Daily Papers

Multi-turn tool calling is challenging for Large Language Models (LLMs) because rewards are sparse and exploration is expensive. A common recipe, SFT followed by GRPO, can stall when within-group reward variation is low (e.g., more rollouts in a group receive the all 0 or all 1 reward), making the group-normalized advantage uninformative and yielding vanishing updates. To address this problem, we propose RC-GRPO (Reward-Conditioned Group Relative Policy Optimization), which treats exploration as a controllable steering problem via discrete reward tokens. We first fine-tune a Reward-Conditioned Trajectory Policy (RCTP) on mixed-quality trajectories with reward goal special tokens (e.g., <|high_reward|>, <|low_reward|>) injected into the prompts, enabling the model to learn how to generate distinct quality trajectories on demand. Then during RL, we sample diverse reward tokens within each GRPO group and condition rollouts on the sampled token to improve within-group diversity, improving advantage gains. On the Berkeley Function Calling Leaderboard v4 (BFCLv4) multi-turn benchmark, our method yields consistently improved performance than baselines, and the performance on Qwen-2.5-7B-Instruct even surpasses all closed-source API models.

Reinforcement learning (RL) plays a central role in large language model (LLM) post-training. Among existing approaches, Group Relative Policy Optimization (GRPO) is widely used, especially for RL with verifiable rewards (RLVR) fine-tuning. In GRPO, each query prompts the LLM to generate a group of rollouts with a fixed group size N. When all rollouts in a group share the same outcome, either all correct or all incorrect, the group-normalized advantages become zero, yielding no gradient signal and wasting fine-tuning compute. We introduce Adaptive Efficient Rollout Optimization (AERO), an enhancement of GRPO. AERO uses an adaptive rollout strategy, applies selective rejection to strategically prune rollouts, and maintains a Bayesian posterior to prevent zero-advantage dead zones. Across three model configurations (Qwen2.5-Math-1.5B, Qwen2.5-7B, and Qwen2.5-7B-Instruct), AERO improves compute efficiency without sacrificing performance. Under the same total rollout budget, AERO reduces total training compute by about 48% while shortening wall-clock time per step by about 45% on average. Despite the substantial reduction in compute, AERO matches or improves Pass@8 and Avg@8 over GRPO, demonstrating a practical, scalable, and compute-efficient strategy for RL-based LLM alignment.

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 reinforcement learning has enhanced the flow matching models on human preference alignment. While stochastic sampling enables the exploration of denoising directions, existing methods which optimize over multiple denoising steps suffer from sparse and ambiguous reward signals. We observe that the high entropy steps enable more efficient and effective exploration while the low entropy steps result in undistinguished roll-outs. To this end, we propose E-GRPO, an entropy aware Group Relative Policy Optimization to increase the entropy of SDE sampling steps. Since the integration of stochastic differential equations suffer from ambiguous reward signals due to stochasticity from multiple steps, we specifically merge consecutive low entropy steps to formulate one high entropy step for SDE sampling, while applying ODE sampling on other steps. Building upon this, we introduce multi-step group normalized advantage, which computes group-relative advantages within samples sharing the same consolidated SDE denoising step. Experimental results on different reward settings have demonstrated the effectiveness of our methods.

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.

Outcome-driven reinforcement learning has advanced reasoning in large language models (LLMs), but prevailing tool-augmented approaches train a single, monolithic policy that interleaves thoughts and tool calls under full context; this scales poorly with long horizons and diverse tools and generalizes weakly to new scenarios. Agentic systems offer a promising alternative by decomposing work across specialized modules, yet most remain training-free or rely on offline training decoupled from the live dynamics of multi-turn interaction. We introduce AgentFlow, a trainable, in-the-flow agentic framework that coordinates four modules (planner, executor, verifier, generator) through an evolving memory and directly optimizes its planner inside the multi-turn loop. To train on-policy in live environments, we propose Flow-based Group Refined Policy Optimization (Flow-GRPO), which tackles long-horizon, sparse-reward credit assignment by converting multi-turn optimization into a sequence of tractable single-turn policy updates. It broadcasts a single, verifiable trajectory-level outcome to every turn to align local planner decisions with global success and stabilizes learning with group-normalized advantages. Across ten benchmarks, AgentFlow with a 7B-scale backbone outperforms top-performing baselines with average accuracy gains of 14.9% on search, 14.0% on agentic, 14.5% on mathematical, and 4.1% on scientific tasks, even surpassing larger proprietary models like GPT-4o. Further analyses confirm the benefits of in-the-flow optimization, showing improved planning, enhanced tool-calling reliability, and positive scaling with model size and reasoning turns.

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.

Reinforcement learning (RL) is widely used for post-training large language models (LLMs) in code editing, where group-relative methods, such as GRPO, are popular due to their critic-free and normalized advantage estimation. However, in real-world code-editing scenarios, reward distributions are often skewed with unpredictable noise, leading to distorted advantage computation and increased rollout outliers. To address this issue, we propose Group Adaptive Policy Optimization (GAPO), which adaptively finds an interval with the highest SNR (Signal to Noise Ratio) per prompt and uses the median of that interval as an adaptive Q to replace the group mean in advantage calculation to reduce noise further. This adaptive Q robustly handles rollout noise while remaining plug-and-play and efficient. We evaluate GAPO on nine instruction-tuned LLMs (3B-14B) using a collected large dataset of 51,844 real-world, history-aware code-editing tasks spanning 10 programming languages. GAPO yields up to 4.35 in-domain (ID) and 5.30 out-of-domain (OOD) exact-match improvements over GRPO and its variant DAPO, while achieving lower clipping ratios and higher GPU throughput. Code: https://github.com/TsingZ0/verl-GAPO.

On-policy self-distillation, where a language model conditions on privileged context to supervise its own generations, is a promising source of dense supervision for sparse-reward reinforcement learning. Actually, it can be instantiated as an auxiliary full-vocabulary student-to-teacher reverse Kullback-Leibler divergence loss. We therefore propose SDPG, a self-distilled policy-gradient framework that combines group-relative verifier advantages with normalized standard deviation, exact full-vocabulary on-policy self-distillation, as well as reference-policy KL regularization. Empirically, SDPG improves stability and performance over RLVR and self-distillation baselines. The code is available at https://github.com/lauyikfung/SDPG.

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

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.

Training Large Language Models (LLMs) for multi-turn Tool-Integrated Reasoning (TIR) - where models iteratively reason, generate code, and verify through execution - remains challenging for existing reinforcement learning (RL) approaches. Current RL methods, exemplified by Group Relative Policy Optimization (GRPO), suffer from coarse-grained, trajectory-level rewards that provide insufficient learning signals for complex multi-turn interactions, leading to training stagnation. To address this issue, we propose Group Turn Policy Optimization (GTPO), a novel RL algorithm specifically designed for training LLMs on multi-turn TIR tasks. GTPO introduces three key innovations: (1) turn-level reward assignment that provides fine-grained feedback for individual turns, (2) return-based advantage estimation where normalized discounted returns are calculated as advantages, and (3) self-supervised reward shaping that exploits self-supervision signals from generated code to densify sparse binary outcome-based rewards. Our comprehensive evaluation demonstrates that GTPO outperforms GRPO by 3.0% on average across diverse reasoning benchmarks, establishing its effectiveness for advancing complex mathematical reasoning in the real world.

Reinforcement learning for agentic large language models (LLMs) typically relies on a sparse, trajectory-level outcome reward, making it difficult to evaluate the contribution of individual tool-calls within multi-turn interactions. Existing approaches to such process credit assignment either depend on separate external process reward models that introduce additional consumption, or tree-based structural rollout that merely redistributes the outcome signal while constraining trajectory diversity. A promising alternative leverages the per-turn change in the policy's predicted probability of the ground-truth, termed Information Gain (IG), as an intrinsic process signal without an external evaluator. However, prior work on leveraging IG signals within the RL training loop faces three systematic challenges: normalizing across turns that face heterogeneous positional contexts can distort the relative standing of individual turns, accumulating a variable number of terms causes advantage magnitudes to drift with trajectory depth, and a fixed clipping range governs policy updates identically for turns with vastly different IG signals. In this paper, we propose A^2TGPO (Agentic Turn-Group Policy Optimization with Adaptive Turn-level Clipping), which retains IG as the intrinsic signal but re-designs how it is normalized, accumulated, and consumed: (i) turn-group normalization: normalizes IG within each (prompt, turn-index) group so that each turn is compared only against peers at the same interaction depth; (ii) variance-rescaled discounted accumulation: divides cumulative normalized IG by square root of accumulated terms to keep advantage magnitudes comparable across turn positions; and (iii) adaptive turn-level clipping: modulates each turn's clipping range based on its normalized IG, widening the update region for informative turns and narrowing it for uninformative ones.

Reinforcement Learning has emerged as the fundamental technique for enhancing reasoning in LLMs. However, existing algorithms apply uniform optimization to all tokens, ignoring their different roles in reasoning process. To address this limitation, we introduce Heterogeneous Adaptive Policy Optimization (HAPO), a comprehensive token-aware algorithm that dynamically adapts optimization based on token entropy. For rollout sampling, we propose Adaptive Temperature Sampling, which adjusts sampling temperature in real time, promoting exploration at high-entropy tokens while preserving coherence at low-entropy ones. For advantage calculation, we introduce Token Level Group Average that normalizes advantages at token level, jointly accounting for sequence-length as in token-mean loss while preserving non-biased treatment. We then develop Differential Advantage Redistribution that leverages entropy and importance ratios to modulate rewards-adjusting updates for tokens with clear signals. For clipping loss, we design Asymmetric Adaptive Clipping, allowing aggressive probability reduction for noisy low-entropy tokens while enabling exploration for high-entropy tokens. Through systematic investigation between entropy and training dynamics, we embedded token-level treatment into every stages to achieve fine-grained control. Extensive experiments demonstrate that HAPO consistently outperforms DAPO across multiple model scales. Our code can be found in https://github.com/starriver030515/HAPO.

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.

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.

