RL for Language Model Reasoning

Modern industrial applications increasingly demand language models that act as agents, capable of multi-step reasoning and tool use in real-world settings. These tasks are typically performed under strict cost and latency constraints, making small agentic models highly desirable. In this paper, we introduce the AgenticQwen family of models, trained via multi-round reinforcement learning (RL) on synthetic data and a limited amount of open-source data. Our training framework combines reasoning RL and agentic RL with dual data flywheels that automatically generate increasingly challenging tasks. The reasoning flywheel increases task difficulty by learning from errors, while the agentic flywheel expands linear workflows into multi-branch behavior trees that better reflect the decision complexity of real-world applications. We validate AgenticQwen on public benchmarks and in an industrial agent system. The models achieve strong performance on multiple agentic benchmarks, and in our industrial agent system, close the gap with much larger models on search and data analysis tasks. Model checkpoints and part of the synthetic data: https://huggingface.co/collections/alibaba-pai/agenticqwen. Data synthesis and RL training code: https://github.com/haruhi-sudo/data_synth_and_rl. The data synthesis pipeline is also integrated into EasyDistill: https://github.com/modelscope/easydistill.

Test-time reinforcement learning (TTRL) always adapts models at inference time via pseudo-labeling, leaving it vulnerable to spurious optimization signals from label noise. Through an empirical study, we observe that responses with medium consistency form an ambiguity region and constitute the primary source of reward noise. Crucially, we find that such spurious signals can be even amplified through group-relative advantage estimation. Motivated by these findings, we propose a unified framework, Debiased and Denoised test-time Reinforcement Learning (DDRL), to mitigate spurious signals. Concretely, DDRL first applies a frequency-based sampling strategy to exclude ambiguous samples while maintaining a balanced set of positive and negative examples. It then adopts a debiased advantage estimation with fixed advantages, removing the bias introduced by group-relative policy optimization. Finally, DDRL incorporates a consensus-based off-policy refinement stage, which leverages the rejection-sampled dataset to enable efficient and stable model updates. Experiments on three large language models across multiple mathematical reasoning benchmarks demonstrate that DDRL consistently outperforms existing TTRL baselines. The code will soon be released at https://github.com/yuyongcan/DDRL.

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

While LLMs demonstrate impressive reasoning capabilities, they remain fragile in multi-step logical deduction, where a single transition error can propagate through the entire reasoning chain, leading to unstable performance. In this work, we identify logical connectives as primary points of this structural fragility. Through empirical analysis, we show that connective tokens function as high entropy forking points, at which models frequently struggle to determine the correct logical direction. Motivated by this observation, we hypothesize that intervening in logical connective selection can guide LLMs toward more correct logical direction, thereby improving the overall reasoning chain. To validate this hypothesis, we propose a multi-layered framework that intervenes specifically at these logic-critical junctions in the reasoning process. Our framework includes (1) Gradient-based Logical Steering to guide LLMs internal representations towards valid reasoning subspaces, (2) Localized Branching to resolve ambiguity via targeted look-ahead search, and (3) Targeted Transition Preference Optimization, a surgical reinforcement learning objective that selectively optimizes single-token preferences at logical pivots. Crucially, by concentrating intervention solely on logic-critical transitions, our framework achieves a favorable accuracy--efficiency trade-off compared to global inference time scaling methods like beam search and self-consistency.

Information handling practices of LLM agents are broadly misaligned with the contextual privacy expectations of their users. Contextual Integrity (CI) provides a principled framework, defining privacy as the appropriate flow of information within context-relative norms. However, existing approaches either double inference cost via supervisor-assistant architectures, or fine-tune on narrow task-specific data. We propose extracting normative simulacra (structured representations of norms and information flows) from fiction novels and using them to fine-tune LLMs via supervised learning followed by GRPO reinforcement learning. Our composite reward function combines programmatic signals, including task clarity (subsuming schema validity, construct discrimination, and extraction confidence), structural completeness, internal consistency, and context identification, with an LLM judge that evaluates whether the model's privacy reasoning is grounded in the held-out normative universe of the source text. To mitigate overfitting, we introduce per-completion contrastive scoring: each completion is evaluated against both the correct normative universe and a randomly selected wrong one, teaching the model to condition on context rather than memorize source-specific norms. We evaluate on five CI-aligned benchmarks spanning distinct societal contexts and ablate the contributions of RL and normative grounding. Across seven models, SFT introduces a conservative prior toward restricting information flow, improving recognition of privacy-relevant situations but not the correctness of privacy judgments. GRPO with normative grounding achieves the highest score on a law compliance benchmark and strongest correlation with crowdsourced human privacy expectations, demonstrating that fiction-derived normative simulacra can teach contextual privacy reasoning that transfers to real-world domains.

