RL for Language Model Reasoning

Reinforcement learning (RL) has emerged as a promising paradigm for training reasoning-oriented models by leveraging rule-based reward signals. However, RL training typically tends to improve single-sample success rates (i.e., Pass@1) while offering limited exploration of diverse reasoning trajectories, which is crucial for multi-sample performance (i.e., Pass@k). Our preliminary analysis reveals that this limitation stems from a fundamental squeezing effect, whereby probability mass is excessively concentrated on a narrow subset of high-reward trajectories, restricting genuine exploration and constraining attainable performance under RL training. To address this issue, in this work, we propose Steering Probability Squeezing (SPS), a training paradigm that interleaves conventional RL with inverse reinforcement learning (IRL). SPS treats on-policy rollouts as demonstrations and employs IRL to explicitly reshape the induced trajectory distribution, thereby enhancing exploration without introducing external supervision. Experiments on five commonly used reasoning benchmarks demonstrate that SPS can enable better exploration and improve Pass@k. Beyond algorithmic contributions, we provide an analysis of RL learning dynamics and identify an empirical upper bound on Pass@k, shedding light on intrinsic exploration limits in RL-based reasoning models. Our findings suggest that alternating between RL and IRL offers an effective pathway toward extending the exploration capacity of reasoning-oriented large language models.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising approach to improve the reasoning abilities of Large Language Models (LLMs). Among RLVR algorithms, Group Relative Policy Optimization (GRPO) and its variants have demonstrated strong performance and high training efficiency. However, GRPO-style objectives exhibit two issues on high accuracy prompts including mastered prompts (rollout accuracy =1) and majority-correct prompts (rollout accuracy in (0.5,1)). For mastered prompts, group-relative advantages vanish, yielding no training signal and unconstrained policy drift that can cause forgetting. For majority-correct prompts, the induced query weight shrinks as accuracy increases, weakening consolidation from partial correctness to mastery. To alleviate this, we propose Mastery-Consolidated Policy Optimization (MCPO), which introduces (i) a hinge-KL regularizer applied exclusively to mastered prompts to bound harmful policy drift between successive gradient steps, and (ii) a weighting mechanism that prioritizes majority-correct prompts to better allocate optimization effort. Extensive experiments across three mathematical benchmarks demonstrate that MCPO consistently improves pass@1 performance. Counter-intuitively, rather than restricting exploration, MCPO boosts pass@k metrics, indicating that mastery consolidation further catalyzes solution diversity.

Large reasoning models that use long chain-of-thought excel at problem-solving yet waste compute on redundant checks. Curbing this overthinking is hard: training-time length penalties can cripple ability, while inference-time early-exit adds system overhead. To bridge this gap, we propose Step-GRPO, a novel post-training framework that internalizes dynamic early-exit capabilities directly into the model. Step-GRPO shifts the optimization objective from raw tokens to semantic steps by utilizing linguistic markers to structure reasoning. We introduce a Dynamic Truncated Rollout mechanism that exposes the model to concise high-confidence trajectories during exploration, synergized with a Step-Aware Relative Reward that dynamically penalizes redundancy based on group-level baselines. Extensive experiments across three model sizes on diverse benchmarks demonstrate that Step-GRPO achieves a superior accuracy-efficiency trade-off. On Qwen3-8B, our method reduces token consumption by 32.0% compared to the vanilla model while avoiding the accuracy degradation observed in traditional length-penalty methods.

Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a primary bottleneck in informal theorem proving as a lack of insight, namely the difficulty of recognizing the core techniques required to solve complex problems. To address this, we propose $\texttt{DeepInsight}$, a unified training framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning. Our framework consists of three components: (1) $\texttt{DeepInsightTheorem}$, a hierarchical dataset that structures informal proofs by explicitly extracting core techniques and proof sketches alongside the final proof; (2) a Progressive Multi-Stage SFT strategy that mimics the human learning process, teaching the model proof writing, planning, and insight identification; and (3) $\texttt{InsightPO}$, a policy optimization method that assigns structured rewards over this insight hierarchy. Our experiments on challenging mathematical benchmarks demonstrate that this insight-aware generation strategy significantly outperforms baselines. These results demonstrate that teaching models to identify and apply core techniques can substantially improve their mathematical reasoning.