Agentic reinforcement learning enables LLM agents to learn through interaction, but sparse trajectory-level rewards reveal success without identifying which intermediate decisions deserve credit. Training-only privileged skills can provide denser supervision by allowing the same frozen policy snapshot to rescore fixed tokens from skill-free trajectories while conditioned on task-matched procedural skills. Existing methods, however, do not jointly calibrate teacher scores across interaction steps, relate teacher confidence to realized returns, and integrate the resulting signal into native reward-to-advantage construction. We introduce Agentic Reinforcement Learning with Self-Distilled Reward Shaping (ADRS), a framework for constructing return-associated token-level credit for multi-turn language agents. ADRS centers and normalizes privileged token scores within each step, modulates them with a return-associated Teacher Value Advantage (TVA) gate based on within-group confidence--return association, and incorporates the gated token signal into native RL credit construction. Together, these components determine what the teacher prefers, when that preference is return-relevant, and how it enters the native reinforcement-learning credit path, while keeping rollouts and inference skill-free. Finally, experiments across three interactive benchmarks show that ADRS consistently improves performance on long-horizon tasks, with gains persisting across RL backbones, reduced-data settings, unseen tasks, and extended training. For anonymous review, our code is available at the following the link: https://github.com/gitrxh/ADRS-arxiv

Multi-reward reinforcement learning trains large language models to satisfy multiple behavioral objectives simultaneously. Reward-wise normalization, as used in GDPO, preserves reward-specific relative information within rollout groups, but different objectives can still exhibit uneven learning progress. We study this behavior through advantage energy, the sum of a reward's squared advantages over a batch. Under idealized GDPO normalization, we show that this energy is proportional to active-group density: the fraction of rollout groups in which the reward provides nonzero relative advantages. This reveals a residual batch-level signal imbalance and provides a basis for calibrating reward contributions. Based on this relation, we propose Density-Aware Reward Aggregation (DARA). We derive an inverse-square-root density correction that gives greater weight to signals from less frequently active rewards. DARA computes its weights from each rollout batch, adapting to changes in reward activity throughout training without modifying the underlying policy optimization objective. Experiments on tool calling and mathematical reasoning show that DARA learns the targeted behaviors faster than GDPO, reaching high format compliance in up to 26% fewer training steps on tool calling and near-saturated length compliance in up to 65% fewer steps on mathematical reasoning, while remaining competitive in final performance. Our code is available at https://github.com/zhaihaotian/DARA.

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

Reinforcement learning has become a powerful paradigm for post-training large language model agents, yet credit assignment in multi-turn environments remains a challenge. Agents often receive sparse, trajectory-level rewards only at the end of an episode, making it difficult to determine which intermediate actions contributed to success or failure. As a result, propagating delayed outcomes back to individual decision steps without relying on costly auxiliary value models remains an open problem. We propose Generalized Advantage Grouped Policy Optimization (GAGPO), a critic-free reinforcement learning method for precise, step-aligned temporal credit assignment. GAGPO constructs a non-parametric grouped value proxy from sampled rollouts and uses it to compute TD/GAE-style temporal advantages, recursively propagating outcome supervision backward through time. Combined with group-wise advantage normalization and an action-level importance ratio, GAGPO extracts stable, localized optimization signals directly from multi-turn trajectories. Experiments on ALFWorld and WebShop show that GAGPO outperforms strong reinforcement learning baselines. Further analyses demonstrate faster early-stage learning, improved interaction efficiency, and smoother optimization dynamics, suggesting that GAGPO offers a simple yet effective framework for multi-turn agentic reinforcement learning.

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

Machine learning models are often personalized with categorical attributes that are protected, sensitive, self-reported, or costly to acquire. In this work, we show models that are personalized with group attributes can reduce performance at a group level. We propose formal conditions to ensure the "fair use" of group attributes in prediction tasks by training one additional model -- i.e., collective preference guarantees to ensure that each group who provides personal data will receive a tailored gain in performance in return. We present sufficient conditions to ensure fair use in empirical risk minimization and characterize failure modes that lead to fair use violations due to standard practices in model development and deployment. We present a comprehensive empirical study of fair use in clinical prediction tasks. Our results demonstrate the prevalence of fair use violations in practice and illustrate simple interventions to mitigate their harm.

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

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

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

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

Machine learning models often have uneven performance among subpopulations (a.k.a., groups) in the data distributions. This poses a significant challenge for the models to generalize when the proportions of the groups shift during deployment. To improve robustness to such shifts, existing approaches have developed strategies that train models or perform hyperparameter tuning using the group-labeled data to minimize the worst-case loss over groups. However, a non-trivial amount of high-quality labels is often required to obtain noticeable improvements. Given the costliness of the labels, we propose to adopt a different paradigm to enhance group label efficiency: utilizing the group-labeled data as a target set to optimize the weights of other group-unlabeled data. We introduce Group-robust Sample Reweighting (GSR), a two-stage approach that first learns the representations from group-unlabeled data, and then tinkers the model by iteratively retraining its last layer on the reweighted data using influence functions. Our GSR is theoretically sound, practically lightweight, and effective in improving the robustness to subpopulation shifts. In particular, GSR outperforms the previous state-of-the-art approaches that require the same amount or even more group labels.

In critical decision-making scenarios, optimizing accuracy can lead to a biased classifier, hence past work recommends enforcing group-based fairness metrics in addition to maximizing accuracy. However, doing so exposes the classifier to another kind of bias called infra-marginality. This refers to individual-level bias where some individuals/subgroups can be worse off than under simply optimizing for accuracy. For instance, a classifier implementing race-based parity may significantly disadvantage women of the advantaged race. To quantify this bias, we propose a general notion of eta-infra-marginality that can be used to evaluate the extent of this bias. We prove theoretically that, unlike other fairness metrics, infra-marginality does not have a trade-off with accuracy: high accuracy directly leads to low infra-marginality. This observation is confirmed through empirical analysis on multiple simulated and real-world datasets. Further, we find that maximizing group fairness often increases infra-marginality, suggesting the consideration of both group-level fairness and individual-level infra-marginality. However, measuring infra-marginality requires knowledge of the true distribution of individual-level outcomes correctly and explicitly. We propose a practical method to measure infra-marginality, and a simple algorithm to maximize group-wise accuracy and avoid infra-marginality.

We consider a binary classification problem under group fairness constraints, which can be one of Demographic Parity (DP), Equalized Opportunity (EOp), or Equalized Odds (EO). We propose an explicit characterization of Bayes optimal classifier under the fairness constraints, which turns out to be a simple modification rule of the unconstrained classifier. Namely, we introduce a novel instance-level measure of bias, which we call bias score, and the modification rule is a simple linear rule on top of the finite amount of bias scores.Based on this characterization, we develop a post-hoc approach that allows us to adapt to fairness constraints while maintaining high accuracy. In the case of DP and EOp constraints, the modification rule is thresholding a single bias score, while in the case of EO constraints we are required to fit a linear modification rule with 2 parameters. The method can also be applied for composite group-fairness criteria, such as ones involving several sensitive attributes.

Diffusion models achieve state-of-the-art generative performance but are fundamentally bottlenecked by their slow, iterative sampling process. While diffusion distillation techniques enable high-fidelity, few-step generation, traditional objectives often restrict the student's performance by anchoring it solely to the teacher. Recent approaches have attempted to break this ceiling by integrating Reinforcement Learning (RL), typically through a simple summation of distillation and RL objectives. In this work, we propose a novel paradigm by re-conceptualizing distribution matching as a reward, denoted as R_dm. This unified perspective bridges the algorithmic gap between Diffusion Matching Distillation (DMD) and RL, providing several primary benefits. (1) Enhanced Optimization Stability: We introduce Group Normalized Distribution Matching (GNDM), which adapts standard RL group normalization to stabilize R_dm estimation. By leveraging group-mean statistics, GNDM establishes a more robust and effective optimization direction. (2) Seamless Reward Integration: Our reward-centric formulation inherently supports adaptive weighting mechanisms, allowing for the fluid combination of DMD with external reward models. (3) Improved Sampling Efficiency: By aligning with RL principles, the framework readily incorporates Importance Sampling (IS), leading to a significant boost in sampling efficiency. Extensive experiments demonstrate that GNDM outperforms vanilla DMD, reducing the FID by 1.87. Furthermore, our multi-reward variant, GNDMR, surpasses existing baselines by striking an optimal balance between aesthetic quality and fidelity, achieving a peak HPS of 30.37 and a low FID-SD of 12.21. Ultimately, R_dm provides a flexible, stable, and efficient framework for real-time, high-fidelity synthesis. Codes are coming soon.

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.

Normalization layers have recently experienced a renaissance in the deep reinforcement learning and continual learning literature, with several works highlighting diverse benefits such as improving loss landscape conditioning and combatting overestimation bias. However, normalization brings with it a subtle but important side effect: an equivalence between growth in the norm of the network parameters and decay in the effective learning rate. This becomes problematic in continual learning settings, where the resulting effective learning rate schedule may decay to near zero too quickly relative to the timescale of the learning problem. We propose to make the learning rate schedule explicit with a simple re-parameterization which we call Normalize-and-Project (NaP), which couples the insertion of normalization layers with weight projection, ensuring that the effective learning rate remains constant throughout training. This technique reveals itself as a powerful analytical tool to better understand learning rate schedules in deep reinforcement learning, and as a means of improving robustness to nonstationarity in synthetic plasticity loss benchmarks along with both the single-task and sequential variants of the Arcade Learning Environment. We also show that our approach can be easily applied to popular architectures such as ResNets and transformers while recovering and in some cases even slightly improving the performance of the base model in common stationary benchmarks.

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

In the field of algorithmic fairness, significant attention has been put on group fairness criteria, such as Demographic Parity and Equalized Odds. Nevertheless, these objectives, measured as global averages, have raised concerns about persistent local disparities between sensitive groups. In this work, we address the problem of local fairness, which ensures that the predictor is unbiased not only in terms of expectations over the whole population, but also within any subregion of the feature space, unknown at training time. To enforce this objective, we introduce ROAD, a novel approach that leverages the Distributionally Robust Optimization (DRO) framework within a fair adversarial learning objective, where an adversary tries to infer the sensitive attribute from the predictions. Using an instance-level re-weighting strategy, ROAD is designed to prioritize inputs that are likely to be locally unfair, i.e. where the adversary faces the least difficulty in reconstructing the sensitive attribute. Numerical experiments demonstrate the effectiveness of our method: it achieves Pareto dominance with respect to local fairness and accuracy for a given global fairness level across three standard datasets, and also enhances fairness generalization under distribution shift.

