages to amplify rare successes on q^{+} into sharp positive guidance while turning rare failures on q^{-} into strong negative penalties. This bidirectional signal provides informative learning feedback for both successes and failures, improving sample efficiency without suppressing exploration. On Qwen2.5-Math-7B, a single paired minibatch per update consistently outperforms a GRPO baseline that selects two prompts via commonly used variance-based selection heuristics: AIME~2025 Pass@8 improves from 16.8 to 22.2, and AMC23 Pass@64 from 94.0 to 97.0, while remaining competitive with large-scale RLVR trained from a pool of 1209 training prompts. Similar gains are observed on Qwen2.5-Math-7B-Instruct.

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.

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.

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.

Reinforcement learning with verifiable rewards (e.g. GRPO) is now a common way to improve mathematical reasoning in Large Language Models (LLMs). However, current methods usually broadcast one sequence-level advantage to all tokens, or use costly process reward models (PRMs) for step-level supervision. Uniform advantage distribution assumes that all tokens contribute equally to the final reward. This dilutes the gradient signal, since flawed reasoning steps and filler words are updated as strongly as valid logical inferences. To address this, we introduce Gradient-Reweighted Advantage (GRAIL), an intrinsic token-wise advantage reweighting method. GRAIL uses gradient-activation saliency to place more weight on tokens that are more locally sensitive to the final answer. Evaluations across five models from the Qwen3, R1-distilled and OctoThinker families show that GRAIL consistently outperforms GRPO. GRAIL achieved an average improvement of 3.60% in accuracy and 3.05% in Pass@3, demonstrating that fine-grained reasoning alignment can be achieved without process-level supervision.

The success of Deepseek-R1 has drawn the LLM community's attention to reinforcement learning (RL) methods like GRPO. However, such rule-based 0/1 outcome reward methods lack the capability to regulate the intermediate reasoning processes during chain-of-thought (CoT) generation, leading to severe overthinking phenomena. In response, recent studies have designed reward functions to reinforce models' behaviors in producing shorter yet correct completions. Nevertheless, we observe that these length-penalty reward functions exacerbate RL training instability: as the completion length decreases, model accuracy abruptly collapses, often occurring early in training. To address this issue, we propose a simple yet effective solution GRPO-lambda, an efficient and stabilized variant of GRPO, which dynamically adjusts the reward strategy by monitoring the correctness ratio among completions within each query-sampled group. A low correctness ratio indicates the need to avoid length penalty that compromises CoT quality, triggering a switch to length-agnostic 0/1 rewards that prioritize reasoning capability. A high ratio maintains length penalties to boost efficiency. Experimental results show that our approach avoids training instability caused by length penalty while maintaining the optimal accuracy-efficiency trade-off. On the GSM8K, GPQA, MATH-500, AMC 2023, and AIME 2024 benchmarks, it improves average accuracy by 1.48% while reducing CoT sequence length by 47.3%.

Multi-agent LLM systems enable advanced reasoning and tool use via role specialization, yet reliable reinforcement learning (RL) post-training for such systems remains difficult. In this work, we theoretically pinpoint a key reason for training instability when extending group-based RL to multi-agent LLM systems. We show that under GRPO-style optimization, a global normalization baseline may deviate from diverse agents' reward distributions, which ultimately leads to gradient-norm instability. Based on this finding, we propose Dr. MAS, a simple and stable RL training recipe for multi-agent LLM systems. Dr. MAS uses an agent-wise remedy: normalizing advantages per agent using each agent's own reward statistics, which calibrates gradient scales and dramatically stabilizes training, both theoretically and empirically. Beyond the algorithm, Dr. MAS provides an end-to-end RL training framework for multi-agent LLM systems, supporting scalable orchestration, flexible per-agent LLM serving and optimization configs, and shared resource scheduling of LLM actor backends. We evaluate Dr. MAS on multi-agent math reasoning and multi-turn search benchmarks using Qwen2.5 and Qwen3 series models. Dr. MAS achieves clear gains over vanilla GRPO (e.g., +5.6\% avg@16 and +4.6\% pass@16 on math, and +15.2\% avg@16 and +13.1\% pass@16 on search) while largely eliminating gradient spikes. Moreover, it remains highly effective under heterogeneous agent-model assignments while improving efficiency.

We prove theoretically that the GRPO RL algorithm induces a non-trivial process reward model (PRM), under certain assumptions regarding within-group overlap of token sequences across completions. We then show empirically that these assumptions are met under real-world conditions: GRPO does in fact induce a non-trivial PRM. Leveraging the framework of GRPO-as-a-PRM, we identify a flaw in the GRPO objective: non-uniformly distributed process steps hinder both exploration and exploitation (under different conditions). We propose a simple modification to the algorithm to mitigate this defect (lambda-GRPO), and show that LLMs trained with lambda-GRPO achieve higher validation accuracy and performance on downstream reasoning tasks-and reach peak performance more rapidly-than LLMs trained with standard GRPO. Our results call into question the advantage of costly, explicitly-defined PRMs for GRPO: we show that it is possible to instead leverage the hidden, built-in PRM structure within the vanilla GRPO algorithm to boost model performance with a negligible impact on training time and cost.

Reinforcement Learning with Verifiable Rewards algorithms like GRPO have emerged as the dominant post-training paradigm for complex reasoning in LLMs, yet commonly suffer from policy entropy collapse during training. We conduct a first-order gradient analysis of token-level entropy dynamics under GRPO and identify a token-level credit assignment mismatch: the per-token entropy variation decomposes into the product of the trajectory-level advantage and an entropy sensitivity function over the next-token distribution, yielding an advantage-surprisal four-quadrant structure and a near-criticality property. Motivated by it, we propose STARE (Surprisal-guided Token-level Advantage Reweighting for policy Entropy stability), which identifies entropy-critical token subsets via batch-internal surprisal quantiles, selectively reweights their effective advantages, and incorporates a target-entropy closed-loop gate for stable entropy regulation. Across model scales from 1.5B to 32B and three task families (Short CoT, Long CoT, and Multi-Turn Tool Use), STARE sustains stable RL training over thousands of steps while maintaining policy entropy within the target band. On AIME24 and AIME25, STARE outperforms DAPO and other competitive baselines by 4%-8% in average accuracy, with reflection tokens and response length growing in tandem, indicating sustained exploration-exploitation balance that further unlocks RL training potential.Code is available at https://github.com/hp-luo/STARE.

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.

Diffusion large language models (dLLMs) are compelling alternatives to autoregressive (AR) models because their denoising models operate over the entire sequence. The global planning and iterative refinement features of dLLMs are particularly useful for code generation. However, current training and inference mechanisms for dLLMs in coding are still under-explored. To demystify the decoding behavior of dLLMs and unlock their potential for coding, we systematically investigate their denoising processes and reinforcement learning (RL) methods. We train a 7B dLLM, DiffuCoder, on 130B tokens of code. Using this model as a testbed, we analyze its decoding behavior, revealing how it differs from that of AR models: (1) dLLMs can decide how causal their generation should be without relying on semi-AR decoding, and (2) increasing the sampling temperature diversifies not only token choices but also their generation order. This diversity creates a rich search space for RL rollouts. For RL training, to reduce the variance of token log-likelihood estimates and maintain training efficiency, we propose coupled-GRPO, a novel sampling scheme that constructs complementary mask noise for completions used in training. In our experiments, coupled-GRPO significantly improves DiffuCoder's performance on code generation benchmarks (+4.4\% on EvalPlus) and reduces reliance on AR causal during decoding. Our work provides deeper insight into the machinery of dLLM generation and offers an effective, diffusion-native RL training framework. https://github.com/apple/ml-diffucoder.

Training vision-language web agents with multi-step RL is compute-intensive, with two dominant forms of inefficiency: idle GPUs in synchronous RL, and trajectories that use more steps and tokens than necessary. We present AsyncWebRL, which addresses both. On the system side, an asynchronous design overlaps rollout, gradient update, and policy refresh across iterations, paired with two web-agent-specific adaptations, namely an everlasting rollout pool and lightweight screenshot handling, that together deliver up to a 2.9times end-to-end training-throughput speedup over the previously fastest open synchronous pipeline (WebGym). On the algorithmic side, we identify the per-trajectory normalizer 1/|τ_i| in multi-step GRPO as the root cause of trajectory-level and token-level inefficiency: because failures are systematically longer than successes, it down-weights the negative gradient on failed tokens, so the policy keeps producing verbose memory schemas. Replacing 1/|τ_i| with a constant 1/k breaks this coupling, contracting trajectories while preserving aggregate success. Together, these contributions set a new open-source state of the art on the WebGym out-of-distribution test split (+5.8% relative over the 42.9% prior best), with the largest gains on the harder slices (+42% relative on Medium, +48% relative on Hard).

Reinforcement learning with verifiable rewards (RLVR) has become a central paradigm for improving reasoning and code generation in large language models, and GRPO-style training is widely adopted for its simplicity and effectiveness. However, an important design choice remains underexplored: how token-level policy gradient terms are aggregated within each sampled group. Standard GRPO uses sequence aggregation, while recent work has advocated token aggregation as a better alternative. We show that these two rules induce different optimization biases: token aggregation introduces sign-length coupling, while sequence aggregation implicitly downweights longer responses through sequence-level equal weighting. To address this tension, we propose Balanced Aggregation (BA), a simple drop-in replacement that computes token-level means separately within the positive and negative subsets and then combines them with sequence-count-based weights. Experiments with Qwen2.5-Math-7B and Qwen3-1.7B on DAPO-17k and Polaris, evaluated on six reasoning and coding benchmarks, show that BA consistently improves training stability and final performance over standard token and sequence aggregation. Our analysis further shows that the relative effectiveness of token and sequence aggregation is largely governed by response-length variation and the positive-negative length gap, highlighting aggregation as a critical design dimension in GRPO-style RLVR.

Recently, Masked Diffusion Models (MDMs) have shown promising potential across vision, language, and cross-modal generation. However, a notable discrepancy exists between their training and inference procedures. In particular, MDM inference is a multi-step, iterative process governed not only by the model itself but also by various schedules that dictate the token-decoding trajectory (e.g., how many tokens to decode at each step). In contrast, MDMs are typically trained using a simplified, single-step BERT-style objective that masks a subset of tokens and predicts all of them simultaneously. This step-level simplification fundamentally disconnects the training paradigm from the trajectory-level nature of inference, leaving the inference schedules never optimized during training. In this paper, we introduce Co-GRPO, which reformulates MDM generation as a unified Markov Decision Process (MDP) that jointly incorporates both the model and the inference schedule. By applying Group Relative Policy Optimization at the trajectory level, Co-GRPO cooperatively optimizes model parameters and schedule parameters under a shared reward, without requiring costly backpropagation through the multi-step generation process. This holistic optimization aligns training with inference more thoroughly and substantially improves generation quality. Empirical results across four benchmarks-ImageReward, HPS, GenEval, and DPG-Bench-demonstrate the effectiveness of our approach. For more details, please refer to our project page: https://co-grpo.github.io/ .

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.

The Canonical Correlation Analysis (CCA) family of methods is foundational in multiview learning. Regularised linear CCA methods can be seen to generalise Partial Least Squares (PLS) and be unified with a Generalized Eigenvalue Problem (GEP) framework. However, classical algorithms for these linear methods are computationally infeasible for large-scale data. Extensions to Deep CCA show great promise, but current training procedures are slow and complicated. First we propose a novel unconstrained objective that characterizes the top subspace of GEPs. Our core contribution is a family of fast algorithms for stochastic PLS, stochastic CCA, and Deep CCA, simply obtained by applying stochastic gradient descent (SGD) to the corresponding CCA objectives. Our algorithms show far faster convergence and recover higher correlations than the previous state-of-the-art on all standard CCA and Deep CCA benchmarks. These improvements allow us to perform a first-of-its-kind PLS analysis of an extremely large biomedical dataset from the UK Biobank, with over 33,000 individuals and 500,000 features. Finally, we apply our algorithms to match the performance of `CCA-family' Self-Supervised Learning (SSL) methods on CIFAR-10 and CIFAR-100 with minimal hyper-parameter tuning, and also present theory to clarify the links between these methods and classical CCA, laying the groundwork for future insights.