Frontier models have demonstrated exceptional capabilities following the integration of task-reward-based reinforcement learning (RL) into their training pipelines, enabling systems to evolve from pure reasoning models into sophisticated agents. However, debate persists regarding whether RL genuinely instills new skills within a base model or merely sharpens its existing distribution to elicit latent capabilities. To address this dichotomy, we present an explicit comparison between distribution sharpening and task-reward-based learning, utilizing RL as a tool to implement both paradigms. Our analysis reveals the inherent limitations of distribution sharpening, demonstrating from first principles how and why the optima can be unfavorable and the approach fundamentally unstable. Furthermore, our experiments using Llama-3.2-3B-Instruct, Qwen2.5-3B-Instruct and Qwen3-4B-Instruct-2507 on math datasets confirm that sharpening yields limited gains, whereas incorporating task-based reward signal can greatly help achieve robust performance improvements and stable learning.

Large language models (LLMs) increasingly rely on chain-of-thought (CoT) reasoning to solve complex tasks. Yet ensuring that the reasoning trace both contributes to and faithfully reflects the processes underlying the model's final answer, rather than merely accompanying it, remains challenging. We introduce AtManRL, a method that leverages differentiable attention manipulation to learn more faithful reasoning through reinforcement learning. By training an additive attention mask that identifies tokens in the CoT crucial for producing correct answers, we derive a saliency reward signal that encourages the model to generate reasoning traces that genuinely influence its final predictions. We integrate this saliency reward with outcome-based rewards within the GRPO framework to jointly optimize for correctness and interpretability. Experiments on GSM8K and MMLU with Llama-3.2-3B-Instruct demonstrate that our approach can identify influential reasoning tokens and enable training more transparent reasoning models.

Verifiers have been demonstrated to enhance LLM reasoning via test-time scaling (TTS). Yet, they face significant challenges in complex domains. Error propagation from incorrect intermediate reasoning can lead to false positives for seemingly plausible solutions, while lacking external grounding makes verifiers unreliable on computation or knowledge-intensive tasks. To address these challenges, we propose Agentic Verifier, a framework that transforms reward modeling into a multi-turn, tool-augmented deliberative process. We introduce complementary forward and backward agents: one traces solutions from premises to conclusions, while the other re-checks conclusions against their underlying premises. This bidirectional process enables a comprehensive, reliable, and interpretable assessment of solutions. To facilitate practical deployment, we propose AgentV-RL. Through proactive exploration and reinforcement learning, the verifier autonomously interleaves tool-use with internal reasoning. Extensive experiments show that Agentic Verifier yields consistent performance gains under both parallel and sequential TTS. Notably, our 4B variant surpasses state-of-the-art ORMs by 25.2%, positioning it as a promising paradigm for agentic reward modeling.

Reinforcement learning has become a powerful approach for enhancing large language model reasoning, but faces a fundamental dilemma: training on easy problems can cause overfitting and pass@k degradation, while training on hard problems often results in sparse rewards. Recent question augmentation methods address this by prepending partial solutions as hints. However, uniform hint provision may introduce redundant information while missing critical reasoning bottlenecks, and excessive hints can reduce reasoning diversity, causing pass@k degradation. We propose \textbf{PieceHint}, a hint injection framework that strategically identifies and provides critical reasoning steps during training. By scoring the importance of different reasoning steps, selectively allocating hints based on problem difficulty, and progressively withdrawing scaffolding, PieceHint enables models to transition from guided learning to independent reasoning. Experiments on six mathematical reasoning benchmarks show that our 1.5B model achieves comparable average performance to 32B baselines while preserving pass@k diversity across all $k$ values.