Large language models have achieved remarkable progress on complex reasoning tasks. However, they often implicitly fabricate information when inputs are incomplete, producing confident but unreliable conclusions -- a failure mode we term ungrounded reasoning. We argue that this issue arises not from insufficient reasoning capability, but from the lack of inferential boundary awareness -- the ability to recognize when the necessary premises for valid inference are missing. To address this issue, we propose Grounded Reasoning via Interactive Reinforcement Learning (GRIL), a multi-turn reinforcement learning framework for grounded reasoning under incomplete information. GRIL decomposes the reasoning process into two stages: clarify and pause, which identifies whether the available information is sufficient, and grounded reasoning, which performs task solving once the necessary premises are established. We design stage-specific rewards to penalize hallucinations, enabling models to detect gaps, stop proactively, and resume reasoning after clarification. Experiments on GSM8K-Insufficient and MetaMATH-Insufficient show that GRIL significantly improves premise detection (up to 45%), leading to a 30% increase in task success while reducing average response length by over 20%. Additional analyses confirm robustness to noisy user responses and generalization to out-of-distribution tasks.

Test-time training (TTT) adapts model parameters on unlabeled test instances during inference time, which continuously extends capabilities beyond the reach of offline training. Despite initial gains, existing TTT methods for LRMs plateau quickly and do not benefit from additional test-time compute. Without external calibration, the self-generated reward signal increasingly drifts as the policy model evolves, leading to both performance plateaus and diversity collapse. We propose TEMPO, a TTT framework that interleaves policy refinement on unlabeled questions with periodic critic recalibration on a labeled dataset. By formalizing this alternating procedure through the Expectation-Maximization (EM) algorithm, we reveal that prior methods can be interpreted as incomplete variants that omit the crucial recalibration step. Reintroducing this step tightens the evidence lower bound (ELBO) and enables sustained improvement. Across diverse model families (Qwen3 and OLMO3) and reasoning tasks, TEMPO improves OLMO3-7B on AIME 2024 from 33.0% to 51.1% and Qwen3-14B from 42.3% to 65.8%, while maintaining high diversity.

Agentic multimodal models have garnered significant attention for their ability to leverage external tools to tackle complex tasks. However, it is observed that such agents often meet premature interaction collapse, caused by two primary reasons: 1) the terminal reward often appending on the last token prevents the advantage from distinguishing trajectories with exploratory behavior; 2) excessively redundant context hinders the agent from absorbing useful feedback. To address these issues, we propose the Deepening Reasoning MMSearchAgent, the framework leverages the structural proximity to derive advantage signals from the whole rollout trajectories in an entire batch, such that trajectories of different lengths are further encouraged to be generated, even when containing the same correct answer. Additionally, differentiated gaussian rewards are employed to dynamically calibrate interaction tolerance, thereby ensuring information reliability and reduce redundancy. To support multi-turn interaction training, we have constructed a multi-step deep-reasoning dataset including 3602 high-quality QA pair with at least 3 reasonning steps. Extensive experiments demonstrate that our method achieves state-of-the-art performance, outperforming the MMSearch-R1 by 8.4$\%$ on FVQA-test.