Large language models (LLMs) are reshaping the recommender system paradigm by enabling users to express preferences and receive recommendations through conversations. Yet, aligning LLMs to the recommendation task remains challenging: pretrained LLMs often generate out-of-catalog items, violate required output formats, and their ranking quality degrades sharply toward the end of the generated list. To this end, we propose ConvRec-R1, a two-stage framework for end-to-end training of LLM-based conversational recommender systems. In Stage 1, we construct a behavioral-cloning dataset with a Remap-Reflect-Adjust pipeline, which produces high-quality, catalog-grounded demonstrations from powerful blackbox LLMs to warm-start the RL training. In Stage 2, we propose Rank-GRPO, a principled extension of group relative policy optimization (GRPO) tailored to tasks with rank-style outputs. Rank-GRPO treats each rank in the recommendation list as the unit instead of token (too fine-grained) or sequence (too coarse), redefining rewards to remove non-causal credit assignment and introducing a rank-level importance ratio based on the geometric mean of rank-wise token probabilities to stabilize policy updates. Experiments on the public Reddit-v2 dataset show that ConvRec-R1 converges faster and achieves higher Recall and NDCG than GRPO-style baselines. Code and datasets are released at https://github.com/yaochenzhu/Rank-GRPO.

Autoregressive rollout generation is a major computational cost in reinforcement learning for large language models. Reusing each rollout batch for additional learner updates amortizes this cost, but later updates become increasingly off-policy as the learner departs from the behavior policy. At a token position, exact off-policy correction must account for both the current action and the probability of reaching its prefix. The cumulative importance ratio provides this correction, but its product form can produce an unwieldy dynamic range. We study Prefix-Normalized Policy Optimization (PNPO), which replaces the cumulative ratio with the geometric mean of likelihood ratios along each causal prefix, preserving causal-prefix dependence at each position while compressing the log-weight scale. In controlled long-context mathematical reasoning experiments, we induce two off-policy regimes by using one or four policy-update epochs per rollout batch. PNPO does not consistently outperform GSPO with one epoch. With four epochs, it attains the highest observed Avg@32 on each benchmark; the unweighted mean of the three independently selected benchmark peaks is 50.24, 3.00 percentage points above GSPO. Under a matched 2,400-update budget, four-epoch PNPO reaches a final macro Avg@32 of 49.66 after 150 rollout batches, comparable to the 49.56 reached after 600 batches with one epoch. These results provide preliminary evidence that PNPO can be advantageous as training moves further off-policy.

We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing and bioinformatics, and in particular, matching graphs with inherent community structure has significance related to de-anonymization of correlated social networks. Compared to the correlated Erdos-Renyi (ER) model, where various efficient algorithms have been developed, among which a few algorithms have been proven to achieve the exact matching with constant edge correlation, no low-order polynomial algorithm has been known to achieve exact matching for the correlated SBMs with constant correlation. In this work, we propose an efficient algorithm for matching graphs with community structure, based on the comparison between partition trees rooted from each vertex, by extending the idea of Mao et al. (2021) to graphs with communities. The partition tree divides the large neighborhoods of each vertex into disjoint subsets using their edge statistics to different communities. Our algorithm is the first low-order polynomial-time algorithm achieving exact matching between two correlated SBMs with high probability in dense graphs.

Recent large reasoning models (LRMs) driven by reinforcement learning algorithms (e.g., GRPO) have achieved remarkable performance on challenging reasoning tasks. However, these models suffer from overthinking, generating unnecessarily long and redundant reasoning even for simple questions, which substantially increases computational cost and response latency. While existing methods incorporate length rewards to GRPO to promote concise reasoning, they incur significant performance degradation. We identify the root cause: when rewards for correct but long rollouts are penalized, GRPO's group-relative advantage function can assign them negative advantages, actively discouraging valid reasoning. To overcome this, we propose Decoupled Reward Policy Optimization (DRPO), a novel framework that decouples the length-based learning signal of correct rollouts from incorrect ones. DRPO ensures that reward signals for correct rollouts are normalized solely within the positive group, shielding them from interference by negative samples. The DRPO's objective is grounded in integrating an optimized positive data distribution, which maximizes length-based rewards under a KL regularization, into a discriminative objective. We derive a closed-form solution for this distribution, enabling efficient computation of the objective and its gradients using only on-policy data and importance weighting. Of independent interest, this formulation is general and can incorporate other preference rewards of positive data beyond length. Experiments on mathematical reasoning tasks demonstrate DRPO's significant superiority over six efficient reasoning baselines. Notably, with a 1.5B model, our method achieves 77\% length reduction with only 1.1\% performance loss on simple questions like GSM8k dataset, while the follow-up baseline sacrifices 4.3\% for 68\% length reduction.

Large Language Models have shown strong potential as rerankers to enhance the overall performance of RAG systems. However, existing reranking paradigms are constrained by a core theoretical and practical dilemma: Pointwise methods, while simple and highly flexible, evaluate documents independently, making them prone to the Ranking Myopia Trap, overlooking the relative importance between documents. In contrast, Listwise methods can perceive the global ranking context, but suffer from inherent List Rigidity, leading to severe scalability and flexibility issues when handling large candidate sets. To address these challenges, we propose Groupwise, a novel reranking paradigm. In this approach, the query and a group of candidate documents are jointly fed into the model, which performs within-group comparisons to assign individual relevance scores to each document. This design retains the flexibility of Pointwise methods while enabling the comparative capability of Listwise methods. We further adopt GRPO for model training, equipped with a heterogeneous reward function that integrates ranking metrics with a distributional reward aimed at aligning score distributions across groups. To overcome the bottleneck caused by the scarcity of high quality labeled data, we further propose an innovative pipeline for synthesizing high quality retrieval and ranking data. The resulting data can be leveraged not only for training the reranker but also for training the retriever. Extensive experiments validate the effectiveness of our approach. On two reasoning intensive retrieval benchmarks, BRIGHT and R2MED.

Rubric-based reinforcement learning enriches language model training by evaluating model outputs against explicit criteria. Yet in GRPO-style pipelines, these structured judgments are reduced to a scalar response-level reward and converted into a response-level advantage, which is broadcast uniformly to all generated tokens. This leaves no explicit mechanism for allocating credit within a response, even when different criteria are grounded in different spans, formatting decisions, or semantic choices. We propose CoRT, a token-level credit weighting method for rubric-conditioned GRPO. Instead of training an auxiliary token scoring model, CoRT uses counterfactual replay to rescore the same sampled response under the original rubric-conditioned prompt and a matched criteria-free prompt. The resulting tokenwise log-likelihood contrasts serve as a proxy for dependence on the rubric context. CoRT maps these contrasts to bounded, response-normalized weights and uses them to redistribute the signed GRPO advantage across tokens, without introducing an auxiliary scorer or changing the response-level reward. Experiments across instruction-tuned models and reward granularities show that CoRT improves over matched response-level GRPO in the vast majority of comparisons, with an average gain of 4.4 percentage points. The method remains competitive with learned token-level credit baselines while avoiding a separate relevance-learning stage. These results suggest that policy-internal counterfactual likelihood contrasts provide an effective training signal for within-response credit allocation while retaining the simplicity and stability of GRPO.

We revisit policy-gradient optimization for Large Language Models (LLMs) from a single-stream perspective. Prevailing group-based methods like GRPO reduce variance with on-the-fly baselines but suffer from critical flaws: frequent degenerate groups erase learning signals, and synchronization barriers hinder scalability. We introduce Single-stream Policy Optimization (SPO), which eliminates these issues by design. SPO replaces per-group baselines with a persistent, KL-adaptive value tracker and normalizes advantages globally across the batch, providing a stable, low-variance learning signal for every sample. Being group-free, SPO enables higher throughput and scales effectively in long-horizon or tool-integrated settings where generation times vary. Furthermore, the persistent value tracker naturally enables an adaptive curriculum via prioritized sampling. Experiments using Qwen3-8B show that SPO converges more smoothly and attains higher accuracy than GRPO, while eliminating computation wasted on degenerate groups. Ablation studies confirm that SPO's gains stem from its principled approach to baseline estimation and advantage normalization, offering a more robust and efficient path for LLM reasoning. Across five hard math benchmarks with Qwen3 8B, SPO improves the average maj@32 by +3.4 percentage points (pp) over GRPO, driven by substantial absolute point gains on challenging datasets, including +7.3 pp on BRUMO 25, +4.4 pp on AIME 25, +3.3 pp on HMMT 25, and achieves consistent relative gain in pass@k across the evaluated k values. SPO's success challenges the prevailing trend of adding incidental complexity to RL algorithms, highlighting a path where fundamental principles, not architectural workarounds, drive the next wave of progress in LLM reasoning.

Entropy control has become an effective tool in reinforcement learning (RL) of large language models (LLMs), helping balance exploration-exploitation trade-off during alignment process. Such RL paradigm is often conducted on mixtures of heterogeneous tasks, which induce distinct entropy regimes under the same policy, making global or token-level entropy regulation insufficient to corresponding heterogeneous needs of exploration. This heterogeneity further makes GRPO-style normalized advantages induce an entropy-dependent bias, making advantage signals across prompt groups statistically non-comparable. To address this issue, we propose Group Entropy-Controlled Policy Optimization (GEPO), a lightweight extension to GRPO that uses group entropy, estimated from existing grouped samples to perform entropy-conditioned asymmetric advantage shaping. GEPO attenuates positive advantages in low-entropy groups to reduce over-exploitation, and negative advantages in high-entropy groups to preserve exploration, with adaptive thresholds derived from historical entropy statistics. Extensive experiments on two base models across thirteen benchmarks spanning mathematics, physics, science, code generation, and instruction following show that GEPO consistently outperforms GRPO and recent entropy-controlled methods, delivering balanced cross-task improvements while preserving task-specific exploration levels throughout training.

Differentially private learning algorithms inject noise into the learning process. While the most common private learning algorithm, DP-SGD, adds independent Gaussian noise in each iteration, recent work on matrix factorization mechanisms has shown empirically that introducing correlations in the noise can greatly improve their utility. We characterize the asymptotic learning utility for any choice of the correlation function, giving precise analytical bounds for linear regression and as the solution to a convex program for general convex functions. We show, using these bounds, how correlated noise provably improves upon vanilla DP-SGD as a function of problem parameters such as the effective dimension and condition number. Moreover, our analytical expression for the near-optimal correlation function circumvents the cubic complexity of the semi-definite program used to optimize the noise correlation matrix in previous work. We validate our theory with experiments on private deep learning. Our work matches or outperforms prior work while being efficient both in terms of compute and memory.