As reinforcement Learning with Verifiable Rewards (RLVR) has become the dominant paradigm for scaling reasoning capabilities in LLMs, a new failure mode emerges: LLMs gaming verifiers. We study this phenomenon on inductive reasoning tasks, where models must induce and output logical rules. We find that RLVR-trained models systematically abandon rule induction. Instead of learning generalizable patterns (e.g., ``trains carrying red cars go east''), they enumerate instance-level labels, producing outputs that pass verifiers without capturing the relational patterns required by the task. We show that this behavior is not a failure of understanding but a form of reward hacking: imperfect verifiers that check only extensional correctness admit false positives. To detect such shortcuts, we introduce Isomorphic Perturbation Testing (IPT), which evaluates a single model output under both extensional and isomorphic verification, where the latter enforces invariance under logically isomorphic tasks. While genuine rule induction remains invariant, shortcut strategies fail. We find that shortcut behavior is specific to RLVR-trained reasoning models (e.g., GPT-5, Olmo3) and absent in non-RLVR models (e.g., GPT-4o, GPT-4.5, Ministral). Moreover, shortcut prevalence increases with task complexity and inference-time compute. In controlled training experiments, extensional verification directly induces shortcut strategies, while isomorphic verification eliminates them. These results show that RLVR can incentivize reward hacking not only through overt manipulation but also by exploiting what the verifier fails to enforce.

Reinforcement learning has emerged as an effective paradigm for training large language models to perform search-augmented reasoning. However, existing approaches rely on trajectory-level rewards that cannot distinguish precise search queries from vague or redundant ones within a rollout group, and collapse to a near-zero gradient signal whenever every sampled trajectory fails. In this paper, we propose IG-Search, a reinforcement learning framework that introduces a step-level reward based on Information Gain (IG). For each search step, IG measures how much the retrieved documents improve the model's confidence in the gold answer relative to a counterfactual baseline of random documents, thereby reflecting the effectiveness of the underlying search query. This signal is fed back to the corresponding search-query tokens via per-token advantage modulation in GRPO, enabling fine-grained, step-level credit assignment within a rollout. Unlike prior step-level methods that require either externally annotated intermediate supervision or shared environment states across trajectories, IG-Search derives its signals from the policy's own generation probabilities, requiring no intermediate annotations beyond standard question-answer pairs. Experiments on seven single-hop and multi-hop QA benchmarks demonstrate that IG-Search achieves an average EM of 0.430 with Qwen2.5-3B, outperforming the strongest trajectory-level baseline (MR-Search) by 1.6 points and the step-level method GiGPO by 0.9 points on average across benchmarks, with particularly pronounced gains on multi-hop reasoning tasks. Despite introducing a dense step-level signal, IG-Search adds only ~6.4% to per-step training wall-clock time over the trajectory-level baseline and leaves inference latency unchanged, while still providing a meaningful gradient signal even when every sampled trajectory answers incorrectly.

Reinforcement Learning (RL) has emerged as a critical driver for enhancing the reasoning capabilities of Large Language Models (LLMs). While recent advancements have focused on reward engineering or data synthesis, few studies exploit the model's intrinsic representation characteristics to guide the training process. In this paper, we first observe the presence of high-magnitude activations within the query and key vectors when processing long contexts. Drawing inspiration from model quantization -- which establishes the criticality of such high-magnitude activations -- and the insight that long-context reasoning inherently exhibits a sparse structure, we hypothesize that these weights serve as the pivotal drivers for effective model optimization. Based on this insight, we propose LongAct, a strategy that shifts from uniform to saliency-guided sparse updates. By selectively updating only the weights associated with these significant activations, LongAct achieves an approximate 8% improvement on LongBench v2 and enhances generalization on the RULER benchmark. Furthermore, our method exhibits remarkable universality, consistently boosting performance across diverse RL algorithms such as GRPO and DAPO. Extensive ablation studies suggest that focusing on these salient features is key to unlocking long-context potential.