Reasoning-capable large language models solve hard problems by emitting long chains of thought, paying heavily in latency, GPU time, and energy. Casual inspection of their traces reveals extensive reformulation, verification, and circular self-reflection, yet how much of this deliberation is actually necessary has never been measured at scale or explained from first principles. This paper closes both gaps. We formalise reasoning redundancy directly in terms of the reasoning model itself: the redundancy of a correct trace is the largest fraction of its trailing segmented steps that can be truncated while $π$, forced to terminate thinking and emit a final answer, still produces the correct answer. A large-scale quantification across four frontier reasoning models and two mathematical benchmarks shows that step-level redundancy is consistently high -- between 61% and 93% across the 8 (model, benchmark) conditions we study, with the median critical prefix equal to a single segmented step in six of the eight conditions -- that the finding is robust to the choice of judge family, and that although $ρ$ decreases with problem difficulty on MATH-500, all four models remain substantially redundant ($ρ\in [46\%, 85\%]$) even on the hardest Level-5 problems. We then prove that this redundancy is a structural consequence of length-agnostic outcome rewards, not a model-specific artefact: under any such reward, no finite expected stopping time is optimal. The result holds regardless of RL algorithm, base model, data distribution, or whether the policy is obtained via RL or distillation; over-thinking is therefore not a bug to be patched in individual models but a structural property of how current reasoning models are trained. Code: https://github.com/zhiyuanZhai20/how-much-thinking-is-enough

We introduce Options LLM (OLLM), a simple, general method that replaces the single next-token prediction of standard LLMs with a \textit{set of learned options} for the next token, indexed by a discrete latent variable. Instead of relying on temperature or sampling heuristics to induce diversity, OLLM models variation explicitly: a small latent space parametrizes multiple plausible next-token options which can be selected or searched by a downstream policy. Architecturally, OLLM is a lightweight "plug-in" that inserts two layers: an encoder and a decoder, before the output head, allowing almost any pretrained LLM to be converted with minimal additional parameters. We apply OLLM to a 1.7B-parameter backbone (only $1.56\%$ of parameters trainable) trained on OpenMathReasoning and evaluated on OmniMath. The SOTA LoRA-adapted baselines peak at $51\%$ final answer correctness, while OLLM's option set allows up to $\sim 70\%$ under optimal latent selection. We then train a compact policy in the latent space that emits latents to control generation. Operating in a low-dimensional option space makes reward optimization far more sample-efficient and substantially reduces common misalignments (e.g., language switching or degenerate reasoning), as the policy is constrained to options learned during SFT. Crucially, this alignment arises from model structure rather than additional KL or handcrafted alignment losses. Our results demonstrate that optionized next-token modeling enhances controllability, robustness, and efficiency in math reasoning, and highlight latent-space policy learning as a promising direction for reinforcement learning in LLMs.

Zero-shot reasoning on text-rich networks (TRNs) remains a challenging frontier, as models must integrate textual semantics with relational structure without task-specific supervision. While graph neural networks rely on fixed label spaces and supervised objectives, recent large language model (LLM)-based approaches often overlook graph context or depend on distillation from larger models, limiting generalisation. We propose TRN-R1-Zero, a post-training framework for TRN reasoning trained solely via reinforcement learning. TRN-R1-Zero directly optimises base LLMs using a Neighbour-aware Group Relative Policy Optimisation objective that dynamically adjusts rewards based on a novel margin gain metric for the informativeness of neighbouring signals, effectively guiding the model toward relational reasoning. Unlike prior methods, TRN-R1-Zero requires no supervised fine-tuning or chain-of-thought data generated from large reasoning models. Extensive experiments across citation, hyperlink, social and co-purchase TRN benchmarks demonstrate the superiority and robustness of TRN-R1-Zero. Moreover, relying strictly on node-level training, TRN-R1-Zero achieves zero-shot inference on edge- and graph-level tasks, extending beyond cross-domain transfer. The codebase is publicly available at https://github.com/superallen13/TRN-R1-Zero.

Despite the growing application of Large Language Models (LLMs) to theoretical physics, there is little academic exploration into how domain-specific physics reasoning ability develops while training these models. To investigate this, we perform the first academic fine-tuning study of small (7B-parameter) reasoning models dedicated specifically to theoretical physics. Because open-source verifiable training data required to train such capabilities is scarce, we developed a robust data generation pipeline that can both create synthetic problems and make existing human-authored problems suitable for model training. Selecting Quantum Field Theory (QFT) as our primary domain, we generated over 2,500 synthetic problems alongside a curated collection of human-adapted problems sourced from arXiv and standard pedagogical resources. We conduct both Reinforcement Learning (RL) and Supervised Fine-Tuning (SFT) experiments, benchmarking performance gains as well as generalization to other physics domains. We perform an extensive analysis of model chains-of-though before and after fine-tuning, to understand how reasoning errors evolve during RL and SFT. Finally, we publicly release our data pipeline, verifiable QFT training data, and $\sim$200M tokens of QFT reasoning traces.