Group-based reinforcement learning (RL), such as GRPO, has advanced the capabilities of large language models on long-horizon agentic tasks. To enable more fine-grained policy updates, recent research has increasingly shifted toward stepwise group-based policy optimization, which treats each step in a rollout trajectory independently while using a memory module to retain historical context. However, we find a key issue in estimating stepwise relative advantages, namely context inconsistency, where steps within the same group may differ in their historical contexts. Empirically, we reveal that this issue can lead to severely biased advantage estimation, thereby degrading policy optimization significantly. To address the issue, in this paper, we propose Hierarchy-of-Groups Policy Optimization (HGPO) for long-horizon agentic tasks. Specifically, within a group of rollout trajectories, HGPO assigns each step to multiple hierarchical groups according to the consistency of historical contexts. Then, for each step, HGPO computes distinct advantages within each group and aggregates them with an adaptive weighting scheme. In this way, HGPO can achieve a favorable bias-variance trade-off in stepwise advantage estimation, without extra models or rollouts. Evaluations on two challenging agentic tasks, ALFWorld and WebShop with Qwen2.5-1.5B-Instruct and Qwen2.5-7B-Instruct, show that HGPO significantly outperforms existing agentic RL methods under the same computational constraints. Code is available at https://github.com/langfengQ/verl-agent/tree/master/recipe/hgpo.

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.

Reinforcement learning for flow-matching text-to-speech is complicated by deterministic ODE sampling: trajectory-level policy-gradient methods typically convert the ODE into an SDE and track per-step likelihood ratios, introducing stochastic perturbations and substantial overhead. We propose GROW, a group-relative advantage-weighted on-policy RL method that acts directly on the standard flow-matching objective. For each prompt, GROW samples a group of on-policy utterances, separately standardizes intelligibility and speaker-similarity rewards within the group, and combines them to reweight flow-matching regression. A Wasserstein-2 velocity penalty anchors the updated model to a frozen pretrained reference. A group-mean reward baseline is introduced to convert reward weighting into advantage weighting. For strong pretrained TTS models with concentrated rewards, positive exponential weighting is dominated by reward-agnostic self-imitation, whereas a zero-mean signed advantage preserves effective within-group credit assignment. Instantiated on DiTAR and evaluated on LibriSpeech and Seed-TTS EN/ZH, GROW reduces average WER from 2.016 to 1.558 and raises speaker similarity from 0.676 to 0.715 while keeping UTMOS. With 10-NFE training rollouts and 32-NFE evaluation, GROW retains comparable performance while training 2.9x faster than 32-NFE DiTAR-GRPO. We will open-source complete GROW codes, faithful DiTAR reproduction, and all model checkpoints.

Reinforcement Learning (RL) for Large Language Models (LLMs) often suffers from training collapse in long-horizon tasks due to exploding gradient variance. To mitigate this, a baseline is commonly introduced for advantage computation; however, traditional value models remain difficult to optimize, and standard group-based baselines overlook sequence heterogeneity. Although classic optimal baseline theory can achieve global variance reduction, it neglects token heterogeneity and requires prohibitive gradient-based computation. In this work, we derive the Optimal Token Baseline (OTB) from first principles, proving that gradient updates should be weighted inversely to their cumulative gradient norm. To ensure efficiency, we propose the Logit-Gradient Proxy that approximates the gradient norm using only forward-pass probabilities. Our method achieves training stability and matches the performance of large group sizes (N=32) with only N=4, reducing token consumption by over 65% across single-turn and tool-integrated reasoning tasks.

Reinforcement Learning with Verifiable Rewards (RLVR) is commonly based on group sampling to estimate advantages and stabilize policy updates. In practice, large group sizes are not feasible due to computational limits, which biases learning toward trajectories that are already likely. Smaller groups often miss rare-correct trajectories while still containing mixed rewards, concentrating probability on common solutions. We derive the probability that updates miss rare-correct modes as a function of group size, showing non-monotonic behavior, and characterize how updates redistribute mass within the correct set, revealing that unsampled-correct mass can shrink even as total correct mass grows. Motivated by this analysis, we propose a difficulty-aware advantage scaling coefficient, inspired by Focal loss, that down-weights updates on high-success prompts. The lightweight modification can be directly integrated into any group-relative RLVR algorithm such as GRPO, DAPO, and CISPO. On Qwen2.5-7B across in-domain and out-of-domain benchmarks, our method improves pass@256 from 64.1 rightarrow 70.3 (GRPO), 69.3 rightarrow 72.5 (DAPO), and 73.2 rightarrow 76.8 (CISPO), while preserving or improving pass@1, without increasing group size or computational cost.

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

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.

Reinforcement Learning with Verifiable Rewards (RLVR), particularly GRPO, has become the standard for eliciting LLM reasoning. However, its efficiency in exploration and difficulty adaptation remains an open challenge. In this work, we argue that these bottlenecks stem from an implicit advantage symmetry inherent in Group Relative Advantage Estimation (GRAE). This symmetry induces two critical limitations: (i) at the group level, strict symmetry in weights between correct and incorrect trajectories leaves unsampled action logits unchanged, thereby hindering exploration of novel correct solution. (ii) at the sample level, the algorithm implicitly prioritizes medium-difficulty samples, remaining agnostic to the non-stationary demands of difficulty focus. Through controlled experiments, we reveal that this symmetric property is sub-optimal, yielding two pivotal insights: (i) asymmetrically suppressing the advantages of correct trajectories encourages essential exploration. (ii) learning efficiency is maximized by a curriculum-like transition-prioritizing simpler samples initially before gradually shifting to complex ones. Motivated by these findings, we propose Asymmetric GRAE (A-GRAE), which dynamically modulates exploration incentives and sample-difficulty focus. Experiments across seven benchmarks demonstrate that A-GRAE consistently improves GRPO and its variants across both LLMs and MLLMs.

Fair representation learning is an attractive approach that promises fairness of downstream predictors by encoding sensitive data. Unfortunately, recent work has shown that strong adversarial predictors can still exhibit unfairness by recovering sensitive attributes from these representations. In this work, we present Fair Normalizing Flows (FNF), a new approach offering more rigorous fairness guarantees for learned representations. Specifically, we consider a practical setting where we can estimate the probability density for sensitive groups. The key idea is to model the encoder as a normalizing flow trained to minimize the statistical distance between the latent representations of different groups. The main advantage of FNF is that its exact likelihood computation allows us to obtain guarantees on the maximum unfairness of any potentially adversarial downstream predictor. We experimentally demonstrate the effectiveness of FNF in enforcing various group fairness notions, as well as other attractive properties such as interpretability and transfer learning, on a variety of challenging real-world datasets.

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

Rubric-based Reinforcement Learning (RL) has emerged as a promising approach for aligning Large Language Models (LLMs) with complex, open-domain instruction following tasks. However, existing methods predominantly rely on response-level rewards, introducing severe reward sparsity and reward ambiguity problems. To address these issues, we propose Rubrics to Tokens (RTT), a novel rubric-based RL framework that bridges coarse response-level scores and fine-grained token-level credit assignment. RTT introduces a Token-Level Relevance Discriminator to predict which tokens in the response are responsible for a specific constraint, and optimizes the policy model via RTT-GRPO, which integrates response-level and token-level advantages within a unified framework. Furthermore, when transitioning from one-dimensional, outcome-level reward to three-dimensional reward space in the token-level rubric-based RL, we propose a novel group normalization method, called Intra-sample Token Group Normalization, to accommodate this shift. Extensive experiments and benchmarks demonstrate that RTT consistently outperforms other baselines in both instruction- and rubric-level accuracy across different models.

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 (RLVR) strengthens LLM reasoning, but training often oscillates between {entropy collapse} and {entropy explosion}. We trace both hazards to the mean baseline used in value-free RL (e.g., GRPO and DAPO), which improperly penalizes negative-advantage samples under reward outliers. We propose {Quantile Advantage Estimation} (QAE), replacing the mean with a group-wise K-quantile baseline. QAE induces a response-level, two-regime gate: on hard queries (p <= 1 - K) it reinforces rare successes, while on easy queries (p > 1 - K) it targets remaining failures. Under first-order softmax updates, we prove {two-sided entropy safety}, giving lower and upper bounds on one-step entropy change that curb explosion and prevent collapse. Empirically, this minimal modification stabilizes entropy, sparsifies credit assignment (with tuned K, roughly 80% of responses receive zero advantage), and yields sustained pass@1 gains on Qwen3-8B/14B-Base across AIME 2024/2025 and AMC 2023. These results identify {baseline design} -- rather than token-level heuristics -- as the primary mechanism for scaling RLVR.

Recent advances in group-based reinforcement learning (RL) have driven frontier large language models (LLMs) in single-turn tasks like mathematical reasoning. However, their scalability to long-horizon LLM agent training remains limited. Unlike static tasks, agent-environment interactions unfold over many steps and often yield sparse or delayed rewards, making credit assignment across individual steps significantly more challenging. In this work, we propose Group-in-Group Policy Optimization (GiGPO), a novel RL algorithm that achieves fine-grained credit assignment for LLM agents while preserving the appealing properties of group-based RL: critic-free, low memory, and stable convergence. GiGPO introduces a two-level structure for estimating relative advantage: (i) At the episode-level, GiGPO computes macro relative advantages based on groups of complete trajectories; (ii) At the step-level, GiGPO introduces an anchor state grouping mechanism that retroactively constructs step-level groups by identifying repeated environment states across trajectories. Actions stemming from the same state are grouped together, enabling micro relative advantage estimation. This hierarchical structure effectively captures both global trajectory quality and local step effectiveness without relying on auxiliary models or additional rollouts. We evaluate GiGPO on two challenging agent benchmarks, ALFWorld and WebShop, using Qwen2.5-1.5B-Instruct and Qwen2.5-7B-Instruct. Crucially, GiGPO delivers fine-grained per-step credit signals and achieves performance gains of > 12\% on ALFWorld and > 9\% on WebShop over the GRPO baseline: all while maintaining the same GPU memory overhead, identical LLM rollout, and incurring little to no additional time cost.

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

Open-ended real-world interaction admits multiple valid behaviors: an agent may answer directly, ask for clarification, provide progress updates, or confirm before acting. This flexibility breaks a core assumption behind group-based RL: rollouts compared within a group are no longer guaranteed to be behaviorally comparable. As a result, reward-model preferences over interaction style can distort relative advantages and steer optimization toward reward-preferred behaviors rather than context-appropriate ones. We formalize this as a reward fairness problem and propose ARC (Advantage Regularization via Conditioning), a training recipe that restores fairer relative comparison through strategy-conditioned rollout grouping, together with hybrid rewards and entropy regularization. We study ARC in our proposed \inter, a novel paradigm for responsive, steerable, and execution-aware user-agent interaction that decouples user-visible communication from latent reasoning and tool use. \inter\ also provides the annotation and distillation pipeline for constructing \inter-86K, our strategy-annotated training corpus for supervised and RL training. Empirically, ARC substantially strengthens the core τ/τ^2 tool-use benchmarks, while \inter\ reduces time-to-first-token from 4.91s to 1.27s relative to a think-style baseline. Together, these results suggest that a central bottleneck in open-ended interactive learning is not only how agents are rewarded, but whether their behaviors are compared fairly in the first place. The ARC implementation and \inter-86K training data will be released.