Recent advances in reinforcement learning (RL) have improved the reasoning capabilities of large language models (LLMs) and vision-language models (VLMs). However, the widely used Group Relative Policy Optimization (GRPO) consistently suffers from entropy collapse, causing the policy to converge prematurely and lose diversity. Existing exploration methods introduce additional bias or variance during exploration, making it difficult to maintain optimization stability. We propose Unified Entropy Control for Reinforcement Learning (UEC-RL), a framework that provides targeted mechanisms for exploration and stabilization. UEC-RL activates more exploration on difficult prompts to search for potential and valuable reasoning trajectories. In parallel, a stabilizer prevents entropy from growing uncontrollably, thereby keeping training stable as the model consolidates reliable behaviors. Together, these components expand the search space when needed while maintaining robust optimization throughout training. Experiments on both LLM and VLM reasoning tasks show consistent gains over RL baselines on both Pass@1 and Pass@$k$. On Geometry3K, UEC-RL achieves a 37.9% relative improvement over GRPO, indicating that it sustains effective exploration without compromising convergence and underscoring UEC-RL as a key for scaling RL-based reasoning in large models. Our code is available at https://github.com/597358816/UEC-RL.

Building general-purpose reasoning models using reinforcement learning with verifiable rewards (RLVR) across diverse domains has been widely adopted by frontier open-weight models. However, their training recipes and domain mixtures are often not disclosed. Joint optimization across domains poses significant challenges: domains vary widely in rollout length, problem difficulty, and sample efficiency. Further, models with long chain-of-thought traces increase inference cost and latency, making efficiency critical for practical deployment. We present Apriel-Reasoner, trained with a reproducible multi-domain RL post-training recipe on Apriel-Base, a 15B-parameter open-weight LLM, across five domains using public datasets: mathematics, code generation, instruction following, logical puzzles, and function calling. We introduce adaptive domain sampling that preserves target completed-rollout ratios despite heterogeneous rollout dynamics, and a difficulty-aware length penalty that, at no additional training overhead, encourages longer reasoning for difficult problems and shorter traces for easy ones. Trained with a strict 16K-token output budget, Apriel-Reasoner remains effective at a 32K output budget and improves over Apriel-Base on AIME 2025, GPQA, MMLU-Pro, and LiveCodeBench while producing 30-50% shorter reasoning traces. Among the evaluated open-weight models of similar scale, it improves the accuracy-token tradeoff using a fully public-data recipe.

Reinforcement learning has become a central post-training paradigm for improving LLM and agent capabilities. Yet existing RL post-training methods share a common blind spot: they construct local learning signals from sampled trajectories, rewards, or feedback-conditioned targets, then update the policy without explicitly verifying whether the resulting policy outperforms its predecessor. Optimizing these local signals does not necessarily produce a better policy, while finite sampling, generation stochasticity and feedback noise can further widen this gap. We argue that the missing ingredient is policy improvement feedback: the ability to measure progress across policy iterations. We introduce Policy Improvement Reinforcement Learning (PIRL), which formulates inter-iteration performance gain as an explicit objective structurally aligned with final task performance. Building on PIRL, we propose Policy Improvement Policy Optimization (PIPO), a plug-in closed-loop framework that verifies the previous update against a sliding-window historical performance anchor. PIPO uses this improvement feedback to modulate the local learning signal of the base policy optimization algorithm, reinforcing updates associated with measured progress and suppressing those associated with performance drops. We provide theoretical evidence that PIPO locally aligns policy updates with the PIRL improvement objective. Experiments on mathematical reasoning, code, tool-use, and self-distillation settings show that PIPO yields consistent gains across PPO, group-relative, and self-distillation policy optimization families.