Training large multimodal models (LMMs) via reinforcement learning (RL) to natively invoke video-processing tools (e.g., cropping) has become a promising route to long-video understanding. However, existing native-RL methods dispatch tool calls sequentially (i.e., one per turn): a single wrong crop propagates errors without peer correction, multi-turn tool calls corrupt context, and inference cost scales linearly with the number of turns. We introduce ParaVT, the first multi-agent end-to-end RL-trained framework for Parallel Video Tool calling, dispatching multiple time-window crops in a single turn for cleaner context and better fault tolerance. Yet applying standard RL to ParaVT reveals an obstacle we term the Tool Prior Paradox: the pretrained tool priors that enable tool exploration also destabilize cold-started structural format and expose the skip-tool reward shortcut under temperature sampling. A cross-model contrast on a weaker-prior LMM supports this claim: format stays stable but RL elicits zero tool calls, indicating that prior strength is the shared driver of both format collapse and tool exploration. We propose PARA-GRPO (Parseability-Anchored and Ratio-gAted GRPO), which augments standard RL with two complementary mechanisms: (i) a targeted format reward applied only at the structural-token positions most prone to collapse, and (ii) a per-prompt frame-budget randomization that creates training prompts where calling the tool yields a measurable reward signal over skipping it. Across six long-video understanding benchmarks, ParaVT improves over the Qwen3-VL baseline by +7.9% on average, with PARA-GRPO lifting training-time format compliance from 0.13 to 0.64. As tool capabilities become increasingly internalized in modern LMMs, RL must cooperate with the resulting priors, and ParaVT offers a general recipe for agentic RL. Code, data, and model weights are publicly available.

Training large language models (LLMs) with reinforcement learning (RL) methods such as PPO and GRPO commonly relies on ratio clipping to stabilise updates. While effective at preventing instability, clipping discards information and introduces gradient discontinuities. We propose Probability Smoothing Policy Optimisation (PSPO), which smooths the current policy's probabilities toward the old (behaviour) policy before computing the importance ratio, analogous to label smoothing. Unlike clipping, PSPO preserves gradient signal, while interpolation toward the old policy creates a soft trust region that discourages large, destabilising updates, with formal guarantees. We instantiate PSPO within GRPO (GR-PSPO) and fine-tune Qwen2.5-0.5B and Qwen2.5-1.5B on GSM8K, evaluating on GSM8K test and the cross-dataset generalisation on SVAMP, ASDiv, and MATH-500. Relative to unclipped GRPO (single iteration; no data reuse, ratio always = 1), GR-PSPO achieves similar performance but improves the reasoning leading to clearer and more concise responses which are more logical. Compared to clipped GRPO, GR-PSPO substantially improves performance both the 0.5B and 1.5B models, with a boost of over 20% on GSM8K (39.7% vs. 17.6% for 0.5B, 59.4% vs. 37.8% for 1.5B).

Reinforcement learning algorithms for Large Language Models (LLMs) are largely distinguished by their variance reduction strategy. Group-relative methods like GRPO reduce gradient variance by sampling multiple rollouts per prompt, but provide only sequence-level credit. Training is also blocked by straggler rollouts, reducing throughput and increasing off-policyness. Learned value functions theoretically address both problems, providing token-level advantages without requiring large groups. However, additional infrastructure engineering challenges combined with the practical success of critic-free methods have made it difficult to justify their inclusion in RL pipelines. We propose two complementary strategies to improve the performance of value function RL: 1) Privileged Value Functions (PVF) which provide an elegant mechanism to inject additional task-relevant token-level signal without biasing the policy objective; 2) TETHER, a baseline that adaptively interpolates between group-relative and value baselines depending on the value function accuracy. Across several reasoning tasks, both strategies consistently improve over the standard value function baseline, and are competitive with or outperform mean-baseline GRPO.

Group Relative Policy Optimization (GRPO) enhances LLM reasoning but often induces overconfidence, where incorrect responses yield lower perplexity than correct ones, degrading relative calibration as described by the Area Under the Curve (AUC). Existing approaches either yield limited improvements in calibration or sacrifice gains in reasoning accuracy. We first prove that this degradation in GRPO-style algorithms stems from their uncertainty-agnostic advantage estimation, which inevitably misaligns optimization gradients with calibration. This leads to improved accuracy at the expense of degraded calibration. We then propose Calibration-Aware Policy Optimization (CAPO). It adopts a logistic AUC surrogate loss that is theoretically consistent and admits regret bound, enabling uncertainty-aware advantage estimation. By further incorporating a noise masking mechanism, CAPO achieves stable learning dynamics that jointly optimize calibration and accuracy. Experiments on multiple mathematical reasoning benchmarks show that CAPO-1.5B significantly improves calibration by up to 15% while achieving accuracy comparable to or better than GRPO, and further boosts accuracy on downstream inference-time scaling tasks by up to 5%. Moreover, when allowed to abstain under low-confidence conditions, CAPO achieves a Pareto-optimal precision-coverage trade-off, highlighting its practical value for hallucination mitigation.

RL-based post-training with GRPO is widely used to improve large language models on individual reasoning tasks. However, real-world deployment requires reliable performance across diverse tasks. A straightforward multi-task adaptation of GRPO often leads to imbalanced outcomes, with some tasks dominating optimization while others stagnate. Moreover, tasks can vary widely in how frequently prompts yield zero advantages (and thus zero gradients), which further distorts their effective contribution to the optimization signal. To address these issues, we propose a novel Multi-Task GRPO (MT-GRPO) algorithm that (i) dynamically adapts task weights to explicitly optimize worst-task performance and promote balanced progress across tasks, and (ii) introduces a ratio-preserving sampler to ensure task-wise policy gradients reflect the adapted weights. Experiments on both 3-task and 9-task settings show that MT-GRPO consistently outperforms baselines in worst-task accuracy. In particular, MT-GRPO achieves 16-28% and 6% absolute improvement on worst-task performance over standard GRPO and DAPO, respectively, while maintaining competitive average accuracy. Moreover, MT-GRPO requires 50% fewer training steps to reach 50% worst-task accuracy in the 3-task setting, demonstrating substantially improved efficiency in achieving reliable performance across tasks.

Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical difficulties of estimating time-varying and high-dimensional covariance matrices often limits existing methods to handling at most a few hundred dimensions or requires making strong assumptions on the dependence between series. We propose to combine an RNN-based time series model with a Gaussian copula process output model with a low-rank covariance structure to reduce the computational complexity and handle non-Gaussian marginal distributions. This permits to drastically reduce the number of parameters and consequently allows the modeling of time-varying correlations of thousands of time series. We show on several real-world datasets that our method provides significant accuracy improvements over state-of-the-art baselines and perform an ablation study analyzing the contributions of the different components of our model.

The Platonic Representation Hypothesis suggests that independently trained neural networks converge to increasingly similar latent spaces. However, current strategies for mapping these representations are inherently pairwise, scaling quadratically with the number of models and failing to yield a consistent global reference. In this paper, we study the alignment of M ge 3 models. We first adapt Generalized Procrustes Analysis (GPA) to construct a shared orthogonal universe that preserves the internal geometry essential for tasks like model stitching. We then show that strict isometric alignment is suboptimal for retrieval, where agreement-maximizing methods like Canonical Correlation Analysis (CCA) typically prevail. To bridge this gap, we finally propose Geometry-Corrected Procrustes Alignment (GCPA), which establishes a robust GPA-based universe followed by a post-hoc correction for directional mismatch. Extensive experiments demonstrate that GCPA consistently improves any-to-any retrieval while retaining a practical shared reference space.

Large Language Models have achieved remarkable success in natural language processing tasks, with Reinforcement Learning playing a key role in adapting them to specific applications. However, obtaining ground truth answers for training LLMs in mathematical problem-solving is often challenging, costly, and sometimes unfeasible. This research delves into the utilization of format and length as surrogate signals to train LLMs for mathematical problem-solving, bypassing the need for traditional ground truth answers.Our study shows that a reward function centered on format correctness alone can yield performance improvements comparable to the standard GRPO algorithm in early phases. Recognizing the limitations of format-only rewards in the later phases, we incorporate length-based rewards. The resulting GRPO approach, leveraging format-length surrogate signals, not only matches but surpasses the performance of the standard GRPO algorithm relying on ground truth answers in certain scenarios, achieving 40.0\% accuracy on AIME2024 with a 7B base model. Through systematic exploration and experimentation, this research not only offers a practical solution for training LLMs to solve mathematical problems and reducing the dependence on extensive ground truth data collection, but also reveals the essence of why our label-free approach succeeds: base model is like an excellent student who has already mastered mathematical and logical reasoning skills, but performs poorly on the test paper, it simply needs to develop good answering habits to achieve outstanding results in exams , in other words, to unlock the capabilities it already possesses.

Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled independently, an assumption that is frequently violated in practice, which may lead to erroneous density estimation and data generation. We propose a likelihood objective of normalizing flows incorporating dependencies between the data points, for which we derive a flexible and efficient learning algorithm suitable for different dependency structures. We show that respecting dependencies between observations can improve empirical results on both synthetic and real-world data, and leads to higher statistical power in a downstream application to genome-wide association studies.

We propose Process-Aware Policy Optimization (PAPO), a method that integrates process-level evaluation into Group Relative Policy Optimization (GRPO) through decoupled advantage normalization, to address two limitations of existing reward designs. Outcome reward models (ORM) evaluate only final-answer correctness, treating all correct responses identically regardless of reasoning quality, and gradually lose the advantage signal as groups become uniformly correct. Process reward models (PRM) offer richer supervision, but directly using PRM scores causes reward hacking, where models exploit verbosity to inflate scores while accuracy collapses. PAPO resolves both by composing the advantage from an outcome component Aout, derived from ORM and normalized over all responses, and a process component Aproc, derived from a rubric-based PRM and normalized exclusively among correct responses. This decoupled design ensures that Aout anchors training on correctness while Aproc differentiates reasoning quality without distorting the outcome signal. Experiments across multiple model scales and six benchmarks demonstrate that PAPO consistently outperforms ORM, reaching 51.3% vs.\ 46.3% on OlympiadBench while continuing to improve as ORM plateaus and declines.

Subject-driven image generation models face a fundamental trade-off between identity preservation (fidelity) and prompt adherence (editability). While online reinforcement learning (RL), specifically GPRO, offers a promising solution, we find that a naive application of GRPO leads to competitive degradation, as the simple linear aggregation of rewards with static weights causes conflicting gradient signals and a misalignment with the temporal dynamics of the diffusion process. To overcome these limitations, we propose Customized-GRPO, a novel framework featuring two key innovations: (i) Synergy-Aware Reward Shaping (SARS), a non-linear mechanism that explicitly penalizes conflicted reward signals and amplifies synergistic ones, providing a sharper and more decisive gradient. (ii) Time-Aware Dynamic Weighting (TDW), which aligns the optimization pressure with the model's temporal dynamics by prioritizing prompt-following in the early, identity preservation in the later. Extensive experiments demonstrate that our method significantly outperforms naive GRPO baselines, successfully mitigating competitive degradation. Our model achieves a superior balance, generating images that both preserve key identity features and accurately adhere to complex textual prompts.

Large language model (LLM) agents increasingly rely on external tools such as search engines to solve complex, multi-step problems, and reinforcement learning (RL) has become a key paradigm for training them. However, the trajectories of search agents are structurally heterogeneous, where variations in the number, placement, and outcomes of search calls lead to fundamentally different answer directions and reward distributions. Standard policy gradient methods, which use a single global baseline, suffer from what we identify and formalize as cross-stratum bias-an "apples-to-oranges" comparison of heterogeneous trajectories. This cross-stratum bias distorts credit assignment and hinders exploration of complex, multi-step search strategies. To address this, we propose Stratified GRPO, whose central component, Stratified Advantage Normalization (SAN), partitions trajectories into homogeneous strata based on their structural properties and computes advantages locally within each stratum. This ensures that trajectories are evaluated only against their true peers. Our analysis proves that SAN eliminates cross-stratum bias, yields conditionally unbiased unit-variance estimates inside each stratum, and retains the global unbiasedness and unit-variance properties enjoyed by standard normalization, resulting in a more pure and scale-stable learning signal. To improve practical stability under finite-sample regimes, we further linearly blend SAN with the global estimator. Extensive experiments on diverse single-hop and multi-hop question-answering benchmarks demonstrate that Stratified GRPO consistently and substantially outperforms GRPO by up to 11.3 points, achieving higher training rewards, greater training stability, and more effective search policies. These results establish stratification as a principled remedy for structural heterogeneity in RL for LLM search agents.