In this article, we introduce a novel normalization technique for neural network weight matrices, which we term weight conditioning. This approach aims to narrow the gap between the smallest and largest singular values of the weight matrices, resulting in better-conditioned matrices. The inspiration for this technique partially derives from numerical linear algebra, where well-conditioned matrices are known to facilitate stronger convergence results for iterative solvers. We provide a theoretical foundation demonstrating that our normalization technique smoothens the loss landscape, thereby enhancing convergence of stochastic gradient descent algorithms. Empirically, we validate our normalization across various neural network architectures, including Convolutional Neural Networks (CNNs), Vision Transformers (ViT), Neural Radiance Fields (NeRF), and 3D shape modeling. Our findings indicate that our normalization method is not only competitive but also outperforms existing weight normalization techniques from the literature.

We present weight normalization: a reparameterization of the weight vectors in a neural network that decouples the length of those weight vectors from their direction. By reparameterizing the weights in this way we improve the conditioning of the optimization problem and we speed up convergence of stochastic gradient descent. Our reparameterization is inspired by batch normalization but does not introduce any dependencies between the examples in a minibatch. This means that our method can also be applied successfully to recurrent models such as LSTMs and to noise-sensitive applications such as deep reinforcement learning or generative models, for which batch normalization is less well suited. Although our method is much simpler, it still provides much of the speed-up of full batch normalization. In addition, the computational overhead of our method is lower, permitting more optimization steps to be taken in the same amount of time. We demonstrate the usefulness of our method on applications in supervised image recognition, generative modelling, and deep reinforcement learning.

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.

Subjective multi-turn dialogue tasks, such as emotional support, require conversational policies that adapt to evolving user states and optimize long-horizon interaction quality. However, reinforcement learning (RL) for such settings remains challenging due to the absence of reliable process supervision. Outcome-only training collapses credit assignment across turns into a single trajectory-level reward, while naïve turn-level group sampling incurs prohibitive rollout costs in interactive environments. We propose a critic-free and efficient RL algorithm named MAPO that leverages dense process feedback from a judge model and propagates long-horizon effects through Monte Carlo returns. To stabilize optimization, we introduce a mixed advantage estimator that combines turn-level normalization with batch-level normalization, enabling fine-grained yet scalable credit assignment. Across multiple subjective dialogue benchmarks, including EMPA, EmoBench, and EQ-Bench, and model scales ranging from 7B to 32B, our method consistently improves both training stability and final performance over outcome-only GRPO and single-level normalization baselines. On EMPA, we improve rates by up to 9 points and increase dialogue scores by as much as +43.2 over the 7B base model. Despite training only on EMPA-style environments, our approach generalizes well, yielding consistent improvements on unseen emotional-intelligence benchmarks, including up to +4 points on EmoBench and +3.5 on EQ-Bench. Together, these results demonstrate that dense process supervision combined with mixed-level normalization enables effective and scalable RL for subjective, open-ended multi-turn dialogue.

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.

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.

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

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

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

Machine learning models often perform poorly on subgroups that are underrepresented in the training data. Yet, little is understood on the variation in mechanisms that cause subpopulation shifts, and how algorithms generalize across such diverse shifts at scale. In this work, we provide a fine-grained analysis of subpopulation shift. We first propose a unified framework that dissects and explains common shifts in subgroups. We then establish a comprehensive benchmark of 20 state-of-the-art algorithms evaluated on 12 real-world datasets in vision, language, and healthcare domains. With results obtained from training over 10,000 models, we reveal intriguing observations for future progress in this space. First, existing algorithms only improve subgroup robustness over certain types of shifts but not others. Moreover, while current algorithms rely on group-annotated validation data for model selection, we find that a simple selection criterion based on worst-class accuracy is surprisingly effective even without any group information. Finally, unlike existing works that solely aim to improve worst-group accuracy (WGA), we demonstrate the fundamental tradeoff between WGA and other important metrics, highlighting the need to carefully choose testing metrics. Code and data are available at: https://github.com/YyzHarry/SubpopBench.

Agentic reinforcement learning (RL) has become a critical stage in the post-training of large language models. Existing critic-free, group-relative methods estimate policy advantages from multiple rollouts, avoiding the substantial memory overhead of conventional proximal policy optimization (PPO) and achieving strong performance on long-horizon interactive tasks. Despite their success, recent studies revealed three limitations: (1) Lack explicit value generalization and effective temporal credit assignment; (2) Suffer from potential advantage collapse in long-horizon complex tasks; (3) Require a costly trade-off between sampling budget and policy performance. In this work, we propose Single-rollout Autoregressive Policy Optimization (SAPO), a low-memory and compute-efficient framework in which the policy and value functions share a single autoregressive backbone. SAPO exploits the autoregressive structure of LLMs to produce policy and value predictions at distinct causal boundaries with shared parameters, while independently optimizing the PPO objectives and auxiliary on-policy SARSA objectives. To robustly estimate the contribution of each turn, we further introduce a trajectory-level generalized advantage estimator that combines lambda-returns with batch normalization. Experiments across ALFWorld and WebShop with Qwen2.5-1.5B/7B show that SAPO trains stably and outperforms PPO and GRPO by mean +15.1 and +12.1 percentage points, respectively, while eliminating the memory cost of a separate critic model and reducing per-iteration runtime by 33.2% over PPO.

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

It is well known that ensemble methods often provide enhanced performance in reinforcement learning. In this paper, we explore this concept further by using group-aided training within the distributional reinforcement learning paradigm. Specifically, we propose an extension to categorical reinforcement learning, where distributional learning targets are implicitly based on the total information gathered by an ensemble. We empirically show that this may lead to much more robust initial learning, a stronger individual performance level, and good efficiency on a per-sample basis.

Reinforcement learning with verifiable rewards improves reasoning, while the allocation of learning signal shapes which solutions remain accessible under repeated sampling. Group-relative objectives assign equal advantages to equally rewarded responses, making aggregate credit proportional to sampled mode frequency. We introduce Exploration-Preserving Policy Optimization (ExPPO), a lightweight advantage-shaping rule that redistributes credit using prompt-relative, length-normalized response surprisal and prompt pass rate. ExPPO combines bounded shaping with shared normalization to preserve verifier polarity and approximately maintain each prompt group's total absolute sequence-advantage mass. Our analysis characterizes response-level credit allocation alongside sampled mode updates, deriving local conditions for gains in entropy and correct-mode discovery. Experiments show improved in-domain and out-of-domain reasoning coverage, higher aggregate response accuracy, and strong coverage at large sampling budgets. A controlled multi-answer evaluation further demonstrates increased correct-mode yield and gains in diversity among verified-correct responses. Code is available at https://github.com/jinhangzhan/ExPPO

The advancement of large language models (LLMs) has made it difficult to differentiate human-written text from AI-generated text. Several AI-text detectors have been developed in response, which typically utilize a fixed global threshold (e.g., {\theta} = 0.5) to classify machine-generated text. However, we find that one universal threshold can fail to account for subgroup-specific distributional variations. For example, when using a fixed threshold, detectors make more false positive errors on shorter human-written text than longer, and more positive classifications on neurotic writing styles than open among long text. These discrepancies can lead to misclassification that disproportionately affects certain groups. We address this critical limitation by introducing FairOPT, an algorithm for group-specific threshold optimization in AI-generated content classifiers. Our approach partitions data into subgroups based on attributes (e.g., text length and writing style) and learns decision thresholds for each group, which enables careful balancing of performance and fairness metrics within each subgroup. In experiments with four AI text classifiers on three datasets, FairOPT enhances overall F1 score and decreases balanced error rate (BER) discrepancy across subgroups. Our framework paves the way for more robust and fair classification criteria in AI-generated output detection.

We systematically explored a spectrum of normalization algorithms related to Batch Normalization (BN) and propose a generalized formulation that simultaneously solves two major limitations of BN: (1) online learning and (2) recurrent learning. Our proposal is simpler and more biologically-plausible. Unlike previous approaches, our technique can be applied out of the box to all learning scenarios (e.g., online learning, batch learning, fully-connected, convolutional, feedforward, recurrent and mixed --- recurrent and convolutional) and compare favorably with existing approaches. We also propose Lp Normalization for normalizing by different orders of statistical moments. In particular, L1 normalization is well-performing, simple to implement, fast to compute, more biologically-plausible and thus ideal for GPU or hardware implementations.

Developing Large Language Models (LLMs) to cooperate and compete effectively within multi-agent systems is a critical step towards more advanced intelligence. While reinforcement learning (RL) has proven effective for enhancing reasoning in single-agent tasks, its extension to multi-turn, multi-agent scenarios remains underexplored due to the challenges of long-horizon credit assignment and agent-specific advantage estimation. To address these challenges, we introduce MARS, an end-to-end RL framework that incentivizes Multi-Agent Reasoning of LLMs through Self-play in both cooperative and competitive games. MARS features a turn-level advantage estimator that aligns learning signals with each interaction for credit assignment, and an agent-specific advantage normalization to stabilize multi-agent training. By learning with self-play across cooperative and competitive games, the MARS agent trained from Qwen3-4B develops strong strategic abilities that generalize to held-out games with up to 28.7% performance improvements. More importantly, the capability acquired through self-play generalizes beyond games, yielding consistent performance gains of multi-agent systems in reasoning benchmarks. When integrated into leading multi-agent systems, our MARS agent achieves significant performance gains of 10.0% on AIME and 12.5% on GPQA-Diamond. These results establish end-to-end RL training with self-play in strategic games as a powerful approach for developing generalizable multi-agent reasoning capabilities in LLMs. Our code and models are publicly available at https://github.com/thu-nics/MARS.

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

Overparameterized neural networks can be highly accurate on average on an i.i.d. test set yet consistently fail on atypical groups of the data (e.g., by learning spurious correlations that hold on average but not in such groups). Distributionally robust optimization (DRO) allows us to learn models that instead minimize the worst-case training loss over a set of pre-defined groups. However, we find that naively applying group DRO to overparameterized neural networks fails: these models can perfectly fit the training data, and any model with vanishing average training loss also already has vanishing worst-case training loss. Instead, the poor worst-case performance arises from poor generalization on some groups. By coupling group DRO models with increased regularization---a stronger-than-typical L2 penalty or early stopping---we achieve substantially higher worst-group accuracies, with 10-40 percentage point improvements on a natural language inference task and two image tasks, while maintaining high average accuracies. Our results suggest that regularization is important for worst-group generalization in the overparameterized regime, even if it is not needed for average generalization. Finally, we introduce a stochastic optimization algorithm, with convergence guarantees, to efficiently train group DRO models.