Masked diffusion large language models (dLLMs) are a promising alternative to autoregressive generation. While reinforcement learning (RL) methods have recently been adapted to dLLM fine-tuning, their objectives typically depend on sequence-level marginal likelihoods, which are intractable for masked diffusion models. To address this, we derive Discrete Tilt Matching (DTM), a likelihood-free method that recasts dLLM fine-tuning as state-level matching of local unmasking posteriors under reward tilting. DTM takes the form of a weighted cross-entropy objective with explicit minimizer, and admits control variates that improve training stability. On a synthetic maze-planning task, we analyze how DTM's annealing schedule and control variates affect training stability and prevent mode collapse. At scale, fine-tuning LLaDA-8B-Instruct with DTM yields strong gains on Sudoku and Countdown while remaining competitive on MATH500 and GSM8K.

Large language models have achieved significant reasoning improvements through reinforcement learning with verifiable rewards (RLVR). Yet as model capabilities grow, constructing high-quality reward signals becomes increasingly difficult, making it essential to understand when RLVR can succeed under weaker forms of supervision. We conduct a systematic empirical study across diverse model families and reasoning domains under three weak supervision settings: scarce data, noisy rewards, and self-supervised proxy rewards. We find that generalization is governed by training reward saturation dynamics: models that generalize exhibit a prolonged pre-saturation phase during which training reward and downstream performance climb together, while models that saturate rapidly memorize rather than learn. We identify reasoning faithfulness, defined as the extent to which intermediate steps logically support the final answer, as the pre-RL property that predicts which regime a model falls into, while output diversity alone is uninformative. Motivated by these findings, we disentangle the contributions of continual pre-training and supervised fine-tuning, finding that SFT on explicit reasoning traces is necessary for generalization under weak supervision, while continual pre-training on domain data amplifies the effect. Applied together to Llama3.2-3B-Base, these interventions enable generalization across all three settings where the base model previously failed.

Recent advancements in Reinforcement Learning with Verifiable Rewards (RLVR) have significantly improved Large Language Model (LLM) reasoning, yet models often struggle to explore novel trajectories beyond their initial policy distribution. While offline teacher guidance and entropy-driven strategies have been proposed to address this, they often lack deep integration or are constrained by the model's inherent capacity. In this paper, we propose OGER (Offline-Guided Exploration Reward), a novel framework that unifies offline teacher guidance and online reinforcement learning through a specialized reward modeling lens. OGER employs multi-teacher collaborative training and constructs an auxiliary exploration reward that leverages both offline trajectories and the model's own entropy to incentivize autonomous exploration. Extensive experiments across mathematical and general reasoning benchmarks demonstrate that OGER consistently outperforms competitive baselines, achieving substantial gains in mathematical reasoning while maintaining robust generalization to out-of-domain tasks. We provide a comprehensive analysis of training dynamics and conduct detailed ablation studies to validate the effectiveness of our entropy-aware reward modulation. Our code is available at https://github.com/ecoli-hit/OGER.git.

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.

LLMs utilizing chain-of-thought reasoning often waste substantial compute by producing long, incorrect responses. Abstention can mitigate this by withholding outputs unlikely to be correct. While most abstention methods decide to withhold outputs before or after generation, dynamic mid-generation abstention considers early termination of unpromising reasoning traces at each token position. Prior work has explored empirical variants of this idea, but principled guidance for the abstention rule remains lacking. We present a formal analysis of dynamic abstention for LLMs, modeling abstention as an explicit action within a regularized reinforcement learning framework. An abstention reward parameter controls the trade-off between compute and information. We show that abstaining when the value function falls below this reward strictly outperforms natural baselines under general conditions. We further derive a principled and efficient method to approximate the value function. Empirical results on mathematical reasoning and toxicity avoidance tasks support our theory and demonstrate improved selective accuracy over existing methods.