Joint-Embedding Predictive Architectures (JEPA) learn view-invariant representations and admit projection-based distribution matching for collapse prevention. Existing approaches regularize representations towards isotropic Gaussian distributions, but inherently favor dense representations and fail to capture the key property of sparsity observed in efficient representations. We introduce Rectified Distribution Matching Regularization (RDMReg), a sliced two-sample distribution-matching loss that aligns representations to a Rectified Generalized Gaussian (RGG) distribution. RGG enables explicit control over expected ell_0 norm through rectification, while preserving maximum-entropy up to rescaling under expected ell_p norm constraints. Equipping JEPAs with RDMReg yields Rectified LpJEPA, which strictly generalizes prior Gaussian-based JEPAs. Empirically, Rectified LpJEPA learns sparse, non-negative representations with favorable sparsity-performance trade-offs and competitive downstream performance on image classification benchmarks, demonstrating that RDMReg effectively enforces sparsity while preserving task-relevant information.

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.

Self-evolution offers a scalable path to stronger reasoning: a pretrained language model improves itself with only minimal external supervision. Yet existing methods either depend on extensively curated or teacher-generated training data, or, when the generator runs unsupervised, reward it by a difficulty heuristic that need not improve the solver. We introduce INFUSER, an iterative co-training framework with two co-evolving roles: a Generator that drafts questions and reference golden answers from a pool of unstructured, automatically collected documents, and a Solver that improves by training on them. The solver is trained with standard correctness rewards against the generator-provided answers, while the generator is rewarded by an optimizer-aware influence score that measures whether each proposed question would actually improve the solver on the target distribution. Because this continuous, noisy influence score is poorly served by standard GRPO, we propose DuGRPO, a dual-normalized variant of GRPO, for generator training. Together, these turn the document pool into an adaptive curriculum that favors questions useful to the current solver, not just hard ones. On Qwen3-8B-Base, INFUSER outperforms strong self-evolution baselines with over 20% relative improvement on Olympiad and SuperGPQA benchmarks, and an 8B INFUSER co-evolving generator outperforms a frozen 32B thinking generator on math and coding. Ablations confirm each design choice is necessary, and two extensions, applying INFUSER to an instruction-finetuned anchor and augmenting it with rule-verifiable RLVR data, further demonstrate the flexibility and generalizability of the framework. Code is available at https://github.com/FFishy-git/INFUSER.

Recent advancements highlight the importance of GRPO-based reinforcement learning methods and benchmarking in enhancing text-to-image (T2I) generation. However, current methods using pointwise reward models (RM) for scoring generated images are susceptible to reward hacking. We reveal that this happens when minimal score differences between images are amplified after normalization, creating illusory advantages that drive the model to over-optimize for trivial gains, ultimately destabilizing the image generation process. To address this, we propose Pref-GRPO, a pairwise preference reward-based GRPO method that shifts the optimization objective from score maximization to preference fitting, ensuring more stable training. In Pref-GRPO, images are pairwise compared within each group using preference RM, and the win rate is used as the reward signal. Extensive experiments demonstrate that PREF-GRPO differentiates subtle image quality differences, providing more stable advantages and mitigating reward hacking. Additionally, existing T2I benchmarks are limited by coarse evaluation criteria, hindering comprehensive model assessment. To solve this, we introduce UniGenBench, a unified T2I benchmark comprising 600 prompts across 5 main themes and 20 subthemes. It evaluates semantic consistency through 10 primary and 27 sub-criteria, leveraging MLLM for benchmark construction and evaluation. Our benchmarks uncover the strengths and weaknesses of both open and closed-source T2I models and validate the effectiveness of Pref-GRPO.

Recent GRPO-based approaches built on flow matching models have shown remarkable improvements in human preference alignment for text-to-image generation. Nevertheless, they still suffer from the sparse reward problem: the terminal reward of the entire denoising trajectory is applied to all intermediate steps, resulting in a mismatch between the global feedback signals and the exact fine-grained contributions at intermediate denoising steps. To address this issue, we introduce DenseGRPO, a novel framework that aligns human preference with dense rewards, which evaluates the fine-grained contribution of each denoising step. Specifically, our approach includes two key components: (1) we propose to predict the step-wise reward gain as dense reward of each denoising step, which applies a reward model on the intermediate clean images via an ODE-based approach. This manner ensures an alignment between feedback signals and the contributions of individual steps, facilitating effective training; and (2) based on the estimated dense rewards, a mismatch drawback between the uniform exploration setting and the time-varying noise intensity in existing GRPO-based methods is revealed, leading to an inappropriate exploration space. Thus, we propose a reward-aware scheme to calibrate the exploration space by adaptively adjusting a timestep-specific stochasticity injection in the SDE sampler, ensuring a suitable exploration space at all timesteps. Extensive experiments on multiple standard benchmarks demonstrate the effectiveness of the proposed DenseGRPO and highlight the critical role of the valid dense rewards in flow matching model alignment.

Aligning denoising generative models with human preferences or verifiable rewards remains a key challenge. While policy-gradient online reinforcement learning (RL) offers a principled post-training framework, its direct application is hindered by the intractable likelihoods of these models. Prior work therefore either optimizes an induced Markov decision process (MDP) over sampling trajectories, which is stable but inefficient, or uses likelihood surrogates based on the diffusion evidence lower bound (ELBO), which have so far underperformed on visual generation. Our key insight is that the ELBO-based approach can, in fact, be made both stable and efficient. By reducing surrogate variance and controlling gradient steps, we show that this approach can beat MDP-based methods. To this end, we introduce Variational GRPO (V-GRPO), a method that integrates ELBO-based surrogates with the Group Relative Policy Optimization (GRPO) algorithm, alongside a set of simple yet essential techniques. Our method is easy to implement, aligns with pretraining objectives, and avoids the limitations of MDP-based methods. V-GRPO achieves state-of-the-art performance in text-to-image synthesis, while delivering a 2times speedup over MixGRPO and a 3times speedup over DiffusionNFT.

Post-training alignment algorithms are predominantly evaluated as black boxes, obscuring how they reshape language models' internal computations. We present a systematic mechanistic analysis of six preference-optimization methods: PPO, DPO, SimPO, ORPO, GRPO, and KTO across three open-weight model families. By integrating layer-wise linear probing, Sparse Autoencoders, and crosscoders, we localize preference representations and quantify alignment-induced geometric transformations in latent space. We find that preference signals consistently concentrate in early--mid or mid--late layers, but different objectives induce qualitatively distinct representational shifts. KTO and GRPO enhance linear separability through constructive feature sharing and sparse, high-salience recruitment. In contrast, DPO and ORPO degrade separability via non-constructive geometric rotation and feature attenuation, while PPO and SimPO largely preserve baseline geometry. These transformations exhibit architecture-dependent variability, demonstrating that behavioral alignment does not imply uniform internal restructuring. Our findings establish alignment as a heterogeneous intervention, motivate standardized feature-level auditing for safety and interpretability, and highlight the need for mechanism-aware optimization objectives.

The success of Large Language Models in mathematical reasoning relies heavily on the generation of diverse and valid solution paths during the rollout phase. However, current rollout techniques face a fundamental trade-off: token-level sampling often yields redundant trajectories that differ only in rephrasing, while embedding-level methods utilizing random noise frequently disrupt semantic consistency. To resolve this, we introduce N-GRPO, a novel exploration strategy integrated into the Group Relative Policy Optimization (GRPO) framework. Rather than relying on token-level sampling or native embedding-level noise, our approach leverages Semantic Neighbor Mixing. This mechanism dynamically constructs input representations by mixing the embeddings of an anchor token and its nearest semantic neighbors, thereby injecting diversity while strictly adhering to the local semantic manifold. Experimental evaluations on the DeepSeek-R1-Distill-Qwen models across different sizes show that N-GRPO not only achieves consistent improvements over strong baselines on math reasoning benchmarks but also exhibits robust generalization capabilities on out-of-distribution tasks.

Reinforcement learning with verifiable rewards (RLVR) has become a standard recipe for improving large language models (LLMs) on reasoning tasks, with Group Relative Policy Optimization (GRPO) widely used in practice. Yet GRPO wastes substantial compute on negative groups: groups in which no sampled response is correct yield zero advantage and thus no gradient. We ask whether negative groups can be leveraged without extra supervision. Starting from a maximum-likelihood (MLE) objective in reward modeling, we show that the MLE gradient is equivalent to a policy gradient for a modified value function. This value function adds a confidence-weighted penalty on incorrect responses, imposing larger penalties on more confident mistakes. We refer to this as Likelihood Estimation with Negative Samples (LENS). LENS modifies GRPO to assign non-zero, confidence-dependent rewards to incorrect generations, making negative groups informative and converting previously wasted samples into useful gradient updates. On the MATH benchmark with Llama-3.1-8B and Qwen-2.5-3B, the proposed variant consistently outperforms GRPO baseline, with significant gains on harder items. These results demonstrate a principled and practical way to "rescue" negative groups, improving efficiency and performance in RLVR.

Recent reinforcement learning approaches, such as outcome-supervised GRPO, have advanced Chain-of-Thought reasoning in large language models (LLMs), yet their adaptation to multimodal LLMs (MLLMs) is unexplored. To address the lack of rigorous evaluation for MLLM post-training methods, we introduce SEED-Bench-R1, a benchmark with complex real-world videos requiring balanced perception and reasoning. It offers a large training set and evaluates generalization across three escalating challenges: in-distribution, cross-environment, and cross-environment-task scenarios. Using SEED-Bench-R1, we find that standard GRPO, while improving answer accuracy, often reduces logical coherence between reasoning steps and answers, with only a 57.9% consistency rate. This stems from reward signals focusing solely on final answers, encouraging shortcuts, and strict KL penalties limiting exploration.To address this, we propose GRPO-CARE, a consistency-aware RL framework optimizing both answer correctness and reasoning coherence without explicit supervision. GRPO-CARE introduces a two-tiered reward: (1) a base reward for answer correctness, and (2) an adaptive consistency bonus, computed by comparing the model's reasoning-to-answer likelihood (via a slowly-evolving reference model) against group peers.This dual mechanism amplifies rewards for reasoning paths that are both correct and logically consistent. Replacing KL penalties with this adaptive bonus, GRPO-CARE outperforms standard GRPO on SEED-Bench-R1, achieving a 6.7% performance gain on the hardest evaluation level and a 24.5% improvement in consistency. It also shows strong transferability, improving model performance across diverse video understanding benchmarks. Our work contributes a systematically designed benchmark and a generalizable post-training framework, advancing the development of more interpretable and robust MLLMs.

Recent advancements, such as Group Relative Policy Optimization (GRPO), have enhanced the reasoning capabilities of large language models by optimizing the arithmetic mean of token-level rewards. However, GRPO suffers from unstable policy updates when processing tokens with outlier importance-weighted rewards, which manifests as extreme importance sampling ratios during training, i.e., the ratio between the sampling probabilities assigned to a token by the current and old policies. In this work, we propose Geometric-Mean Policy Optimization (GMPO), a stabilized variant of GRPO. Instead of optimizing the arithmetic mean, GMPO maximizes the geometric mean of token-level rewards, which is inherently less sensitive to outliers and maintains a more stable range of importance sampling ratio. In addition, we provide comprehensive theoretical and experimental analysis to justify the design and stability benefits of GMPO. Beyond improved stability, GMPO-7B outperforms GRPO by an average of 4.1% on multiple mathematical benchmarks and 1.4% on multimodal reasoning benchmark, including AIME24, AMC, MATH500, OlympiadBench, Minerva, and Geometry3K. Code is available at https://github.com/callsys/GMPO.