We study the problem of online prediction, in which at each time step t, an individual x_t arrives, whose label we must predict. Each individual is associated with various groups, defined based on their features such as age, sex, race etc., which may intersect. Our goal is to make predictions that have regret guarantees not just overall but also simultaneously on each sub-sequence comprised of the members of any single group. Previous work such as [Blum & Lykouris] and [Lee et al] provide attractive regret guarantees for these problems; however, these are computationally intractable on large model classes. We show that a simple modification of the sleeping experts technique of [Blum & Lykouris] yields an efficient reduction to the well-understood problem of obtaining diminishing external regret absent group considerations. Our approach gives similar regret guarantees compared to [Blum & Lykouris]; however, we run in time linear in the number of groups, and are oracle-efficient in the hypothesis class. This in particular implies that our algorithm is efficient whenever the number of groups is polynomially bounded and the external-regret problem can be solved efficiently, an improvement on [Blum & Lykouris]'s stronger condition that the model class must be small. Our approach can handle online linear regression and online combinatorial optimization problems like online shortest paths. Beyond providing theoretical regret bounds, we evaluate this algorithm with an extensive set of experiments on synthetic data and on two real data sets -- Medical costs and the Adult income dataset, both instantiated with intersecting groups defined in terms of race, sex, and other demographic characteristics. We find that uniformly across groups, our algorithm gives substantial error improvements compared to running a standard online linear regression algorithm with no groupwise regret guarantees.

Critic-free reinforcement learning methods, particularly group policies, have attracted considerable attention for their efficiency in complex tasks. However, these methods rely heavily on multiple sampling and comparisons within the policy to estimate advantage, which may cause the policy to fall into local optimum and increase computational cost. To address these issues, we propose PVPO, an efficient reinforcement learning method enhanced by an advantage reference anchor and data pre-sampling. Specifically, we use the reference model to rollout in advance and employ the calculated reward score as a reference anchor. Our approach effectively corrects the cumulative bias introduced by intra-group comparisons and significantly reduces reliance on the number of rollouts during training. Meanwhile, the reference model can assess sample difficulty during data pre-sampling, enabling effective selection of high-gain data to improve training efficiency. Moreover, PVPO is orthogonal to other advanced critic-free RL algorithms, making it compatible with and complementary to these methods. Experiments conducted on nine datasets across two domains demonstrate that PVPO achieves State-Of-The-Art (SOTA) performance. Our approach not only demonstrates robust generalization across multiple tasks, but also exhibits scalable performance across models of varying scales.

Standard policy gradients weight each sampled action by advantage alone, regardless of how likely that action was under the current policy. This creates two pathologies: within a single decision context (e.g. one image or prompt), a rare negative-advantage action can disproportionately distort the update direction; across many such contexts in a batch, the expected gradient over-allocates budget to contexts the policy already handles well. We introduce the Delightful Policy Gradient (DG), which gates each term with a sigmoid of delight, the product of advantage and action surprisal (negative log-probability). For K-armed bandits, DG provably improves directional accuracy in a single context and, across multiple contexts, shifts the expected gradient strictly closer to the supervised cross-entropy oracle. This second effect is not variance reduction: it persists even with infinite samples. Empirically, DG outperforms REINFORCE, PPO, and advantage-weighted baselines across MNIST, transformer sequence modeling, and continuous control, with larger gains on harder tasks.

Group-based policy optimization methods like GRPO and GSPO have become standard for training multimodal models, leveraging group-wise rollouts and relative advantage estimation. However, they suffer from a critical gradient vanishing problem when all responses within a group receive identical rewards, causing advantage estimates to collapse and training signals to diminish. Existing attempts to mitigate this issue fall into two paradigms: filtering-based and sampling-based methods. Filtering-based methods first generate rollouts broadly and then retroactively filter out uninformative groups, leading to substantial computational overhead. Sampling-based methods proactively select effective samples before rollout but rely on static criteria or prior dataset knowledge, lacking real-time adaptability. To address these issues, we propose VADE, a Variance-Aware Dynamic sampling framework via online sample-level difficulty Estimation. Our framework integrates three key components: online sample-level difficulty estimation using Beta distributions, a Thompson sampler that maximizes information gain through the estimated correctness probability, and a two-scale prior decay mechanism that maintains robust estimation under policy evolution. This three components design enables VADE to dynamically select the most informative samples, thereby amplifying training signals while eliminating extra rollout costs. Extensive experiments on multimodal reasoning benchmarks show that VADE consistently outperforms strong baselines in both performance and sample efficiency, while achieving a dramatic reduction in computational overhead. More importantly, our framework can serves as a plug-and-play component to be seamlessly integrated into existing group-based RL algorithms. Code and models are available at https://VADE-RL.github.io.

Modern Text-to-SQL systems generate multiple candidate SQL queries and rank them to judge a final prediction. However, existing methods face two limitations. First, they often score functionally equivalent SQL queries inconsistently despite identical execution results. Second, ranking cannot recover when the correct SQL is absent from the candidate pool. We propose R^3-SQL, a Text-to-SQL framework that addresses both issues through unified reward for ranking and resampling. R^3-SQL first groups candidates by execution result and ranks groups for consistency. To score each group, it combines a pairwise preference across groups with a pointwise utility from the best group rank and size, capturing relative preference, consistency, and candidate quality. To improve candidate recall, R^3-SQL introduces agentic resampling, which judges the generated candidate pool and selectively resamples when the correct SQL is likely absent. R^3-SQL achieves 75.03 execution accuracy on BIRD-dev, a new state of the art among methods using models with disclosed sizes, with consistent gains across five benchmarks.

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

Dataset Distillation aims to compress a large dataset into a small synthetic one while maintaining predictive performance. We show that as different demographic groups exhibit distinct predictive patterns, the distillation process struggles to simultaneously preserve informative signals for all subgroups, regardless of whether group sizes are mildly or severely imbalanced. Consequently, models trained on distilled data can experience substantial performance drops for certain subgroups, leading to fairness gaps. Crucially, these gaps do not disappear by merely correcting group imbalance, since they stem from fundamental mismatches in subgroup predictive patterns rather than from sample-size disparities alone. We therefore formally analyze the interaction between these two sources of bias and cast the solution as identifying a group-imbalance-agnostic barycenter of the predictive information that induces similar representations across all subgroups. By distilling toward this shared aggregate representation, we show that group fairness concerns can be reduced. Our approach is compatible with existing distillation methods, and empirical results show that it substantially reduces bias introduced by dataset distillation.

Conformal prediction is often calibrated with a single pooled threshold, but this can hide cross-group heterogeneity in score distributions and distort group-wise coverage. We study this phenomenon through the population score distributions underlying split conformal calibration. First, we derive a conservation law and lower bound showing that pooled calibration incurs irreducible group-wise coverage distortion at a scale set by cross-group quantile heterogeneity. Second, we demonstrate that the two leading fairness definitions for conformal prediction, Equalized Coverage and Equalized Set Size, are fundamentally in tension. Third, we quantify the cost of moving between policies which treat groups separately or pool them. Experiments on synthetic and real data confirm the same bidirectional trade-off after finite-sample calibration. Our results show that, for the policy families studied here, calibration choice does not remove cross-group heterogeneity; it determines whether the resulting distortion appears in the coverage or size dimension, providing a principled lens for analyzing fairness-oriented calibration choices in practice.

Low-bit quantization is challenging to maintain high performance with limited model capacity (e.g., 4-bit for both weights and activations). Naturally, the distribution of both weights and activations in deep neural network are Gaussian-like. Nevertheless, due to the limited bitwidth of low-bit model, uniform-like distributed weights and activations have been proved to be more friendly to quantization while preserving accuracy~Han2015Learning. Motivated by this, we propose Scale-Clip, a Distribution Reshaping technique that can reshape weights or activations into a uniform-like distribution in a dynamic manner. Furthermore, to increase the model capability for a low-bit model, a novel Group-based Quantization algorithm is proposed to split the filters into several groups. Different groups can learn different quantization parameters, which can be elegantly merged in to batch normalization layer without extra computational cost in the inference stage. Finally, we integrate Scale-Clip technique with Group-based Quantization algorithm and propose the Group-based Distribution Reshaping Quantization (GDQR) framework to further improve the quantization performance. Experiments on various networks (e.g. VGGNet and ResNet) and vision tasks (e.g. classification, detection and segmentation) demonstrate that our framework achieves good performance.

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.

This work presents an information-theoretic perspective to group fairness trade-offs in federated learning (FL) with respect to sensitive attributes, such as gender, race, etc. Existing works often focus on either global fairness (overall disparity of the model across all clients) or local fairness (disparity of the model at each client), without always considering their trade-offs. There is a lack of understanding regarding the interplay between global and local fairness in FL, particularly under data heterogeneity, and if and when one implies the other. To address this gap, we leverage a body of work in information theory called partial information decomposition (PID), which first identifies three sources of unfairness in FL, namely, Unique Disparity, Redundant Disparity, and Masked Disparity. We demonstrate how these three disparities contribute to global and local fairness using canonical examples. This decomposition helps us derive fundamental limits on the trade-off between global and local fairness, highlighting where they agree or disagree. We introduce the Accuracy and Global-Local Fairness Optimality Problem (AGLFOP), a convex optimization that defines the theoretical limits of accuracy and fairness trade-offs, identifying the best possible performance any FL strategy can attain given a dataset and client distribution. We also present experimental results on synthetic datasets and the ADULT dataset to support our theoretical findings.

When facing data with imbalanced classes or groups, practitioners follow an intriguing strategy to achieve best results. They throw away examples until the classes or groups are balanced in size, and then perform empirical risk minimization on the reduced training set. This opposes common wisdom in learning theory, where the expected error is supposed to decrease as the dataset grows in size. In this work, we leverage extreme value theory to address this apparent contradiction. Our results show that the tails of the data distribution play an important role in determining the worst-group-accuracy of linear classifiers. When learning on data with heavy tails, throwing away data restores the geometric symmetry of the resulting classifier, and therefore improves its worst-group generalization.