While large language models (LLMs) have demonstrated strong performance on complex reasoning tasks such as competitive programming (CP), existing methods predominantly focus on single-attempt settings, overlooking their capacity for iterative refinement. In this paper, we present RefineRL, a novel approach designed to unleash the self-refinement capabilities of LLMs for CP problem solving. RefineRL introduces two key innovations: (1) Skeptical-Agent, an iterative self-refinement agent equipped with local execution tools to validate generated solutions against public test cases of CP problems. This agent always remains skeptical of its own outputs and thereby enforces rigorous self-refinement even when validation suggests correctness. (2) A reinforcement learning (RL) solution to incentivize LLMs to self-refine with only standard RLVR data (i.e., problems paired with their verifiable answers). Extensive experiments on Qwen3-4B and Qwen3-4B-2507 demonstrate that our method yields substantial gains: after our RL training, these compact 4B models integrated with the Skeptical-Agent not only outperform much larger 32B models but also approach the single-attempt performance of 235B models. Notably, although our models are trained solely on CP coding data, RefineRL also substantially improves their performance on mathematical reasoning benchmarks, suggesting that the learned self-refinement behavior can transfer beyond coding-specific tasks. These findings highlight self-refinement as a promising direction for scaling LLMs' general reasoning ability.

Acute poly-substance intoxication requires rapid, life-saving decisions under substantial uncertainty, as clinicians must rely on incomplete ingestion details and nonspecific symptoms. Effective diagnostic reasoning in this chaotic environment requires fusing unstructured, non-medical narratives (e.g. paramedic scene descriptions and unreliable patient self-reports or known histories), with structured medical data like vital signs. While Large Language Models (LLMs) show potential for processing such heterogeneous inputs, they struggle in this setting, often underperforming simple baselines that rely solely on patient histories. To address this, we present DeToxR (Decision-support for Toxicology with Reasoning), the first adaptation of Reinforcement Learning (RL) to emergency toxicology. We design a robust data-fusion engine for multi-label prediction across 14 substance classes based on an LLM finetuned with Group Relative Policy Optimization (GRPO). We optimize the model's reasoning directly using a clinical performance reward. By formulating a multi-label agreement metric as the reward signal, the model is explicitly penalized for missing co-ingested substances and hallucinating absent poisons. Our model significantly outperforms its unadapted base LLM counterpart and supervised baselines. Furthermore, in a preliminary clinical validation study, the model indicates a clinical advantage by achieving higher micro-F1 (0.644 vs 0.473) and recall in identifying the correct poisons. These results demonstrate the potential of RL-aligned LLMs to synthesize unstructured pre-clinical narratives and structured medical data for decision support in high-stakes environments.

Reinforcement Learning with Verifiable Rewards (RLVR) enhances Large Language Model (LLM) reasoning but is suffer from advantage collapse: when all rollouts of a query receive identical rewards, the group variance vanishes, most damagingly on hard samples, where scaling rollout budgets yields little. We introduce Joint Policy and Prompt Optimization (P O) to mitigate this collapse by alternating continuous policy updates with discrete prompt evolution. P O mines hard samples with a success-rate threshold, evolves reasoning prompts for them with GEPA, and internalizes the elicited trajectories via context distillation, which optimizes each trajectory under the original query and thus removes inference-time prompting, with a Context Ratio Mask (CRM) filtering out extreme likelihood ratios. P O restores critical advantage signals and surpasses the GRPO baseline by up to 8.2 points in average accuracy on six held-out benchmarks across all training datasets and backbones, while also outperforming DAPO and other baselines. The gains are especially pronounced on hard benchmarks, reaching up to 16.3 points above GRPO on average across AIME24 and AIME25. Our findings expose the limits of standard exploration in sparse-reward environments, illuminating the potential of unifying evolutionary algorithms with reinforcement learning. This integration of discrete semantic search and continuous parameter updates provides a self-reinforcing framework that facilitates more effective LLM alignment.

Conversational assistants powered by large language models (LLMs) excel at tool-use tasks but struggle with adhering to complex, business-specific rules. While models can reason over business rules provided in context, including all policies for every query introduces high latency and wastes compute. Furthermore, these lengthy prompts lead to long contexts, harming overall performance due to the 'needle-in-a-haystack' problem. To address these challenges, we propose a multi-stage alignment method that teaches models to recall and apply relevant business policies during chain-of-thought reasoning at inference time, without including the full business policy in-context. Furthermore, we introduce a novel Policy Recall reward based on the Jaccard score and a Hallucination Penalty for GRPO training. Altogether, our best model outperforms the baseline by 16 points and surpasses comparable in-context baselines of similar model size by 3 points, while using 40% fewer words.