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.

Although GRPO substantially enhances flow matching models in human preference alignment of image generation, methods such as FlowGRPO still exhibit inefficiency due to the necessity of sampling and optimizing over all denoising steps specified by the Markov Decision Process (MDP). In this paper, we propose MixGRPO, a novel framework that leverages the flexibility of mixed sampling strategies through the integration of stochastic differential equations (SDE) and ordinary differential equations (ODE). This streamlines the optimization process within the MDP to improve efficiency and boost performance. Specifically, MixGRPO introduces a sliding window mechanism, using SDE sampling and GRPO-guided optimization only within the window, while applying ODE sampling outside. This design confines sampling randomness to the time-steps within the window, thereby reducing the optimization overhead, and allowing for more focused gradient updates to accelerate convergence. Additionally, as time-steps beyond the sliding window are not involved in optimization, higher-order solvers are supported for sampling. So we present a faster variant, termed MixGRPO-Flash, which further improves training efficiency while achieving comparable performance. MixGRPO exhibits substantial gains across multiple dimensions of human preference alignment, outperforming DanceGRPO in both effectiveness and efficiency, with nearly 50% lower training time. Notably, MixGRPO-Flash further reduces training time by 71%. Codes and models are available at https://github.com/Tencent-Hunyuan/MixGRPO{MixGRPO}.

Complex reinforcement learning environments frequently employ multi-task and mixed-reward formulations. In these settings, heterogeneous reward distributions and correlated reward dimensions often destabilize the construction of scalar advantages. To address these challenges, we propose Reward-Decorrelated Policy Optimization (RDPO), a reward-processing method designed to explicitly target both failure modes. RDPO first utilizes Magnitude-Aware Quantile normalization to stabilize prompt-level advantage allocation across binary, fractional, and continuous rewards. It then applies Mahalanobis whitening within each active reward subspace to mitigate correlation redundancy prior to aggregation. When applied during the post-training of LongCat-Flash, RDPO enhances instruction following, writing quality, and robustness to hard prompts while remaining broadly competitive on reasoning and coding evaluations.

GRPO-based LLM post-training commonly samples multiple trajectories from the same prompt and then trains on the resulting group. In long-context GRPO workloads, this shared prompt-side prefix can contain retrieved passages, visual tokens, tool schemas, system instructions, or task context, while the full rollout group is still too large to pack into one training microbatch. Standard dense trainers therefore recompute the same prefix forward and backward for every trajectory. We present a schedule-level reuse mechanism that decouples prefix and suffix computation. The schedule runs prefix forward once, executes suffixes as ordinary microbatches while reading prefix K/V and accumulating prefix-side gK/gV , and then runs prefix backward once on the accumulated gradient cache. This reordered schedule is equivalent to baseline training over real arithmetic and aligns numerically within finite-precision tolerance. Because only K/V and gK/gV are hot during suffix computation, the approach offloads dormant prefix activations, integrates with TP/EP/CP/PP and DP-style placement at the execution level, and preserves aux-loss-based MoE router semantics through logical prefix-token accounting. On dense Llama3-8B, Qwen3-8B, and MoE Qwen3-MoE-30B-A3B configurations, the schedule matches optimizer updates across TP/CP/PP/EP combinations, aligns on a 100-step real GRPO actor-update trace replay, reaches up to 4.395x speedup (2.930x under a conservative compile-on comparison) as prefix ratio and GRPO group size grow, and reduces Phase-B peak HBM by up to 59.1%, extending the Llama3-8B capacity frontier from 17,920 to 29,696 total tokens.

Reinforcement learning, including reinforcement learning with verifiable rewards (RLVR), has emerged as a powerful approach for LLM post-training. Central to these approaches is the design of the importance sampling (IS) ratio used in off-policy policy-gradient estimation. Existing methods face a fundamental bias-variance dilemma: token-level IS ratios, as adopted by PPO (Schulman et al., 2017) and GRPO (Shao et al., 2024), introduce bias by ignoring prefix state distribution mismatch; full sequence ratios provide exact trajectory-level correction but suffer from high variance due to the multiplicative accumulation of per-token ratios, while GSPO (Zheng et al., 2025) improves numerical stability via length normalization at the cost of deviating from the exact full-sequence IS correction. In this work, we identify the cumulative token IS ratio, the product of per-token ratios up to position t, as a theoretically principled solution to this dilemma. We prove that, under the token-level policy-gradient formulation, this ratio provides an unbiased prefix correction for each token-level gradient term and has strictly lower variance than the full sequence ratio. Building on this insight, we propose CTPO (Cumulative Token Policy Optimization), which combines the cumulative token IS ratio with position-adaptive clipping that scales log-space clip bounds according to the natural t growth of the cumulative log-ratio. This yields more consistent regularization across token positions. We implement and evaluate CTPO in the tool-integrated reasoning setting on several challenging mathematical reasoning benchmarks, achieving the best average performance across both model scales compared with strong GRPO and GSPO baselines. Code will be available at https://github.com/horizon-llm/CTPO.

We consider estimating the conditional distribution of a multivariate outcome given covariates when its coordinates may be continuous, binary, categorical, ordinal or rankings, and are conditionally dependent on one another. Different statistical methods have been developed for each outcome type, and most of them target a summary of the conditional distribution, such as the mean of each coordinate, rather than the joint distribution of the outcome vector. We develop generalized engression models, a unified nonparametric distributional regression framework for outcomes of any type. The proposed method builds upon engression, a scoring-rule-based deep generative model, and introduces a data-type-specific link function and a stochastic perturbation that smooths the loss, enabling gradient-based training even with discontinuous links. We establish universal representation results for continuous, discrete and mixed outcomes. In simulations and in two applications, 242 species in a community ecology benchmark and a 17-dimensional mixed-type health outcome, the method matches type-specific models on marginal scores, improves on them on the joint distribution, and matches or exceeds purpose-built state-of-the-art joint species distribution models. Software is available in Python.

Recent progress, such as DeepSeek-R1, has shown that the GRPO algorithm, a Reinforcement Learning (RL) approach, can effectively train Chain-of-Thought (CoT) reasoning in Large Language Models (LLMs) and Vision-Language Models (VLMs). In this paper, we analyze three challenges of GRPO: gradient coupling between thoughts and answers, sparse reward signals caused by limited parallel sampling, and unstable advantage estimation. To mitigate these challenges, we propose GRPO-MA, a simple yet theoretically grounded method that leverages multi-answer generation from each thought process, enabling more robust and efficient optimization. Theoretically, we show that the variance of thought advantage decreases as the number of answers per thought increases. Empirically, our gradient analysis confirms this effect, showing that GRPO-MA reduces gradient spikes compared to GRPO. Experiments on math, code, and diverse multimodal tasks demonstrate that GRPO-MA substantially improves performance and training efficiency. Our ablation studies further reveal that increasing the number of answers per thought consistently enhances model performance.

Recent progress in aligning image and video generative models with Group Relative Policy Optimization (GRPO) has improved human preference alignment, but existing variants remain inefficient due to sequential rollouts and large numbers of sampling steps, unreliable credit assignment: sparse terminal rewards are uniformly propagated across timesteps, failing to capture the varying criticality of decisions during denoising. In this paper, we present BranchGRPO, a method that restructures the rollout process into a branching tree, where shared prefixes amortize computation and pruning removes low-value paths and redundant depths. BranchGRPO introduces three contributions: (1) a branching scheme that amortizes rollout cost through shared prefixes while preserving exploration diversity; (2) a reward fusion and depth-wise advantage estimator that transforms sparse terminal rewards into dense step-level signals; and (3) pruning strategies that cut gradient computation but leave forward rollouts and exploration unaffected. On HPDv2.1 image alignment, BranchGRPO improves alignment scores by up to 16\% over DanceGRPO, while reducing per-iteration training time by nearly 55\%. A hybrid variant, BranchGRPO-Mix, further accelerates training to 4.7x faster than DanceGRPO without degrading alignment. On WanX video generation, it further achieves higher Video-Align scores with sharper and temporally consistent frames compared to DanceGRPO. Codes are available at https://fredreic1849.github.io/BranchGRPO-Webpage/{BranchGRPO}.

Leveraging the models' outputs, specifically the logits, is a common approach to estimating the test accuracy of a pre-trained neural network on out-of-distribution (OOD) samples without requiring access to the corresponding ground truth labels. Despite their ease of implementation and computational efficiency, current logit-based methods are vulnerable to overconfidence issues, leading to prediction bias, especially under the natural shift. In this work, we first study the relationship between logits and generalization performance from the view of low-density separation assumption. Our findings motivate our proposed method MaNo which (1) applies a data-dependent normalization on the logits to reduce prediction bias, and (2) takes the L_p norm of the matrix of normalized logits as the estimation score. Our theoretical analysis highlights the connection between the provided score and the model's uncertainty. We conduct an extensive empirical study on common unsupervised accuracy estimation benchmarks and demonstrate that MaNo achieves state-of-the-art performance across various architectures in the presence of synthetic, natural, or subpopulation shifts.

Reinforcement learning improves LLM reasoning, yet sparse delayed reward over long sequences makes token-level credit assignment the key bottleneck. We study the verifiable-reward setting, where the final answer is checkable and multiple responses can be drawn per prompt. Reasoning tasks in math and medical QA align with this setup, where only a few decision tokens significantly impact the outcome. PPO offers token-level advantages with a learned value model, but it is complex to train both the actor and critic models simultaneously, and it is not easily generalizable, as the token-level values from the critic model can make training prone to overfitting. GRPO is critic-free and supports verifiable rewards, but spreads a single sequence-level return across tokens and ignores branching. We introduce Prefix-to-Tree (P2T), a simple procedure that converts a group of responses into a prefix tree and computes nonparametric prefix values \(V(s)\) by aggregating descendant outcomes. Built on P2T, we propose TEMPO (\textbf{Tree-Estimated Mean Prefix Value for Policy Optimization}), a critic-free algorithm that augments the group-relative outcome signal of GRPO with branch-gated temporal-difference corrections derived from the tree. At non-branch tokens, the temporal-difference (TD) term is zero, so TEMPO reduces to GRPO; at branching tokens, it supplies precise token-level credit without a learned value network or extra judges/teachers. On Qwen3-1.7B/4B, TEMPO outperforms PPO and GRPO on in-distribution (MATH, MedQA) and out-of-distribution (GSM-HARD, AMC23, MedMCQA, MMLU-Medical) benchmarks, and reaches higher validation accuracy with roughly the same wall-clock time.

Large language models trained with reinforcement learning with verifiable rewards tend to trade accuracy for length--inflating response lengths to achieve gains in accuracy. While longer answers may be warranted for harder problems, many tokens are merely "filler": repetitive, verbose text that makes no real progress. We introduce GFPO (Group Filtered Policy Optimization), which curbs this length explosion by sampling larger groups per problem during training and filtering responses to train on based on two key metrics: (1) response length and (2) token efficiency: reward per token ratio. By sampling more at training time, we teach models to think less at inference time. On the Phi-4-reasoning model, GFPO cuts GRPO's length inflation by 46-71% across challenging STEM and coding benchmarks (AIME 24/25, GPQA, Omni-MATH, LiveCodeBench) while maintaining accuracy. Optimizing for reward per token further increases reductions in length inflation to 71-85%. We also propose Adaptive Difficulty GFPO, which dynamically allocates more training resources to harder problems based on real-time difficulty estimates, improving the balance between computational efficiency and accuracy especially on difficult questions. GFPO demonstrates that increased training-time compute directly translates to reduced test-time compute--a simple yet effective trade-off for efficient reasoning.