Reinforcement Learning (RL) enhances LLM reasoning, yet a paradox emerges as models scale: strong base models saturate standard benchmarks (e.g., MATH), yielding correct but homogeneous solutions. In such environments, the lack of failure cases causes the advantage signal in group-relative algorithms (e.g., GRPO) to vanish, driving policies into mode collapse. To address this, we propose Constrained Uniform Top-K Sampling (CUTS), a parameter-free decoding strategy enforcing structure-preserving exploration. Unlike standard sampling that follows model biases, CUTS flattens the local optimization landscape by sampling uniformly from constrained high-confidence candidates. We integrate this into Mixed-CUTS, a training framework synergizing exploitative and exploratory rollouts to amplify intra-group advantage variance. Experiments on Qwen3 models demonstrate that our approach prevents policy degeneration and significantly boosts out-of-domain generalization. Notably, Mixed-CUTS improves Pass@1 accuracy on the challenging AIME25 benchmark by up to 15.1% over standard GRPO, validating that maintaining diversity within the semantic manifold is critical for rigorous reasoning.

This paper presents a comprehensive evaluation of instance segmentation models with respect to real-world image corruptions as well as out-of-domain image collections, e.g. images captured by a different set-up than the training dataset. The out-of-domain image evaluation shows the generalization capability of models, an essential aspect of real-world applications and an extensively studied topic of domain adaptation. These presented robustness and generalization evaluations are important when designing instance segmentation models for real-world applications and picking an off-the-shelf pretrained model to directly use for the task at hand. Specifically, this benchmark study includes state-of-the-art network architectures, network backbones, normalization layers, models trained starting from scratch versus pretrained networks, and the effect of multi-task training on robustness and generalization. Through this study, we gain several insights. For example, we find that group normalization enhances the robustness of networks across corruptions where the image contents stay the same but corruptions are added on top. On the other hand, batch normalization improves the generalization of the models across different datasets where statistics of image features change. We also find that single-stage detectors do not generalize well to larger image resolutions than their training size. On the other hand, multi-stage detectors can easily be used on images of different sizes. We hope that our comprehensive study will motivate the development of more robust and reliable instance segmentation models.

As machine learning (ML) systems increasingly impact critical sectors such as hiring, financial risk assessments, and criminal justice, the imperative to ensure fairness has intensified due to potential negative implications. While much ML fairness research has focused on enhancing training data and processes, addressing the outputs of already deployed systems has received less attention. This paper introduces 'BiasGuard', a novel approach designed to act as a fairness guardrail in production ML systems. BiasGuard leverages Test-Time Augmentation (TTA) powered by Conditional Generative Adversarial Network (CTGAN), a cutting-edge generative AI model, to synthesize data samples conditioned on inverted protected attribute values, thereby promoting equitable outcomes across diverse groups. This method aims to provide equal opportunities for both privileged and unprivileged groups while significantly enhancing the fairness metrics of deployed systems without the need for retraining. Our comprehensive experimental analysis across diverse datasets reveals that BiasGuard enhances fairness by 31% while only reducing accuracy by 0.09% compared to non-mitigated benchmarks. Additionally, BiasGuard outperforms existing post-processing methods in improving fairness, positioning it as an effective tool to safeguard against biases when retraining the model is impractical.

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 foundation models, such as Group Relative Policy Optimization (GRPO), have significantly improved the performance of foundation models on reasoning tasks. Notably, the advantage function serves as a central mechanism in GRPO for ranking the trajectory importance. However, existing explorations encounter both advantage reversion and advantage mirror problems, which hinder the reasonable advantage allocation across different query samples. In this work, we propose an easy but effective GRPO strategy, Mixed Advantage Policy Optimization (MAPO). We reveal that the trajectory appears with different certainty and propose the advantage percent deviation for samples with high-certainty trajectories. Furthermore, we dynamically reweight the advantage function for samples with varying trajectory certainty, thereby adaptively configuring the advantage function to account for sample-specific characteristics. Comparison with related state-of-the-art methods, along with ablation studies on different advantage variants, validates the effectiveness of our approach.

Most competitive 4-bit LLM research pipelines now open the same way: apply a linear, function-preserving transform (rotation, scaling, permutation, non-orthogonal affine) so the outlier mass sits more favorably against the group scales, and only then round. Yet we are aware of no survey dedicated to this transform stage, and its literature is quietly re-deriving an older theory. We identify and formalize the principle that organizes it, the Great Inversion: allocation-flexible coding rewards energy concentration, whereas the grouped shared-scale quantization a deployed matrix instruction performs rewards within-group flattening. Classical transform coding (1963: decorrelate, allocate bits, quantize) spends different bits per coordinate at a fixed total rate; for a Gaussian source at high rate the Karhunen-Loeve transform's concentration minimizes distortion. A deployed operand tile instead carries one absolute-maximum scale per group and equal bits everywhere, with no allocation; on a uniform grid that objective rewards flattening, approached by Hadamard incoherence. We prove that opposition under within-group majorization: the prescriptions point in opposite directions, each backed by a proof against its own objective, and for a generic spectrum no optimality guarantee transfers. A second axis is the number format: the non-uniform FP4 grid makes flattening buy less, MXFP4's power-of-two block scale still rewards a rotation confined to that block, and NVFP4's mantissa-carrying scale largely removes that pull, so the target pole depends jointly on allocation regime and format. We survey 200 works to a June 2026 cutoff; classify 43 transform methods by structure, data-awareness, searched-versus-constructed, and runtime cost; record, where reported, how they compose with GPTQ rounding; distill a first-choice guide by deployment regime; and close with the open problems it exposes.

We present a general framework for symmetrizing an arbitrary neural-network architecture and making it equivariant with respect to a given group. We build upon the proposals of Kim et al. (2023); Kaba et al. (2023) for symmetrization, and improve them by replacing their conversion of neural features into group representations, with an optimization whose loss intuitively measures the distance between group orbits. This change makes our approach applicable to a broader range of matrix groups, such as the Lorentz group O(1, 3), than these two proposals. We experimentally show our method's competitiveness on the SO(2) image classification task, and also its increased generality on the task with O(1, 3). Our implementation will be made accessible at https://github.com/tiendatnguyen-vision/Orbit-symmetrize.

We aim to improve model performance in multi-reward reinforcement learning training process. Existing Group reward-Decoupled Normalization Policy Optimization (GDPO) has mitigated the issue of reward signals masking one another during direct scalarization by normalizing each reward dimension separately before aggregation. However, our experiments show that GDPO still struggles to balance reward signals with different granularities. Specifically, in some particular training tasks, the model may receive a dense reward that assigns fine-grained scores ranging from 0.1 to 1.0, together with a sparse reward that provides only binary feedback of either 0 or 1. In such cases, we find that the sparse reward may provide an insufficient optimization signal, preventing its corresponding capability from being effectively reinforced. Therefore, how can we strengthen the optimization signal from the sparse reward without sacrificing the capability already learned from the fine-grained reward? To overcome this limitation, we propose Specialize-and-Merge Online Policy Distillation (SMOPD), a two-stage training method for multi-reward optimization. Stage1-Specialize: SMOPD first employs reward-priority configurations to train multiple reward-specialized teachers, allowing each reward to be learned under conditions where its signal can effectively drive optimization. Stage2-Merge: SMOPD then utilizes online policy distillation to combine the reward-specialized capabilities of these teachers into a single student policy, while maintaining balanced task-level optimization. To validate our method, we conduct experiments on two multi-reward settings: complementary rewards(tool-calling accuracy and format) and conflicting rewards (helpful and harmless rewards). Based on above settings, SMOPD outperforms GDPO across 1.5B, 3B and 7B backbones.

We consider the problem of subset selection where one is given multiple rankings of items and the goal is to select the highest ``quality'' subset. Score functions from the multiwinner voting literature have been used to aggregate rankings into quality scores for subsets. We study this setting of subset selection problems when, in addition, rankings may contain systemic or unconscious biases toward a group of items. For a general model of input rankings and biases, we show that requiring the selected subset to satisfy group fairness constraints can improve the quality of the selection with respect to unbiased rankings. Importantly, we show that for fairness constraints to be effective, different multiwinner score functions may require a drastically different number of rankings: While for some functions, fairness constraints need an exponential number of rankings to recover a close-to-optimal solution, for others, this dependency is only polynomial. This result relies on a novel notion of ``smoothness'' of submodular functions in this setting that quantifies how well a function can ``correctly'' assess the quality of items in the presence of bias. The results in this paper can be used to guide the choice of multiwinner score functions for the subset selection setting considered here; we additionally provide a tool to empirically enable this.

Mixture-of-Experts (MoE) language models are universally sensitive to demographic content at the routing level, yet exploiting this sensitivity for fairness control is structurally limited. We introduce Fairness-Aware Routing Equilibrium (FARE), a diagnostic framework designed to probe the limits of routing-level stereotype intervention across diverse MoE architectures. FARE reveals that routing-level preference shifts are either unachievable (Mixtral, Qwen1.5, Qwen3), statistically non-robust (DeepSeekMoE), or accompanied by substantial utility cost (OLMoE, -4.4%p CrowS-Pairs at -6.3%p TQA). Critically, even where log-likelihood preference shifts are robust, they do not transfer to decoded generation: expanded evaluations on both non-null models yield null results across all generation metrics. Group-level expert masking reveals why: bias and core knowledge are deeply entangled within expert groups. These findings indicate that routing sensitivity is necessary but insufficient for stereotype control, and identify specific architectural conditions that can inform the design of more controllable future MoE systems.

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.

Training state-of-the-art, deep neural networks is computationally expensive. One way to reduce the training time is to normalize the activities of the neurons. A recently introduced technique called batch normalization uses the distribution of the summed input to a neuron over a mini-batch of training cases to compute a mean and variance which are then used to normalize the summed input to that neuron on each training case. This significantly reduces the training time in feed-forward neural networks. However, the effect of batch normalization is dependent on the mini-batch size and it is not obvious how to apply it to recurrent neural networks. In this paper, we transpose batch normalization into layer normalization by computing the mean and variance used for normalization from all of the summed inputs to the neurons in a layer on a single training case. Like batch normalization, we also give each neuron its own adaptive bias and gain which are applied after the normalization but before the non-linearity. Unlike batch normalization, layer normalization performs exactly the same computation at training and test times. It is also straightforward to apply to recurrent neural networks by computing the normalization statistics separately at each time step. Layer normalization is very effective at stabilizing the hidden state dynamics in recurrent networks. Empirically, we show that layer normalization can substantially reduce the training time compared with previously published techniques.