Fine-tuning Large Language Models (LLMs) typically relies on large quantities of high-quality annotated data, or questions with well-defined ground truth answers in the case of Reinforcement Learning with Verifiable Rewards (RLVR). While previous work has explored the benefits to model reasoning capabilities by scaling both data and compute used for RLVR, these results lack applicability in many real-world settings where annotated data and accessible compute may be scarce. In this work, we present a comprehensive empirical study of open-source Small Language Model (SLM) performance after RLVR in low data regimes. Across three novel datasets covering number counting problems, graph reasoning, and spatial reasoning, we characterize how model performance scales with dataset size, diversity, and complexity. We demonstrate that (1) procedural datasets allow for fine-grained evaluation and training dataset development with controllable properties (size, diversity, and complexity), (2) under RLVR, models trained on lower complexity tasks can generalize to higher complexity tasks, and (3) training on mixed complexity datasets is associated with the greatest benefits in low data regimes, providing up to 5x sample efficiency versus training on easy tasks. These findings inspire future work on the development of data scaling laws for RLVR and the use of procedural data generators to further understand effective data development for efficient LLM fine-tuning.

Reinforcement learning for multi-step reasoning with large language models (LLMs) typically relies on sparse terminal rewards, which creates a poorly conditioned credit-assignment problem: the final feedback is propagated uniformly across all intermediate decisions. This leads to high gradient variance, unstable training, and many ineffective updates, ultimately limiting sustained model improvement. We propose a counterfactual-comparison framework for credit assignment. For each input, the framework samples multiple reasoning trajectories and treats their differences as implicit approximations to alternative decisions. This yields an implicit process-level advantage estimator that converts sparse terminal rewards into step-sensitive learning signals. Building on this framework, we introduce Implicit Behavior Policy Optimization (IBPO), which substantially improves training stability and the performance ceiling on mathematical and code-reasoning benchmarks. Our results point to a promising direction for unlocking the reasoning potential of LLMs.

Search agents achieve strong question-answering performance through multi-turn interactions with search engines, with Group Relative Policy Optimization (GRPO) being a widely used training algorithm. However, GRPO-style algorithms still face several challenges in multi-hop search settings. First, correct intermediate steps are often penalized when the final answer is wrong. Second, training is highly unstable, often causing degradation of natural language ability or even catastrophic training collapse. Our analysis attributes these issues to coarse-grained advantage assignment and an imbalance between positive and negative advantages. To address these problems, we propose CalibAdv, an advantage calibration method specifically designed for search agents that enables more accurate and more stable modeling of penalties and rewards. Specifically, CalibAdv leverages the correctness of intermediate steps to downscale excessive negative advantages at a fine-grained level. It then further rebalances positive and negative advantages to improve training stability. Importantly, CalibAdv adopts a lightweight design that calibrates advantages from standard rollout signals, making it simple and easy to deploy. Extensive experiments across three models and seven benchmarks demonstrate that CalibAdv improves both model performance and training stability. Our code is available at https://github.com/wujwyi/CalibAdv.

Large Audio-Language Models (LALMs) have made significant progress in audio understanding, yet they primarily operate as perception-and-answer systems without explicit reasoning processes. Existing methods for enhancing audio reasoning rely either on supervised chain-of-thought (CoT) fine-tuning, which is limited by training data quality, or on reinforcement learning (RL) with coarse rewards that do not directly evaluate reasoning quality. As a result, the generated reasoning chains often appear well-structured yet lack specific acoustic grounding. We propose Audio-DeepThinker, a framework built on two core ideas. First, we introduce a hybrid reasoning similarity reward that directly supervises the quality of generated reasoning chains by combining an LLM evaluator assessing logical path alignment, key step coverage, and analytical depth with an embedding similarity component enforcing semantic alignment with reference reasoning chains. Second, we propose a progressive two-stage curriculum that enables high-quality CoT reasoning to emerge through pure RL exploration, without any supervised reasoning fine-tuning, from an instruction-tuned model that possesses no prior chain-of-thought capability. Stage 1 trains on foundational audio QA with the hybrid reward to foster basic reasoning patterns, while Stage 2 shifts to acoustically challenging boundary cases with an LLM-only reward for greater reasoning diversity. Audio-DeepThinker achieves state-of-the-art results on MMAR (74.0%), MMAU-test-mini (78.5%), and MMSU (77.26%), winning 1st Place in the Interspeech 2026 Audio Reasoning Challenge (Single Model Track). Interpretability analyses further reveal that RL training primarily reshapes upper-layer MoE gating mechanisms and that reasoning tokens crystallize progressively in the upper transformer layers, offering mechanistic insights into how audio reasoning emerges through exploration.