Reinforcement Learning with Verifiable Rewards (RLVR) has become the standard paradigm for LLM mathematical reasoning, with Group Relative Policy Optimization (GRPO) serving as the dominant algorithm. We identify two overlooked inefficiencies inherent in GRPO. First, a fixed KL coefficient overly restricts policy exploration at moments when the model needs to diverge significantly from the reference policy. Second, uniform question sampling overlooks that moderately difficult problems produce the most informative gradient signals. We propose FG-ExPO, short for Frontier-Guided Exploration-Prioritized Policy Optimization, which integrates two lightweight components. Accuracy-Conditioned KL Scaling (AKL) adjusts the KL penalty strength through a smooth nonlinear function of batch average accuracy, loosening the constraint when the model performs poorly and strengthening it when the model achieves satisfactory results. Gaussian Curriculum Sampling (GCS) assigns sampling weights to questions following a Gaussian distribution centered at a moderate accuracy level around 0.5, focusing model training on its learning frontier. We conduct evaluations on DeepSeek-R1-Distill-Qwen-1.5B and Qwen3-8B-Base across six mainstream mathematical reasoning benchmarks. Experimental results demonstrate that FG-ExPO consistently outperforms vanilla GRPO. It delivers an absolute improvement of 13.34 on the AIME 2025 pass@32 metric, rising from 63.33 percent to 76.67 percent, and obtains an average pass@32 gain of 2.66 on the 8B model. The substantially larger performance gains observed on pass@32 compared to pass@1 verify that FG-ExPO enlarges the model's effective exploration space under a fixed inference budget.

RL (reinforcement learning) methods (e.g., GRPO) for MLLM (Multimodal LLM) perception ability has attracted wide research interest owing to its remarkable generalization ability. Nevertheless, existing reinforcement learning methods still face the problem of low data quality, where data samples cannot elicit diverse responses from MLLMs, thus restricting the exploration scope for MLLM reinforcement learning. Some methods attempt to mitigate this problem by imposing constraints on entropy, but none address it at its root. Therefore, to tackle this problem, this work proposes Syn-GRPO (Synthesis-GRPO), which employs an online data generator to synthesize high-quality training data with diverse responses in GRPO training. Specifically, Syn-GRPO consists of two components: (1) data server; (2) GRPO workflow. The data server synthesizes new samples from existing ones using an image generation model, featuring a decoupled and asynchronous scheme to achieve high generation efficiency. The GRPO workflow provides the data server with the new image descriptions, and it leverages a diversity reward to supervise the MLLM to predict image descriptions for synthesizing samples with diverse responses. Experiment results across three visual perception tasks demonstrate that Syn-GRPO improves the data quality by a large margin, achieving significant superior performance to existing MLLM perception methods, and Syn-GRPO presents promising potential for scaling long-term self-evolving RL. Our code is available at https://github.com/hqhQAQ/Syn-GRPO.

Retrieval-augmented agents can query external evidence, yet their reliability in multi-step reasoning remains limited: noisy retrieval may derail multi-hop question answering, while outcome-only reinforcement learning provides credit signals that are too coarse to optimize intermediate steps. We propose EvalAct (Evaluate-as-Action), which converts implicit retrieval quality assessment into an explicit action and enforces a coupled Search-to-Evaluate protocol so that each retrieval is immediately followed by a structured evaluation score, yielding process signals aligned with the interaction trajectory. To leverage these signals, we introduce Process-Calibrated Advantage Rescaling (PCAR), a GRPO-based optimization method that rescales advantages at the segment level according to evaluation scores, emphasizing reliable segments while updating uncertain ones conservatively. Experiments on seven open-domain QA benchmarks show that EvalAct achieves the best average accuracy, with the largest gains on multi-hop tasks, and ablations verify that the explicit evaluation loop drives the primary improvements while PCAR provides consistent additional benefits.

Optimizing communication topology is fundamental to the efficiency and effectiveness of Large Language Model (LLM)-based Multi-Agent Systems (MAS). While recent approaches utilize reinforcement learning to dynamically construct task-specific graphs, they typically rely on single-sample policy gradients with absolute rewards (e.g., binary correctness). This paradigm suffers from severe gradient variance and the credit assignment problem: simple queries yield non-informative positive rewards for suboptimal structures, while difficult queries often result in failures that provide no learning signal. To address these challenges, we propose Graph-GRPO, a novel topology optimization framework that integrates Group Relative Policy Optimization. Instead of evaluating a single topology in isolation, Graph-GRPO samples a group of diverse communication graphs for each query and computes the advantage of specific edges based on their relative performance within the group. By normalizing rewards across the sampled group, our method effectively mitigates the noise derived from task difficulty variance and enables fine-grained credit assignment. Extensive experiments on reasoning and code generation benchmarks demonstrate that Graph-GRPO significantly outperforms state-of-the-art baselines, achieving superior training stability and identifying critical communication pathways previously obscured by reward noise.

Recent advances in reinforcement learning for language model post-training, such as Group Relative Policy Optimization (GRPO), have shown promise in low-resource settings. However, GRPO typically relies on solution-level and scalar reward signals that fail to capture the semantic diversity among sampled completions. This leads to what we identify as a diversity-quality inconsistency, where distinct reasoning paths may receive indistinguishable rewards. To address this limitation, we propose Diversity-aware Reward Adjustment (DRA), a method that explicitly incorporates semantic diversity into the reward computation. DRA uses Submodular Mutual Information (SMI) to downweight redundant completions and amplify rewards for diverse ones. This encourages better exploration during learning, while maintaining stable exploitation of high-quality samples. Our method integrates seamlessly with both GRPO and its variant DR.~GRPO, resulting in DRA-GRPO and DGA-DR.~GRPO. We evaluate our method on five mathematical reasoning benchmarks and find that it outperforms recent strong baselines. It achieves state-of-the-art performance with an average accuracy of 58.2%, using only 7,000 fine-tuning samples and a total training cost of approximately $55. The code is available at https://github.com/xiwenc1/DRA-GRPO.

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

The concept class of low-degree polynomial threshold functions (PTFs) plays a fundamental role in machine learning. In this paper, we study PAC learning of K-sparse degree-d PTFs on R^n, where any such concept depends only on K out of n attributes of the input. Our main contribution is a new algorithm that runs in time ({nd}/{epsilon})^{O(d)} and under the Gaussian marginal distribution, PAC learns the class up to error rate epsilon with O(K^{4d}{epsilon^{2d}} cdot log^{5d} n) samples even when an eta leq O(epsilon^d) fraction of them are corrupted by the nasty noise of Bshouty et al. (2002), possibly the strongest corruption model. Prior to this work, attribute-efficient robust algorithms are established only for the special case of sparse homogeneous halfspaces. Our key ingredients are: 1) a structural result that translates the attribute sparsity to a sparsity pattern of the Chow vector under the basis of Hermite polynomials, and 2) a novel attribute-efficient robust Chow vector estimation algorithm which uses exclusively a restricted Frobenius norm to either certify a good approximation or to validate a sparsity-induced degree-2d polynomial as a filter to detect corrupted samples.

Graph Neural Networks (GNNs) show promising results for graph tasks. However, existing GNNs' generalization ability will degrade when there exist distribution shifts between testing and training graph data. The cardinal impetus underlying the severe degeneration is that the GNNs are architected predicated upon the I.I.D assumptions. In such a setting, GNNs are inclined to leverage imperceptible statistical correlations subsisting in the training set to predict, albeit it is a spurious correlation. In this paper, we study the problem of the generalization ability of GNNs in Out-Of-Distribution (OOD) settings. To solve this problem, we propose the Learning to Reweight for Generalizable Graph Neural Network (L2R-GNN) to enhance the generalization ability for achieving satisfactory performance on unseen testing graphs that have different distributions with training graphs. We propose a novel nonlinear graph decorrelation method, which can substantially improve the out-of-distribution generalization ability and compares favorably to previous methods in restraining the over-reduced sample size. The variables of the graph representation are clustered based on the stability of the correlation, and the graph decorrelation method learns weights to remove correlations between the variables of different clusters rather than any two variables. Besides, we interpose an efficacious stochastic algorithm upon bi-level optimization for the L2R-GNN framework, which facilitates simultaneously learning the optimal weights and GNN parameters, and avoids the overfitting problem. Experimental results show that L2R-GNN greatly outperforms baselines on various graph prediction benchmarks under distribution shifts.

Value-model-free RLVR methods such as GRPO assign uniform advantages to all tokens in a rollout, ignoring that tokens contribute unequally. Recent methods use token entropy as an importance proxy but compute it globally across the batch, conflating importance with prompt difficulty and positional trends. We argue that importance should instead be measured relative to the local context of each token. We introduce proximal entropy, a local measure of token importance relative to neighboring tokens, and prove it is invariant to both confounders. Proximal Entropy Policy Optimization (PEPO) uses it to weight per-token advantages and outperforms GRPO and entropy-based baselines on mathematical reasoning across Qwen3-1.7B, Qwen3-4B, and Llama-3.2-3B-Instruct. We also show the formulation generalizes to other algorithms where substituting proximal entropy into existing methods improves, and applying it to single-stream RL succeeds where global entropy fails.

Reinforcement learning from verifiable rewards assigns one terminal reward to an entire reasoning trajectory, obscuring how individual reasoning steps contributed to the outcome. GRPO broadcasts a group-normalized advantage to every response token, while finer-grained approaches often rely on dense auxiliary rollouts or branching schemes that can also alter the data used for policy updates. We cast the missing middle as budgeted measurement: with a limited rollout budget, which partial solutions should be evaluated, and how should their value estimates refine credit? ProbePO selects partial-solution states with a reward-free uncertainty score and estimates their expected verifier rewards under a capped continuation budget. ProbePO redistributes, rather than replaces, GRPO's trajectory-level advantage across tokens while preserving each trajectory's mean token-level advantage; probe continuations serve only as measurements. Across three DeepSeekMath and Qwen-family models spanning 1.5B-7B parameters, ProbePO consistently outperforms GRPO and achieves the highest accuracy among the four evaluated methods in 16 of 18 model-benchmark comparisons. Against dense-probing VinePPO on DeepSeekMath-7B, ProbePO achieves higher accuracy on all six benchmarks with 76% less end-to-end training time.

Recent advancements in Large Reasoning Models (LRMs), exemplified by DeepSeek-R1, have underscored the potential of scaling inference-time compute through Group Relative Policy Optimization (GRPO). However, GRPO frequently suffers from gradient signal attenuation when encountering problems that are either too trivial or overly complex. In these scenarios, the disappearance of inter-group advantages makes the gradient signal susceptible to noise, thereby jeopardizing convergence stability. While variants like DAPO attempt to rectify gradient vanishing, they do not alleviate the substantial computational overhead incurred by exhaustive rollouts on low-utility samples. In this paper, we propose Difficulty-Estimated Policy Optimization (DEPO), a novel framework designed to optimize the efficiency and robustness of reasoning alignment. DEPO integrates an online Difficulty Estimator that dynamically assesses and filters training data before the rollout phase. This mechanism ensures that computational resources are prioritized for samples with high learning potential. Empirical results demonstrate that DEPO achieves up to a 2x reduction in rollout costs without compromising model performance. Our approach significantly lowers the computational barrier for training high-performance reasoning models, offering a more sustainable path for reasoning scaling. Code and data will be released upon acceptance.