In this paper, we present a novel end-to-end group collaborative learning network, termed GCoNet+, which can effectively and efficiently (250 fps) identify co-salient objects in natural scenes. The proposed GCoNet+ achieves the new state-of-the-art performance for co-salient object detection (CoSOD) through mining consensus representations based on the following two essential criteria: 1) intra-group compactness to better formulate the consistency among co-salient objects by capturing their inherent shared attributes using our novel group affinity module (GAM); 2) inter-group separability to effectively suppress the influence of noisy objects on the output by introducing our new group collaborating module (GCM) conditioning on the inconsistent consensus. To further improve the accuracy, we design a series of simple yet effective components as follows: i) a recurrent auxiliary classification module (RACM) promoting model learning at the semantic level; ii) a confidence enhancement module (CEM) assisting the model in improving the quality of the final predictions; and iii) a group-based symmetric triplet (GST) loss guiding the model to learn more discriminative features. Extensive experiments on three challenging benchmarks, i.e., CoCA, CoSOD3k, and CoSal2015, demonstrate that our GCoNet+ outperforms the existing 12 cutting-edge models. Code has been released at https://github.com/ZhengPeng7/GCoNet_plus.

Speech models may be affected by performance imbalance in different population subgroups, raising concerns about fair treatment across these groups. Prior attempts to mitigate unfairness either focus on user-defined subgroups, potentially overlooking other affected subgroups, or do not explicitly improve the internal representation at the subgroup level. This paper proposes the first adoption of contrastive learning to mitigate speech model bias in underperforming subgroups. We employ a three-level learning technique that guides the model in focusing on different scopes for the contrastive loss, i.e., task, subgroup, and the errors within subgroups. The experiments on two spoken language understanding datasets and two languages demonstrate that our approach improves internal subgroup representations, thus reducing model bias and enhancing performance.

While deep learning models have shown remarkable performance in various tasks, they are susceptible to learning non-generalizable spurious features rather than the core features that are genuinely correlated to the true label. In this paper, beyond existing analyses of linear models, we theoretically examine the learning process of a two-layer nonlinear convolutional neural network in the presence of spurious features. Our analysis suggests that imbalanced data groups and easily learnable spurious features can lead to the dominance of spurious features during the learning process. In light of this, we propose a new training algorithm called PDE that efficiently enhances the model's robustness for a better worst-group performance. PDE begins with a group-balanced subset of training data and progressively expands it to facilitate the learning of the core features. Experiments on synthetic and real-world benchmark datasets confirm the superior performance of our method on models such as ResNets and Transformers. On average, our method achieves a 2.8% improvement in worst-group accuracy compared with the state-of-the-art method, while enjoying up to 10x faster training efficiency.

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/.

Reinforcement learning (RL) paradigms have demonstrated strong performance on reasoning-intensive tasks such as code generation. However, limited trajectory diversity often leads to diminishing returns, which constrains the achievable performance ceiling. Search-enhanced RL alleviates this issue by introducing structured exploration, which remains constrained by the single-agent policy priors. Meanwhile, leveraging multiple interacting policies can acquire more diverse exploratory signals, but existing approaches are typically decoupled from structured search. We propose MARS^2 (Multi-Agent Reinforced Tree-Search Scaling), a unified RL framework in which multiple independently-optimized agents collaborate within a shared tree-structured search environment. MARS^2 models the search tree as a learnable multi-agent interaction environment, enabling heterogeneous agents to collaboratively generate and refine candidate solutions within a shared search topology. To support effective learning, we introduce a path-level group advantage formulation based on tree-consistent reward shaping, which facilitates effective credit assignment across complex search trajectories. Experiments on code generation benchmarks show that MARS^2 consistently improves performance across diverse model combinations and training settings, demonstrating the effectiveness of coupling multi-agent collaboration with tree search for enhancing reinforcement learning. Our code is publicly available at https://github.com/TsinghuaC3I/MARTI.

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.

Multi-agent LLM systems are often expected to improve as team size increases, yet the scaling behavior may depend on task structure. Our central contribution is to introduce Steiner's taxonomy of group tasks as a framework for analyzing multi-agent LLM scaling and focusing the analysis on disjunctive and compensatory tasks. We model independently sampled agents as conditionally independent given the item, which yields their large-team limits: plurality voting converges to the model's modal answer, and averaging converges to the model's item-level bias. Across selected representative benchmarks, 13 open-weight models, and teams of up to 30 agents, we find qualitatively different scaling behavior. On disjunctive tasks, the probability that at least one agent is correct grows by 5-20 points with team size, but plurality voting over agents that answer directly realises almost none of this potential, as the model predicts to within 0.5 points on average. Multi-round revision raises accuracy considerably, yet the gain is nearly the same with one peer as with 29. In contrast, scaling provides little benefit on Fermi estimation, despite its natural suitability for aggregation: item-level biases shared across the samples of a model account for about 87% of the squared error, so averaging reduces error by only about 6%. Combining model families helps on Fermi estimation but does not surpass the strongest member on disjunctive tasks. These results show that task structure, together with the mechanism combining member outputs, is a fundamental determinant of team scaling.

The number of groups (g) in group convolution (GConv) is selected to boost the predictive performance of deep neural networks (DNNs) in a compute and parameter efficient manner. However, we show that naive selection of g in GConv creates an imbalance between the computational complexity and degree of data reuse, which leads to suboptimal energy efficiency in DNNs. We devise an optimum group size model, which enables a balance between computational cost and data movement cost, thus, optimize the energy-efficiency of DNNs. Based on the insights from this model, we propose an "energy-efficient group convolution" (E2GC) module where, unlike the previous implementations of GConv, the group size (G) remains constant. Further, to demonstrate the efficacy of the E2GC module, we incorporate this module in the design of MobileNet-V1 and ResNeXt-50 and perform experiments on two GPUs, P100 and P4000. We show that, at comparable computational complexity, DNNs with constant group size (E2GC) are more energy-efficient than DNNs with a fixed number of groups (FgGC). For example, on P100 GPU, the energy-efficiency of MobileNet-V1 and ResNeXt-50 is increased by 10.8% and 4.73% (respectively) when E2GC modules substitute the FgGC modules in both the DNNs. Furthermore, through our extensive experimentation with ImageNet-1K and Food-101 image classification datasets, we show that the E2GC module enables a trade-off between generalization ability and representational power of DNN. Thus, the predictive performance of DNNs can be optimized by selecting an appropriate G. The code and trained models are available at https://github.com/iithcandle/E2GC-release.

This paper presents a whitening-based contrastive learning method for sentence embedding learning (WhitenedCSE), which combines contrastive learning with a novel shuffled group whitening. Generally, contrastive learning pulls distortions of a single sample (i.e., positive samples) close and push negative samples far away, correspondingly facilitating the alignment and uniformity in the feature space. A popular alternative to the "pushing'' operation is whitening the feature space, which scatters all the samples for uniformity. Since the whitening and the contrastive learning have large redundancy w.r.t. the uniformity, they are usually used separately and do not easily work together. For the first time, this paper integrates whitening into the contrastive learning scheme and facilitates two benefits. 1) Better uniformity. We find that these two approaches are not totally redundant but actually have some complementarity due to different uniformity mechanism. 2) Better alignment. We randomly divide the feature into multiple groups along the channel axis and perform whitening independently within each group. By shuffling the group division, we derive multiple distortions of a single sample and thus increase the positive sample diversity. Consequently, using multiple positive samples with enhanced diversity further improves contrastive learning due to better alignment. Extensive experiments on seven semantic textual similarity tasks show our method achieves consistent improvement over the contrastive learning baseline and sets new states of the art, e.g., 78.78\% (+2.53\% based on BERT\ba) Spearman correlation on STS tasks.

Recent studies, including DeepSeek-R1 and Kimi-k1.5, have demonstrated that reinforcement learning with rule-based, binary-valued reward functions can significantly enhance the reasoning capabilities of large language models. These models primarily utilize REINFORCE-based policy optimization techniques, such as REINFORCE with baseline and group relative policy optimization (GRPO). However, a key limitation remains: current policy optimization methods either neglect reward normalization or employ static normalization strategies, which fail to adapt to the dynamic nature of policy updates during training. This may result in unstable gradient estimates and hinder training stability. To address this issue, we propose Beta Normalization Policy Optimization (BNPO), a novel policy optimization method that adaptively normalizes rewards using a Beta distribution with dynamically updated parameters. BNPO aligns the normalization with the changing policy distribution, enabling more precise and lower-variance gradient estimation, which in turn promotes stable training dynamics. We provide theoretical analysis demonstrating BNPO's variance-reducing properties and show that it generalizes both REINFORCE and GRPO under binary-valued reward settings. Furthermore, we introduce an advantage decomposition mechanism to extend BNPO's applicability to more complex reward systems. Experimental results confirm that BNPO achieves state-of-the-art performance among policy optimization methods on reasoning tasks. The code is available at https://github.com/changyi7231/BNPO.

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.

LLM-based multi-agent systems excel at planning, tool use, and role coordination, but their openness and interaction complexity also expose them to jailbreak, prompt-injection, and adversarial collaboration. Existing defenses fall into two lines: (i) self-verification that asks each agent to pre-filter unsafe instructions before execution, and (ii) external guard modules that police behaviors. The former often underperforms because a standalone agent lacks sufficient capacity to detect cross-agent unsafe chains and delegation-induced risks; the latter increases system overhead and creates a single-point-of-failure-once compromised, system-wide safety collapses, and adding more guards worsens cost and complexity. To solve these challenges, we propose AdvEvo-MARL, a co-evolutionary multi-agent reinforcement learning framework that internalizes safety into task agents. Rather than relying on external guards, AdvEvo-MARL jointly optimizes attackers (which synthesize evolving jailbreak prompts) and defenders (task agents trained to both accomplish their duties and resist attacks) in adversarial learning environments. To stabilize learning and foster cooperation, we introduce a public baseline for advantage estimation: agents within the same functional group share a group-level mean-return baseline, enabling lower-variance updates and stronger intra-group coordination. Across representative attack scenarios, AdvEvo-MARL consistently keeps attack-success rate (ASR) below 20%, whereas baselines reach up to 38.33%, while preserving-and sometimes improving-task accuracy (up to +3.67% on reasoning tasks). These results show that safety and utility can be jointly improved without relying on extra guard agents or added system overhead.

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.