Chain-of-thought reasoning has driven striking advances in language model capability, yet every reasoning step grows the KV cache, creating a bottleneck to scaling this paradigm further. Current approaches manage these constraints on the model's behalf using hand-designed criteria. A more scalable approach would let end-to-end learning subsume this design choice entirely, following a broader pattern in deep learning. After all, if a model can learn to reason, why can't it learn to forget? We introduce Neural Garbage Collection (NGC), in which a language model learns to forget while learning to reason, trained end-to-end from outcome-based task reward alone. As the model reasons, it periodically pauses, decides which KV cache entries to evict, and continues to reason conditioned on the remaining cache. By treating tokens in a chain-of-thought and cache-eviction decisions as discrete actions sampled from the language model, we can use reinforcement learning to jointly optimize how the model reasons and how it manages its own memory: what the model evicts shapes what it remembers, what it remembers shapes its reasoning, and the correctness of that reasoning determines its reward. Crucially, the model learns this behavior entirely from a single learning signal - the outcome-based task reward - without supervised fine-tuning or proxy objectives. On Countdown, AMC, and AIME tasks, NGC maintains strong accuracy relative to the full-cache upper bound at 2-3x peak KV cache size compression and substantially outperforms eviction baselines. Our results are a first step towards a broader vision where end-to-end optimization drives both capability and efficiency in language models.

Reinforcement Learning with Verifiable Reward (RLVR) has proven effective for training reasoning-oriented large language models, but existing methods largely assume high-resource settings with abundant training data. In low-resource scenarios, RLVR is prone to more severe entropy collapse, which substantially limits exploration and degrades reasoning performance. To address this issue, we propose Hybrid-domain Entropy dynamics ALignment (HEAL), a framework tailored for few-shot RLVR. HEAL first selectively incorporates high-value general-domain data to promote more diverse exploration. Then, we introduce Entropy Dynamics Alignment (EDA), a reward mechanism that aligns trajectory-level entropy dynamics between the target and general domains, capturing both entropy magnitude and fine-grained variation. Through this alignment, EDA not only further mitigates entropy collapse but also encourages the policy to acquire more diverse exploration behaviors from the general domain. Experiments across multiple domains show that HEAL consistently improves few-shot RLVR performance. Notably, using only 32 target-domain samples, HEAL matches or even surpasses full-shot RLVR trained with 1K target-domain samples.

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

Recently, latent reasoning has been introduced into large language models (LLMs) to leverage rich information within a continuous space. However, without stochastic sampling, these methods inevitably collapse to deterministic inference, failing to discover diverse reasoning paths. To bridge the gap, we inject controllable stochasticity into latent reasoning via Gumbel-Softmax, restoring LLMs' exploratory capacity and enhancing their compatibility with Reinforcement Learning (RL). Building on this, we propose \textbf{\underline{L}}atent R\textbf{\underline{e}}asoning \textbf{\underline{P}}olicy \textbf{\underline{O}}ptimization~(\textbf{LEPO}), a novel framework that applies RL directly to continuous latent representations. Specifically, in rollout stage, LEPO maintains stochasticity to enable diverse trajectory sampling, while in optimization stage, LEPO constructs a unified gradient estimation for both latent representations and discrete tokens. Extensive experiments show that LEPO significantly outperforms existing RL methods for discrete and latent reasoning.

Games offer a compelling paradigm for developing general reasoning capabilities in language models, as they naturally demand strategic planning, probabilistic inference, and adaptive decision-making. However, existing self-play approaches rely solely on terminal game outcomes, providing no mechanism to distinguish transferable reasoning patterns from game-specific heuristics. We present STRATAGEM, which addresses two fundamental barriers to reasoning transfer: domain specificity, where learned patterns remain anchored in game semantics, and contextual stasis, where static game contexts fail to cultivate progressive reasoning. STRATAGEM selectively reinforces trajectories exhibiting abstract, domain-agnostic reasoning through a Reasoning Transferability Coefficient, while incentivizing adaptive reasoning development via a Reasoning Evolution Reward. Experiments across mathematical reasoning, general reasoning, and code generation benchmarks demonstrate substantial improvements, with particularly strong gains on competition-level mathematics where multi-step reasoning is critical. Ablation studies and human evaluation confirm that both components contribute to transferable reasoning.