Multimodal geometry reasoning requires VLMs to extract precise visual relations and preserve them through multi-step deduction. Existing free-form traces obscure the decisions that determine the answer, and trajectory-level reinforcement learning distributes a single terminal signal across the entire response. We introduce credit-addressable reasoning, in which the semantic units exposed during inference also define where learning compares alternatives and assigns credit. We instantiate this principle with Code-CoT, which retains the diagram, represents visual relations as line-addressable executable code, and organizes reasoning into typed events, and CE-GRPO, which selects event boundaries using structural priors and type-normalized entropy, samples complete continuations from shared prefixes, and converts outcome differences into localized advantages. Across nine geometry benchmarks, CE-GRPO achieves an average accuracy of 76.04, outperforming Qwen3-VL-8B and trajectory-level GRPO by 8.09 and 3.43 points, respectively. Its relative advantage increases with the number of intermediate events, demonstrating the value of representation--optimization co-design for long, dependency-heavy multimodal reasoning.

We propose two approaches to extend the notion of knowledge distillation to Gaussian Process Regression (GPR) and Gaussian Process Classification (GPC); data-centric and distribution-centric. The data-centric approach resembles most current distillation techniques for machine learning, and refits a model on deterministic predictions from the teacher, while the distribution-centric approach, re-uses the full probabilistic posterior for the next iteration. By analyzing the properties of these approaches, we show that the data-centric approach for GPR closely relates to known results for self-distillation of kernel ridge regression and that the distribution-centric approach for GPR corresponds to ordinary GPR with a very particular choice of hyperparameters. Furthermore, we demonstrate that the distribution-centric approach for GPC approximately corresponds to data duplication and a particular scaling of the covariance and that the data-centric approach for GPC requires redefining the model from a Binomial likelihood to a continuous Bernoulli likelihood to be well-specified. To the best of our knowledge, our proposed approaches are the first to formulate knowledge distillation specifically for Gaussian Process models.

Reinforcement learning methods such as GRPO have seen great popularity in LLM post-training. In GRPO, models produce completions to a set of prompts, which are rewarded, and the policy is updated towards the relatively high reward completions. Due to the auto-regressive nature of models, the generation phase of such style of training can be extremely time consuming. As a solution, prior work has sought to distribute the inference step across many nodes, working parallel. These works assume primarily homogeneous models in the training in order to keep samples as close to on-policy as possible. This assumption may be impractical in decentralized systems, where parties with various computes and preferences may wish to collaborate on the same task. Thus, decentralized training requires an approach that can handle heterogeneous models - different models collaborating on the same tasks. However, this leads to highly off-policy samples presented during training, which prior work has identified that off-policy samples can hurt GRPO convergence. To enable heterogeneity, we propose Filtered Truncated Importance Sampling (F-TIS) - a GRPO-style training paradigm that can use off-policy samples to improve local model's learning. Our framework allows various models to collaborate in the same RL training run while being communication efficient. We extensively evaluate F-TIS in various heterogeneous setups and we show that it exhibits identical final model convergence to purely on-sample training. Furthermore, we observe in some setups better generalization on out-of-distribution tasks than on-policy training, increasing model's performance by up to 12\%.

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/.

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

We introduce MVN-Grad (Momentum on Variance-Normalized Gradients), an Adam-style optimizer that improves stability and performance by combining two complementary ideas: variance-based normalization and momentum applied after normalization. MVN-Grad scales each coordinate by an exponential moving average of gradient uncertainty and applies momentum to the resulting normalized gradients, eliminating the cross-time coupling between stale momentum and a stochastic normalizer present in standard Adam-type updates. We prove that this decoupling yields strictly smaller one-step conditional update variance than momentum-then-normalize variance methods under standard noise assumptions, and that MVN-Grad is robust to outliers: it has a uniformly bounded response to single gradient spikes. In low-variance regimes, we further show variance normalization avoids sign-type collapse associated with second-moment scaling and can yield accelerated convergence. Across CIFAR-100 image classification and GPT-style language modeling benchmarks, MVN-Grad matches or outperforms Adam, AdaBelief, and LaProp, delivering smoother training and improved generalization with no added overhead.

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.

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.

Critic-free methods like GRPO reduce memory demands by estimating advantages from multiple rollouts but tend to converge slowly, as critical learning signals are diluted by an abundance of uninformative samples and tokens. To tackle this challenge, we propose the Dynamic Dual-Level Down-Sampling (D^3S) framework that prioritizes the most informative samples and tokens across groups to improve the efficient of policy optimization. D^3S operates along two levels: (1) the sample-level, which selects a subset of rollouts to maximize advantage variance (Var(A)). We theoretically proven that this selection is positively correlated with the upper bound of the policy gradient norms, yielding higher policy gradients. (2) the token-level, which prioritizes tokens with a high product of advantage magnitude and policy entropy (|A_{i,t}|times H_{i,t}), focusing updates on tokens where the policy is both uncertain and impactful. Moreover, to prevent overfitting to high-signal data, D^3S employs a dynamic down-sampling schedule inspired by curriculum learning. This schedule starts with aggressive down-sampling to accelerate early learning and gradually relaxes to promote robust generalization. Extensive experiments on Qwen2.5 and Llama3.1 demonstrate that integrating D^3S into advanced RL algorithms achieves state-of-the-art performance and generalization while requiring fewer samples and tokens across diverse reasoning benchmarks. Our code is added in the supplementary materials and will be made publicly available.

As a significant part of post-training of the Large Language Models (LLMs), Reinforcement Learning from Verifiable Reward (RLVR) has greatly improved LLMs' reasoning skills. However, some RLVR algorithms, such as GRPO (Group Relative Policy Optimization) and GSPO (Group Sequence Policy Optimization), are observed to suffer from unstable policy updates and low usage of sampling data, respectively. The importance ratio of GRPO is calculated at the token level, which focuses more on optimizing a single token. This will be easily affected by outliers, leading to model training collapse. GSPO proposed the calculation of the response level importance ratio, which solves the problem of high variance and training noise accumulation in the calculation of the GRPO importance ratio. However, since all the response tokens share a common importance ratio, extreme values can easily raise or lower the overall mean, leading to the entire response being mistakenly discarded, resulting in a decrease in the utilization of sampled data. This paper introduces SSPO, which applies sentence-level importance ratio, taking the balance between GRPO and GSPO. SSPO not only avoids training collapse and high variance, but also prevents the whole response tokens from being abandoned by the clipping mechanism. Furthermore, we apply sentence entropy to PPO-CLIP to steadily adjust the clipping bounds, encouraging high-entropy tokens to explore and narrow the clipping range of low-entropy tokens. In particular, SSPO achieves an average score of 46.57 across five datasets, surpassing GRPO (43.01) and GSPO (44.42), and wins state-of-the-art performance on three datasets. These results highlight SSPO's effectiveness in leveraging generated data by taking the essence of GSPO but rejecting its shortcomings.

Three of the most popular methods for training language models to reason look like three different tricks. They are not. All three adjust a single number: standard deviation, reflecting how much a prompt's sampled answers disagree. When such a model is trained, it answers each problem many times, and an automatic checker marks every answer right or wrong. The standard deviation of those marks measures the disagreement: largest when the answers split evenly between right and wrong, and zero when they all agree. Group Relative Policy Optimization (GRPO) divides by this number, GRPO Done Right (Dr. GRPO) drops the division, and Decoupled Clip and Dynamic Sampling Policy Optimization (DAPO) discards the groups where it is zero. Each is presented as its own fix, yet this paper proves they are three settings of one dial. That dial is not cosmetic: for right-or-wrong rewards, the disagreement is exactly the size of the training update, the group-standard-deviation identity. A split group teaches the most, while a unanimous group teaches nothing and falls silent. The same result says which problems deserve the most weight and how many tries each one needs. This paper confirms the intuition on a large real difficulty dataset (Big-Math) and in a controlled training run. What looks like a harmless normalization step is the dial that decides where learning happens and how strongly.

Streaming autoregressive (AR) video generators combined with few-step distillation achieve low-latency, high-quality synthesis, yet remain difficult to align via reinforcement learning from human feedback (RLHF). Existing SDE-based GRPO methods face challenges in this setting: few-step ODEs and consistency model samplers deviate from standard flow-matching ODEs, and their short, low-stochasticity trajectories are highly sensitive to initialization noise, rendering intermediate SDE exploration ineffective. We propose AR-CoPO (AutoRegressive Contrastive Policy Optimization), a framework that adapts the Neighbor GRPO contrastive perspective to streaming AR generation. AR-CoPO introduces chunk-level alignment via a forking mechanism that constructs neighborhood candidates at a randomly selected chunk, assigns sequence-level rewards, and performs localized GRPO updates. We further propose a semi-on-policy training strategy that complements on-policy exploration with exploitation over a replay buffer of reference rollouts, improving generation quality across domains. Experiments on Self-Forcing demonstrate that AR-CoPO improves both out-of-domain generalization and in-domain human preference alignment over the baseline, providing evidence of genuine alignment rather than reward hacking.

Traditional retrieval pipelines optimize utility through stages of candidate retrieval and reranking, where ranking operates over a predefined candidate set. Large Language Models (LLMs) broaden this into a generative process: given a candidate pool, an LLM can generate a subset and order it within a single autoregressive pass. However, this flexibility introduces a new optimization challenge: the model must search a combinatorial output space while receiving utility feedback only after the full ranked list is generated. Because this feedback is defined over the completed sequence, it cannot distinguish whether a poor result arises from failing to generate a relevant subset or from failing to rank that subset correctly. This credit assignment gap makes end-to-end optimization unstable and sample-inefficient. Existing systems often address this by separating candidate generation from ranking. However, such decoupling remains misaligned with downstream utility because ranking is limited by the candidate set it receives. To bridge this gap, we propose a unified framework that performs both within a single autoregressive rollout and optimizes them end-to-end via factorized group-relative policy optimization (F-GRPO). Our framework factorizes the policy into candidate generation and ranking while sharing a single LLM backbone, and jointly trains them with an order-invariant coverage reward and a position-aware utility reward. To address the resulting phase-specific credit assignment problem, we use separate group-relative advantages for generation and ranking within a two-phase sequence-level objective. Across sequential recommendation and multi-hop question answering benchmarks, F-GRPO improves top-ranked performance over GRPO and decoupled baselines, outperforms supervised alternatives, and remains competitive with strong zero-shot rerankers, with no architectural changes at inference time.

Recent work on enhancing the reasoning abilities of large language models (LLMs) has introduced explicit length control as a means of constraining computational cost while preserving accuracy. However, existing approaches rely on fixed-length training budgets, which do not take advantage of the natural progression from exploration to compression during learning. In this work, we propose a curriculum learning strategy for length-controlled reasoning using Group Relative Policy Optimization (GRPO). Our method starts with generous token budgets and gradually tightens them over training, encouraging models to first discover effective solution strategies and then distill them into more concise reasoning traces. We augment GRPO with a reward function that balances three signals: task correctness (via verifier feedback), length efficiency, and formatting adherence (via structural tags). Experiments on GSM8K, MATH500, SVAMP, College Math, and GSM+ demonstrate that curriculum-based training consistently outperforms fixed-budget baselines at the same final budget, achieving higher accuracy and significantly improved token efficiency. We further ablate the impact of reward weighting and decay schedule design, showing that progressive constraint serves as a powerful inductive bias for training efficient reasoning models. Our code and checkpoints are released at: https://github.com/hammoudhasan/curriculum_grpo.

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for enhancing the reasoning capabilities of Large Language Models (LLMs). However, dominant approaches like Group Relative Policy Optimization (GRPO) face critical stability challenges: they suffer from high estimator variance under computational constraints (small group sizes) and vanishing gradient signals in saturated failure regimes where all responses yield identical zero rewards. To address this, we propose Empirical Bayes Policy Optimization (EBPO), a novel framework that regularizes local group-based baselines by borrowing strength from the policy's accumulated global statistics. Instead of estimating baselines in isolation, EBPO employs a shrinkage estimator that dynamically balances local group statistics with a global prior updated via Welford's online algorithm. Theoretically, we demonstrate that EBPO guarantees strictly lower Mean Squared Error (MSE), bounded entropy decay, and non-vanishing penalty signals in failure scenarios compared to GRPO. Empirically, EBPO consistently outperforms GRPO and other established baselines across diverse benchmarks, including AIME and OlympiadBench. Notably, EBPO exhibits superior training stability, achieving high-performance gains even with small group sizes, and benefits significantly from difficulty-stratified curriculum learning.