Layer normalization (LN) is a widely adopted deep learning technique especially in the era of foundation models. Recently, LN has been shown to be surprisingly effective in federated learning (FL) with non-i.i.d. data. However, exactly why and how it works remains mysterious. In this work, we reveal the profound connection between layer normalization and the label shift problem in federated learning. To understand layer normalization better in FL, we identify the key contributing mechanism of normalization methods in FL, called feature normalization (FN), which applies normalization to the latent feature representation before the classifier head. Although LN and FN do not improve expressive power, they control feature collapse and local overfitting to heavily skewed datasets, and thus accelerates global training. Empirically, we show that normalization leads to drastic improvements on standard benchmarks under extreme label shift. Moreover, we conduct extensive ablation studies to understand the critical factors of layer normalization in FL. Our results verify that FN is an essential ingredient inside LN to significantly improve the convergence of FL while remaining robust to learning rate choices, especially under extreme label shift where each client has access to few classes.

Multimodal large language models (MLLMs) have become a prevailing paradigm for unified video perception. However, post-training on large multi-task datasets remains challenging, as existing reinforcement learning methods sample on-policy groups with few high-quality rollouts even with costly chain-of-thought (CoT) generation. In this paper, we study the sample efficiency and scalability of RL post-training for video MLLMs and introduce OraRL. We identify an overlooked role for annotations: Beyond scoring rollouts, each can enter its on-policy group as an oracle rollout, a direct positive optimization target. Direct oracle integration, however, is nontrivial: a high-reward oracle raises the group baseline and inverts otherwise positive policy advantages, a failure we term advantage inversion. At the core of OraRL is a decoupled advantage estimator: policy rollouts determine an oracle-free baseline, while the oracle-policy gap modulates both a directional gain and a separate detached oracle advantage. Sign-balanced pruning improves efficiency: by retaining only the oracle and the strongest rollouts of each sign, OraRL requires just 2.2x the step time of SFT, less than half the 4.9x required by GRPO with CoT. OraRL scales with model size and data, surpassing its backbone from 0.8B to 9B and GRPO up to 100k prompts. Without chain-of-thought, Video-ORA-9B decodes in 130 ms instead of 4,780 ms. Compared with the respective prior best models, it raises temporal mIoU from 62.5 to 66.0, tracking AO from 73.0 to 78.2, segmentation from 64.3 to 70.4, and the three-benchmark spatial-intelligence macro average from 51.0 to 56.1; on VSI-Bench, it scores 73.1 against 55.0 for GPT-5 and 55.1 for Gemini-3-Pro.

In machine learning systems, bias mitigation approaches aim to make outcomes fairer across privileged and unprivileged groups. Bias mitigation methods work in different ways and have known "waterfall" effects, e.g., mitigating bias at one place may manifest bias elsewhere. In this paper, we aim to characterise impacted cohorts when mitigation interventions are applied. To do so, we treat intervention effects as a classification task and learn an explainable meta-classifier to identify cohorts that have altered outcomes. We examine a range of bias mitigation strategies that work at various stages of the model life cycle. We empirically demonstrate that our meta-classifier is able to uncover impacted cohorts. Further, we show that all tested mitigation strategies negatively impact a non-trivial fraction of cases, i.e., people who receive unfavourable outcomes solely on account of mitigation efforts. This is despite improvement in fairness metrics. We use these results as a basis to argue for more careful audits of static mitigation interventions that go beyond aggregate metrics.

Reinforcement learning has significantly enhanced the reasoning capabilities of Large Language Models (LLMs) in complex problem-solving tasks. Recently, the introduction of DeepSeek R1 has inspired a surge of interest in leveraging rule-based rewards as a low-cost alternative for computing advantage functions and guiding policy optimization. However, a common challenge observed across many replication and extension efforts is that when multiple sampled responses under a single prompt converge to identical outcomes, whether correct or incorrect, the group-based advantage degenerates to zero. This leads to vanishing gradients and renders the corresponding samples ineffective for learning, ultimately limiting training efficiency and downstream performance. To address this issue, we propose a consistency-aware policy optimization framework that introduces a structured global reward based on outcome consistency, the global loss based on it ensures that, even when model outputs show high intra-group consistency, the training process still receives meaningful learning signals, which encourages the generation of correct and self-consistent reasoning paths from a global perspective. Furthermore, we incorporate an entropy-based soft blending mechanism that adaptively balances local advantage estimation with global optimization, enabling dynamic transitions between exploration and convergence throughout training. Our method introduces several key innovations in both reward design and optimization strategy. We validate its effectiveness through substantial performance gains on multiple mathematical reasoning benchmarks, highlighting the proposed framework's robustness and general applicability. Code of this work has been released at https://github.com/hijih/copo-code.git.

Large reasoning models improve with more test-time computation, but often overthink, producing unnecessarily long chains-of-thought that raise cost without improving accuracy. Prior reinforcement learning approaches typically rely on a single outcome reward with trajectory-level length penalties, which cannot distinguish essential from redundant reasoning steps and therefore yield blunt compression. Although recent work incorporates step-level signals, such as offline pruning, supervised data construction, or verifier-based intermediate rewards, reasoning length is rarely treated as an explicit step-level optimization objective during RL. We propose Step-wise Adaptive Penalization (SWAP), a fine-grained framework that allocates length reduction across steps based on intrinsic contribution. We estimate step importance from the model's on-policy log-probability improvement toward the correct answer, then treat excess length as a penalty mass redistributed to penalize low-importance steps more heavily while preserving high-importance reasoning. We optimize with a unified outcome-process advantage within group-relative policy optimization. Extensive experiments demonstrate that SWAP reduces reasoning length by 64.3% on average while improving accuracy by 5.7% relative to the base model.

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.

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.

High memory demands of generative language models have drawn attention to quantization, which reduces computational cost, memory usage, and latency by mapping model weights to lower-precision integers. Approaches such as GPTQ effectively minimize input-weight product errors during quantization; however, recent empirical studies show that they can increase biased outputs and degrade performance on fairness benchmarks, and it remains unclear which specific weights cause this issue. In this work, we draw new links between quantization and model fairness by adding explicit group-fairness constraints to the quantization objective and introduce Fair-GPTQ, the first quantization method explicitly designed to reduce unfairness in large language models. The added constraints guide the learning of the rounding operation toward less-biased text generation for protected groups. Specifically, we focus on stereotype generation involving occupational bias and discriminatory language spanning gender, race, and religion. Fair-GPTQ has minimal impact on performance, preserving at least 90% of baseline accuracy on zero-shot benchmarks, reduces unfairness relative to a half-precision model, and retains the memory and speed benefits of 4-bit quantization. We also compare the performance of Fair-GPTQ with existing debiasing methods and find that it achieves performance on par with the iterative null-space projection debiasing approach on racial-stereotype benchmarks. Overall, the results validate our theoretical solution to the quantization problem with a group-bias term, highlight its applicability for reducing group bias at quantization time in generative models, and demonstrate that our approach can further be used to analyze channel- and weight-level contributions to fairness during quantization.

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

Recent 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.

Ensuring equitable treatment (fairness) across protected attributes (such as gender or ethnicity) is a critical issue in machine learning. Most existing literature focuses on binary classification, but achieving fairness in regression tasks-such as insurance pricing or hiring score assessments-is equally important. Moreover, anti-discrimination laws also apply to continuous attributes, such as age, for which many existing methods are not applicable. In practice, multiple protected attributes can exist simultaneously; however, methods targeting fairness across several attributes often overlook so-called "fairness gerrymandering", thereby ignoring disparities among intersectional subgroups (e.g., African-American women or Hispanic men). In this paper, we propose a distance covariance regularisation framework that mitigates the association between model predictions and protected attributes, in line with the fairness definition of demographic parity, and that captures both linear and nonlinear dependencies. To enhance applicability in the presence of multiple protected attributes, we extend our framework by incorporating two multivariate dependence measures based on distance covariance: the previously proposed joint distance covariance (JdCov) and our novel concatenated distance covariance (CCdCov), which effectively address fairness gerrymandering in both regression and classification tasks involving protected attributes of various types. We discuss and illustrate how to calibrate regularisation strength, including a method based on Jensen-Shannon divergence, which quantifies dissimilarities in prediction distributions across groups. We apply our framework to the COMPAS recidivism dataset and a large motor insurance claims dataset.

Reinforcement Learning with Verifiable Rewards (RLVR) can elicit strong multi-step reasoning, yet it often encourages overly verbose traces. Moreover, naive length penalties in group-relative optimization can severely hurt accuracy. We attribute this failure to two structural issues: (i) Dilution of Length Baseline, where incorrect responses (with zero length reward) depress the group baseline and over-penalize correct solutions; and (ii) Difficulty-Penalty Mismatch, where a static penalty cannot adapt to problem difficulty, suppressing necessary reasoning on hard instances while leaving redundancy on easy ones. We propose Dynamic Decoupled Conditional Advantage (DDCA) to decouple efficiency optimization from correctness. DDCA computes length advantages conditionally within the correct-response cluster to eliminate baseline dilution, and dynamically scales the penalty strength using the group pass rate as a proxy for difficulty. Experiments on GSM8K, MATH500, AMC23, and AIME25 show that DDCA consistently improves the efficiency--accuracy trade-off relative to adaptive baselines, reducing generated tokens by approximately 60% on simpler tasks (e.g., GSM8K) versus over 20% on harder benchmarks (e.g., AIME25), thereby maintaining or improving accuracy. Code is available at https://github.com/alphadl/DDCA.

We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs (y, g cdot y), where g is drawn from a finite group acting on the data. Our method jointly learns a latent space and a group representation in which group actions correspond to invertible linear maps -- without relying on group-specific inductive biases. We validate our approach on the infinite dSprites dataset with structured transformations defined by the finite group G:= (R_m times Z_n times Z_n), combining discrete rotations and periodic translations. The resulting embeddings exhibit high-fidelity equivariance, with group operations faithfully reproduced in latent space. On synthetic data, we further validate the approach on the non-abelian orthogonal group O(n) and the general linear group GL(n). We also provide a theoretical proof for identifiability. While broad evaluation across diverse group types on real-world data remains future work, our results constitute the first successful demonstration of general-purpose encoder-only equivariant learning from group action observations alone, including non-trivial non-abelian groups and a product group motivated by modeling affine equivariances in computer vision.

As neural networks become deeper, the redundancy within their parameters increases. This phenomenon has led to several methods that attempt to reduce the correlation between convolutional filters. We propose a computationally efficient regularization technique that encourages orthonormality between groups of filters within the same layer. Our experiments show that when incorporated into recent adaptation methods for diffusion models and vision transformers (ViTs), this regularization improves performance on downstream tasks. We further show improved robustness when group orthogonality is enforced during adversarial training. Our code is available at https://github.com/YoavKurtz/GOR.