Reinforcement Learning with Verifiable Rewards improves reasoning in large language models, yet on-policy learning often suffers from cold-start challenges in sparse-reward settings. Recent mixed-policy approaches address this by combining off-policy teacher data with on-policy training. However, simply combining these introduce a persistent off-policy gradient mass that risks training collapse and instability. To address this challenge, we propose Hindsight-Anchored Policy Optimization (HAPO), a framework that allows teacher intervention to act as a temporary support. HAPO employs Beta-Binomial confidence gating, an adaptive gating mechanism that decides when to open the gate for teacher intervention. The intervention operates with Synthetic Success Injection, which replaces the group's lowest-reward rollout with a verified teacher trajectory. We also introduce adaptive threshold annealing, which gradually retracts the support and restores on-policy training within a finite horizon to mitigate persistent off-policy drift. We demonstrate that HAPO can be layered on top of existing mixed-policy methods in a generalizable manner. Across six math reasoning benchmarks and two model scales, HAPO improves the average accuracy of three major mixed-policy methods while maintaining training stability.

Psychiatric consultation requires agents to elicit discriminative evidence, map uncertain narratives to diagnostic criteria, and decide when evidence suffices. Existing dialogue and retrieval-augmented systems condition policies on raw histories or appended passages, leaving observed evidence, missing checks, differentials, and support reliability entangled. We introduce MIND, a criteria-grounded evidence-state decision interface. At each turn, MIND constructs a typed state containing observed evidence, unresolved criterion checks, active differentials, criterion-linked supports, and reliability metadata. A training-split Psychiatric Reasoning Bank supplies gated supports, turning retrieval into state construction rather than prompt injection. The same state conditions action selection, process rewards, information-gain scoring, and trajectory rectification. Under EMR-grounded simulator protocols, MIND improves accuracy by 8.8 and 7.3 points over strong inference-only, RAG, and RL baselines, with gains transferring to public MDD-5k dialogues. Matched interventions attribute these gains to the shared state rather than prompt length, retrieval text, or formatting. MIND targets screening-level decision support, not autonomous diagnosis. Code is available at https://github.com/Lingxi-mental-health/MIND.Å

Reinforcement learning has emerged as an effective paradigm for training large language models to interleave reasoning with search engine calls. However, existing approaches face a fundamental credit assignment problem: methods like Search-R1 assign a single outcome reward to the entire multi-step trajectory, providing no signal about which reasoning or retrieval decisions were responsible for success or failure. Process-reward methods such as StepSearch introduce step-level supervision but still sample complete trajectories independently, so advantage estimates at any given step are contaminated by the randomness of all other steps. We propose SLATE (Step-Level Advantage estimation for Truncated Exploration), which addresses both problems through two complementary ideas. First, truncated step-level sampling generates k continuations from a shared prefix, isolating all variation to a single decision point. We prove this reduces the variance of advantage estimates by up to a factor of T compared to full-trajectory sampling for T-step trajectories, the first formal variance guarantee for step-level RL in retrieval-augmented reasoning. Second, dense, decomposed process rewards separately evaluate reasoning quality, query quality, and answer correctness on a ternary scale via an LLM judge, providing richer supervision than binary outcome signals or heuristic step-level scores. Experiments on seven QA benchmarks show that SLATE consistently outperforms both sparse-reward and process-reward baselines, achieving a 7.0% relative improvement over Search-R1 on the 7B model and 30.7% on the 3B model. Gains are largest on challenging multi-hop tasks, and ablations confirm that truncated sampling and dense rewards provide complementary benefits.