Uncertainty quantification in Knowledge Graph Embedding (KGE) methods is crucial for ensuring the reliability of downstream applications. A recent work applies conformal prediction to KGE methods, providing uncertainty estimates by generating a set of answers that is guaranteed to include the true answer with a predefined confidence level. However, existing methods provide probabilistic guarantees averaged over a reference set of queries and answers (marginal coverage guarantee). In high-stakes applications such as medical diagnosis, a stronger guarantee is often required: the predicted sets must provide consistent coverage per query (conditional coverage guarantee). We propose CondKGCP, a novel method that approximates predicate-conditional coverage guarantees while maintaining compact prediction sets. CondKGCP merges predicates with similar vector representations and augments calibration with rank information. We prove the theoretical guarantees and demonstrate empirical effectiveness of CondKGCP by comprehensive evaluations.

Reinforcement learning with verifiable rewards (RLVR) has become a practical route to improve large language model reasoning, and Group Relative Policy Optimization (GRPO) is a widely used optimizer in this setting. However, RLVR training is typically performed with limited control over generalization. We revisit GRPO through a robustness-based generalization view, where the generalization loss is upper bounded by a combination of the empirical loss and a sharpness surrogate measured by the gradient norm. Building on this perspective, we propose Sharpness-Guided GRPO (GRPO-SG), a simple token-weighted variant of GRPO that downweights tokens likely to cause overly large gradients, reducing sharp updates and stabilizing optimization, thereby improving generalization. Experiments across mathematical reasoning, logic puzzles and tool-augmented question answering show consistent improvements over GRPO, along with smoother gradient-norm trajectories, supporting GRPO-SG as a simple and effective generalization-oriented upgrade to GRPO for RLVR.

Post-training alignment determines the reasoning and human preference following capabilities of large language models, yet most existing works withhold detailed data construction, filtering rules and training recipes, which hinders community reproducibility and lightweight model optimization. This work presents NebulaExp, a fully transparent, ablation-driven post-training pipeline built on Qwen3-8B-base, covering two orthogonal model branches: general instruct model and complex reasoning-specialized model. We curate a raw corpus of 3.84M multi-source SFT samples and a 200K verifiable RL candidate pool, and design an end-to-end data processing stack including response distillation, multi-dimensional cross-verification filtering, fine-grained difficulty grading, task classification and diversity-aware sampling. For the Instruct branch, our three-stage optimized supervised fine-tuning approach NebulaExp-Ins-SFT improves the average benchmark score from the 55.01 baseline of Qwen3-8B-nothink to 60.99. GRPO reinforcement learning then further elevates the average score to 61.85. For the Reasoning branch, medium-difficulty GRPO RL improves average reasoning score from 73.88 to 75.17. To address RL's dependency on task verifiers, we systematically investigate single-teacher and multi-teacher OPD (MOPD): utilizing merely 4K instruction-following samples and outperforms RL baseline by 3.26 points on IFEval with +4.43 average overall gain; MOPD fuses four domain-specialist teachers with merely 10K samples, lifting average performance by 4.18 over the base model. This report provides a fully reproducible empirical post-training recipe for 8B-scale LLMs, and comprehensively dissects the capability trade-offs among instruction adherence, mathematical reasoning, code generation and general knowledge.

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%.

Supervised fine-tuning (SFT) followed by Group Relative Policy Optimization (GRPO) is a common post-training recipe. We conduct a controlled ablation over SFT-GRPO data overlap, evaluating Qwen3-8B (thinking disabled) post-trained for Lean 4 autoformalization under six conditions that differ solely in training recipe: a base model, SFT-only, GRPO-only, and three SFT+GRPO configurations where 0 percent, 30 percent, or 100 percent of the GRPO prompts coincide with the SFT corpus. Keeping SFT and GRPO data disjoint consistently outperforms full overlap at zero additional compute cost. Evaluating on Gaokao-Formal and PutnamBench under both compile pass at k and semantic pass at k assessed by an LLM judge, we find that lower overlap is monotonically associated with higher compilation and semantic accuracy. At 0 percent overlap, GRPO yields a 10.4 percentage point semantic gain over SFT alone on Gaokao, while at 100 percent overlap both metrics remain flat, rendering the GRPO stage effectively redundant. We further show that dual-metric evaluation reveals compile semantic gaps exceeding 30 percentage points for the highest compiling models, a disparity invisible under compile-only benchmarking. To our knowledge, this is the first controlled investigation of SFT-GRPO data overlap as a post-training hyperparameter, demonstrating how model behavior varies based on the degree of data sharing between training stages.

We focus on the classification problem with a separable dataset, one of the most important and classical problems from machine learning. The standard approach to this task is logistic regression with gradient descent (LR+GD). Recent studies have observed that LR+GD can find a solution with arbitrarily large step sizes, defying conventional optimization theory. Our work investigates this phenomenon and makes three interconnected key observations about LR+GD with large step sizes. First, we find a remarkably simple explanation of why LR+GD with large step sizes solves the classification problem: LR+GD reduces to a batch version of the celebrated perceptron algorithm when the step size gamma to infty. Second, we observe that larger step sizes lead LR+GD to higher logistic losses when it tends to the perceptron algorithm, but larger step sizes also lead to faster convergence to a solution for the classification problem, meaning that logistic loss is an unreliable metric of the proximity to a solution. Surprisingly, high loss values can actually indicate faster convergence. Third, since the convergence rate in terms of loss function values of LR+GD is unreliable, we examine the iteration complexity required by LR+GD with large step sizes to solve the classification problem and prove that this complexity is suboptimal. To address this, we propose a new method, Normalized LR+GD - based on the connection between LR+GD and the perceptron algorithm - with much better theoretical guarantees.

Normalization techniques are a boon for modern deep learning. They let weights converge more quickly with often better generalization performances. It has been argued that the normalization-induced scale invariance among the weights provides an advantageous ground for gradient descent (GD) optimizers: the effective step sizes are automatically reduced over time, stabilizing the overall training procedure. It is often overlooked, however, that the additional introduction of momentum in GD optimizers results in a far more rapid reduction in effective step sizes for scale-invariant weights, a phenomenon that has not yet been studied and may have caused unwanted side effects in the current practice. This is a crucial issue because arguably the vast majority of modern deep neural networks consist of (1) momentum-based GD (e.g. SGD or Adam) and (2) scale-invariant parameters. In this paper, we verify that the widely-adopted combination of the two ingredients lead to the premature decay of effective step sizes and sub-optimal model performances. We propose a simple and effective remedy, SGDP and AdamP: get rid of the radial component, or the norm-increasing direction, at each optimizer step. Because of the scale invariance, this modification only alters the effective step sizes without changing the effective update directions, thus enjoying the original convergence properties of GD optimizers. Given the ubiquity of momentum GD and scale invariance in machine learning, we have evaluated our methods against the baselines on 13 benchmarks. They range from vision tasks like classification (e.g. ImageNet), retrieval (e.g. CUB and SOP), and detection (e.g. COCO) to language modelling (e.g. WikiText) and audio classification (e.g. DCASE) tasks. We verify that our solution brings about uniform gains in those benchmarks. Source code is available at https://github.com/clovaai/AdamP.

Reinforcement Learning with Verifiable Rewards has recently advanced the capabilities of Large Language Models in complex reasoning tasks by providing explicit rule-based supervision. Among RLVR methods, GRPO and its variants have achieved strong empirical performance. Despite their success, we identify that they suffer from Gradient Misassignment in Positives and Gradient Domination in Negatives, which lead to inefficient and suboptimal policy updates. To address these issues, we propose Rewards as Labels (REAL), a novel framework that revisits verifiable rewards as categorical labels rather than scalar weights, thereby reformulating policy optimization as a classification problem. Building on this, we further introduce anchor logits to enhance policy learning. Our analysis reveals that REAL induces a monotonic and bounded gradient weighting, enabling balanced gradient allocation across rollouts and effectively mitigating the identified mismatches. Extensive experiments on mathematical reasoning benchmarks show that REAL improves training stability and consistently outperforms GRPO and strong variants such as DAPO. On the 1.5B model, REAL improves average Pass@1 over DAPO by 6.7%. These gains further scale to 7B model, REAL continues to outperform DAPO and GSPO by 6.2% and 1.7%, respectively. Notably, even with a vanilla binary cross-entropy, REAL remains stable and exceeds DAPO by 4.5% on average.

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.

We explore reinforcement learning (RL) techniques to enhance reasoning within targeted problem spaces in large language models (LLMs) under memory and compute constraints. Our focus is on critic-free methods compatible with LoRA fine-tuning on a single 40GB GPU, a common limitation in academic settings. We introduce S-GRPO, a memory-efficient variant of Group Relative Policy Optimization, and T-SPMO, a token-level prefix matching strategy for fine-grained credit assignment. Despite limited resources, when used to fine-tune Qwen2-1.5B both methods significantly improve SVAMP benchmark accuracy from 46% to above 70% using LoRA training. T-SPMO also excels in multi-digit multiplication tasks, underscoring the potential of RL fine-tuning under hardware constraints. Additionally, we find that our full-token GRPO baseline under LoRA fine-tuning did not improve model performance (compared to base model) on either task, suggesting that our memory-efficient methods may act as a form of regularization that stabilizes training when only a small subset of parameters are updated.

We propose refined GRFs (GRFs++), a new class of Graph Random Features (GRFs) for efficient and accurate computations involving kernels defined on the nodes of a graph. GRFs++ resolve some of the long-standing limitations of regular GRFs, including difficulty modeling relationships between more distant nodes. They reduce dependence on sampling long graph random walks via a novel walk-stitching technique, concatenating several shorter walks without breaking unbiasedness. By applying these techniques, GRFs++ inherit the approximation quality provided by longer walks but with greater efficiency, trading sequential, inefficient sampling of a long walk for parallel computation of short walks and matrix-matrix multiplication. Furthermore, GRFs++ extend the simplistic GRFs walk termination mechanism (Bernoulli schemes with fixed halting probabilities) to a broader class of strategies, applying general distributions on the walks' lengths. This improves the approximation accuracy of graph kernels, without incurring extra computational cost. We provide empirical evaluations to showcase all our claims and complement our results with theoretical analysis.

Evaluating conditional coverage remains one of the most persistent challenges in assessing the reliability of predictive systems. Although conformal methods can give guarantees on marginal coverage, no method can guarantee to produce sets with correct conditional coverage, leaving practitioners without a clear way to interpret local deviations. To overcome sample-inefficiency and overfitting issues of existing metrics, we cast conditional coverage estimation as a classification problem. Conditional coverage is violated if and only if some classifier can achieve lower risk than the target coverage. Through the choice of a (proper) loss function, the resulting risk difference gives a conservative estimate of natural miscoverage measures such as L1 and L2 distance, and can even separate the effects of over- and under-coverage, and non-constant target coverages. We call the resulting family of metrics excess risk of the target coverage (ERT). We show experimentally that the use of modern classifiers provides much higher statistical power than simple classifiers underlying established metrics like CovGap. Additionally, we use our metric to benchmark different conformal prediction methods. Finally, we release an open-source package for ERT as well as previous conditional coverage metrics. Together, these contributions provide a new lens for understanding, diagnosing, and improving the conditional reliability of predictive systems.