Exploration is a cornerstone of learning from experience: it enables agents to find solutions to complex problems, generalize to novel ones, and scale performance with test-time compute. In this paper, we present a framework for post-training language models (LMs) that explicitly encourages optimistic exploration and promotes a synergy between exploration and exploitation. The central idea is to train the LM to generate sets of responses that are collectively accurate under the reward function and exploratory in their reasoning strategies. We first develop a general recipe for optimizing LMs with set reinforcement learning (set RL) under arbitrary objective functions, showing how standard RL algorithms can be adapted to this setting through a modification to the advantage computation. We then propose Polychromic Exploratory Policy Optimization (Poly-EPO), which instantiates this framework with an objective that explicitly synergizes exploration and exploitation. Across a range of reasoning benchmarks, we show that Poly-EPO improves generalization, as evidenced by higher pass@$k$ coverage, preserves greater diversity in model generations, and effectively scales with test-time compute.

The central challenge of reinforcement learning for reasoning lies not only in the sparsity of outcome-level supervision, but more fundamentally in how to transform feedback provided only at the end of a sequence into fine-grained learning signals that can guide intermediate reasoning steps. Existing approaches either rely on outcome-level rewards for sequence-level optimization, which makes precise credit assignment difficult, or depend on externally constructed process supervision, which is costly and difficult to scale sustainably. To address this, we propose a new perspective: reinforcement learning for reasoning can be understood as the problem of internalizing outcome supervision into process supervision. From this perspective, we introduce a supervision-internalization method for reinforcement learning for reasoning, enabling the model to automatically extract process-level learning signals through identifying, correcting, and reusing failed reasoning trajectories, thereby achieving finer-grained policy optimization under outcome-only supervision. We further abstract this idea into a new training paradigm, in which the model continually generates and refines its own internal process supervision during reinforcement learning, opening a new path for fine-grained credit assignment in reinforcement learning for reasoning that differs from externally provided process supervision.

Previous LLMs-based RL studies typically follow either supervised learning with high annotation costs, or unsupervised paradigms using voting or entropy-based rewards. However, their performance remains far from satisfactory due to the substantial annotation cost and issues such as model collapse or reward hacking. To address these issues, we introduce a new perspective inspired by cognitive learning theory and propose a novel approach called EasyRL. The core of EasyRL is to simulate the human cognitive acquisition curve by integrating reliable knowledge transfer from easy labeled data with a progressive divide-and-conquer strategy that tackles increasingly difficult unlabeled data. Specifically, we initialize a warm-up model using supervised RL with few-shot labeled data. This is followed by a divide-and-conquer pseudo-labeling strategy on difficult unlabeled data, combining consistency-based selection for low-uncertainty cases and reflection-based resolution for medium-uncertainty cases. Finally, difficulty-progressive self-training with iterative pseudo-labeling and RL further strengthens the model's reasoning capability. EasyRL provides a unified self-evolving framework that facilitates data-efficient post-training of LLMs. Experimental results on mathematical and scientific benchmarks demonstrate that EasyRL, using only 10% of easy labeled data, consistently outperforms state-of-the-art baselines.

Reinforcement fine-tuning improves the reasoning ability of large language models, but it can also encourage them to answer unanswerable queries by guessing or hallucinating missing information. Existing abstention methods either train models to produce generic refusals or encourage follow-up clarifications without verifying whether those clarifications identify the key missing information. We study queries that are clear in meaning but cannot be reliably resolved from the given information, and argue that a reliable model should not only abstain, but also explain what is missing. We propose a clarification-aware RLVR reward that, while rewarding correct answers on answerable queries, jointly optimizes explicit abstention and semantically aligned post-refusal clarification on unanswerable queries. Using this reward, we train Abstain-R1, a 3B model that improves abstention and clarification on unanswerable queries while preserving strong performance on answerable ones. Experiments on Abstain-Test, Abstain-QA, and SelfAware show that Abstain-R1 substantially improves over its base model and achieves unanswerable-query behavior competitive with larger systems including DeepSeek-R1, suggesting that calibrated abstention and clarification can be learned through verifiable rewards rather than emerging from scale alone.