Time series reasoning tasks often start with a natural language question and require targeted analysis of a time series. Evidence may span the full series or appear in a few short intervals, so the model must decide what to inspect. Most existing approaches encode the entire time series into a fixed representation before inference, regardless of whether or not the entire sequence is relevant. We introduce ARTIST, which formulates time-series reasoning as a sequential decision problem. ARTIST interleaves reasoning with adaptive temporal segment selection. It adopts a controller-reasoner architecture and uses reinforcement learning to train the controller role to select informative segments and the reasoner role to generate segment-conditioned reasoning traces and final answers. During inference, the model actively acquires task-relevant information instead of relying on a static summary of the full sequence. We use a novel hierarchical policy optimization approach for post-training that allows the model to excel in both segment selection and question-answering behavior. We evaluate ARTIST on six time-series reasoning benchmarks and compare it with large language models, vision-language models, and prior time-series reasoning systems. ARTIST improves average accuracy by 6.46 absolute percentage points over the strongest baseline. The largest gains appear on rare event localization and multi-segment reasoning tasks. Supervised fine-tuning improves performance, and reinforcement learning provides additional gains by optimizing question-adaptive segment selection. These results show that selective data use drives effective time-series reasoning.

Reinforcement learning with verifiable rewards (RLVR) has been a main driver of recent breakthroughs in large reasoning models. Yet it remains a mystery how rewards based solely on final outcomes can help overcome the long-horizon barrier to extended reasoning. To understand this, we develop a theory of the training dynamics of RLVR for transformers on compositional reasoning tasks. Our theory shows that mixed-difficulty training naturally induces an implicit curriculum: without any explicit schedule, easier problems become learnable first and shape the frontier for harder ones, creating a learning progression from easy to hard during optimization. The effectiveness of this curriculum is governed by the smoothness of the difficulty spectrum. When the spectrum is smooth, training dynamics enter a well-behaved relay regime, in which persistent gradient signals on easier problems make slightly harder ones tractable and keep training at the edge of competence. When the spectrum contains abrupt discontinuities, training undergoes grokking-type phase transitions with prolonged plateaus before progress recurs. As a technical contribution, our analysis develops and adapts techniques from Fourier analysis on finite groups to our setting. We validate the predicted mechanisms empirically via controlled synthetic experiments and real-model RLVR runs.

While reasoning models have achieved remarkable success in complex reasoning tasks, their increasing power necessitates stringent safety measures. For safety alignment, the core challenge lies in the inherent trade-off between safety and utility. However, prevailing alignment strategies typically construct CoT training data with explicit safety rules via context distillation. This approach inadvertently limits reasoning capabilities by creating a rigid association between rule memorization and refusal. To mitigate the safety-utility trade-off, we propose the Adaptive Safe Context Learning~(ASCL) framework to improve the reasoning given proper context. ASCL formulates safety alignment as a multi-turn tool-use process, empowering the model to autonomously decide when to consult safety rules and how to generate the ongoing reasoning. Furthermore, to counteract the preference for rule consultation during RL, we introduce Inverse Frequency Policy Optimization~(IFPO) to rebalance advantage estimates. By decoupling rule retrieval and subsequent reasoning, our method achieves higher overall performance compared to baselines. Our code is publicly available at https://github.com/ybwang119/ASCL.

Large Language Models (LLMs) demonstrate transformative potential, yet their reasoning remains inconsistent and unreliable. Reinforcement learning (RL)-based fine-tuning is a key mechanism for improvement, but its effectiveness is fundamentally governed by reward design. Despite its importance, the relationship between reward modeling and core LLM challenges--such as evaluation bias, hallucination, distribution shift, and efficient learning--remains poorly understood. This work argues that reward modeling is not merely an implementation detail but a central architect of reasoning alignment, shaping what models learn, how they generalize, and whether their outputs can be trusted. We introduce Reasoning-Aligned Reinforcement Learning (RARL), a reasoning-centric taxonomic perspective that organizes diverse reward paradigms for multi-step reasoning. Within this perspective, we present a taxonomy of reward mechanisms, analyze reward hacking as a pervasive failure mode, and examine how reward signals unify challenges ranging from inference-time scaling to hallucination mitigation. We further critically evaluate existing benchmarks, highlighting vulnerabilities such as data contamination and reward misalignment, and outline directions for more robust evaluation. By integrating fragmented research threads and clarifying the interplay between reward design and fundamental reasoning capabilities, this work provides a foundational roadmap for building reasoning models that are robust, verifiable, and trustworthy.

Process rewards have been widely used in deep reinforcement learning to improve training efficiency, reduce variance, and prevent reward hacking. In LLM reasoning, existing works also explore various solutions for learning effective process reward models (PRM) with or without the help of an expert policy. However, existing methods either rely on strong assumptions about the expert policies (e.g., requiring their reward functions) or suffer intrinsic limitations (e.g., entropy collapse), resulting in weak PRMs or limited generalizability. In this paper, we introduce rePIRL, an inverse RL-inspired framework that learns effective PRMs with minimal assumptions about expert policies. Specifically, we design a dual learning process that updates the policy and the PRM interchangeably. Our learning algorithm has customized techniques to address the challenges of scaling traditional inverse RL to LLMs. We theoretically show that our proposed learning framework can unify both online and offline PRM learning methods, justifying that rePIRL can learn PRMs with minimal assumptions. Empirical evaluations on standardized math and coding reasoning datasets demonstrate the effectiveness of rePIRL over existing methods. We further show the application of our trained PRM in test-time training, test-time scaling, and providing an early signal for training hard problems. Finally, we validate our training recipe and key design choices via a detailed ablation study.

Reinforcement Learning with Verifiable Rewards (RLVR) is commonly based on group sampling to estimate advantages and stabilize policy updates. In practice, computational limits often rule out very large groups, so training proceeds with finite rollout sets that can reinforce only the correct behavior they expose. At practical group sizes, updates can miss rare-correct trajectories while still containing mixed rewards, concentrating probability on more common sampled solutions. We derive the probability of such prompt-local tail-miss events as a function of group size, showing non-monotonic behavior, and in the categorical abstraction characterize how unsampled-correct mass can shrink even as total correct mass grows. Motivated by this analysis, we propose a difficulty-aware scaling coefficient, inspired by Focal loss, that down-weights updates on high-success sampled groups. Empirically, categorical simulation illustrates the same effect in the categorical setting, Maze provides a single-solution test, and LLM experiments include a representative GRPO group-size sweep together with fixed-$N$ transfer across GRPO, DAPO, and CISPO. On Qwen2.5-7B at $N{=}8$, our method improves average math pass@256 from 64.1 $\rightarrow$ 70.3 (GRPO), 69.3 $\rightarrow$ 72.5 (DAPO), and 73.2 $\rightarrow$ 76.8 (CISPO); OOD pass@256 also improves in all three cases, without increasing group size or computational cost.

Privacy and computational constraints limit the use of large language models in psychiatry, while adapting small language models (SLMs) often requires substantial data and expert annotation. We developed ClinMPO, an evidence-guided reinforcement-learning framework guided by the psychiatrist-defined Clinical Psychiatry Thinking Strategy (CPTS). ClinMPO uses ClinRM, a reward model trained on 18,569 question--answer pairs from 4,474 psychiatry articles. We evaluated four Qwen3 sizes on 1,737 model-screened questions. ClinMPO outperformed Base, supervised fine-tuning and standard group relative policy optimization across scales. From responses by 300 senior pre-licensure medical students, we established the human baseline, a medical-student reference. The 4B model approached this baseline, whereas the 8B model surpassed it and ranked first among 31 models and post-training variants. ClinMPO improved performance across two complementary schemes covering ICD-11 diagnostic categories and psychiatric practice competencies. Blinded assessment by three clinicians showed improved rationale quality across CPTS criteria. These findings highlight how existing clinical evidence and specialist knowledge can be incorporated into the development of medical AI systems through evidence-guided learning.

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), 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 identify an implicit advantage symmetry inherent in Group Relative Advantage Estimation (GRAE) as a structural property that provides a new perspective for understanding these bottlenecks. 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 the 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 down-weighting the advantages of correct trajectories encourages essential exploration but risks instability; (ii) learning efficiency can be boosted 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. Code is available at https://github.com/HKU-HealthAI/A-GRAE