RL for Language Model Reasoning

RL: Reinforcement Learning

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This field studies how reward feedback can teach language models to solve multi-step problems, use tools, and decide how much reasoning a task needs. A common approach is reinforcement learning from verifiable rewards (RLVR), often using group-relative policy optimization, where sampled solutions are scored for correctness; other methods add step-level rewards, process verifiers, search, or teacher guidance to address sparse feedback. Work also explores curricula, adaptive rollout budgets, self-distillation, and controls for reasoning length and diversity. Key open tensions include balancing exploration with stable learning, ensuring rewards and verifiers do not encourage shortcuts, and improving generalization without excessive computation or overthinking.

Latest papers

1,105 papers170 papers in the last four weeks, up 124% on the four weeks before. 1.0% of all new papers.

Apr 10, 2026

Aryabhata 2: Scaling Reinforcement Learning for Advanced STEM Reasoning

Competitive STEM examinations such as JEE and NEET require multi-step symbolic reasoning, precise numerical computation, and deep conceptual understanding across physics, chemistry, and mathematics. Recent large language models perform strongly on common reasoning benchmarks, yet they remain difficult to deploy at scale, where millions of student doubts demand domain-specific, consistently structured problem solving. We introduce Aryabhata 2, a reasoning-focused language model for competitive STEM examinations, trained via reinforcement-learning post-training. Using PhysicsWallah's internal question banks, we construct a high-quality training curriculum and post-train GPT-OSS-20B through reinforcement learning with verifiable rewards. Training combines prolonged reinforcement learning with broadened exploration via progressively larger rollout group sizes. We evaluate Aryabhata 2 on competitive examination benchmarks, including JEE Main, JEE Advanced, and NEET, as well as out-of-distribution reasoning datasets such as AIME, HMMT, MMLU-Pro, MMLU-Redux 2.0, and GPQA. Results show that Aryabhata 2 outperforms its base model GPT-OSS-20B on competitive STEM reasoning while requiring substantially fewer output tokens (up to 64% fewer).

Ritvik Rastogi, Vishal Singh, Tejas Chaudhari +1

PhysicsWallah

Scientific Reasoning in Language Models Efficient Language Model Reasoning RL for Language Model Reasoning

Apr 10, 2026

Bridging SFT and RL: Dynamic Policy Optimization for Robust Reasoning

Post-training paradigms for Large Language Models (LLMs), primarily Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), face a fundamental dilemma: SFT provides stability (low variance) but suffers from high fitting bias, while RL enables exploration (low bias) but grapples with high gradient variance. Existing unified optimization strategies often employ naive loss weighting, overlooking the statistical conflict between these distinct gradient signals. In this paper, we provide a rigorous theoretical analysis of this bias-variance trade-off and propose DYPO (Dynamic Policy Optimization), a unified framework designed to structurally mitigate this conflict. DYPO integrates three core components: (1) a Group Alignment Loss (GAL) that leverages intrinsic group dynamics to significantly reduce RL gradient variance; (2) a Multi-Teacher Distillation mechanism that corrects SFT fitting bias via diverse reasoning paths; and (3) a Dynamic Exploitation-Exploration Gating mechanism that adaptively arbitrates between stable SFT and exploratory RL based on reward feedback. Theoretical analysis confirms that DYPO linearly reduces fitting bias and minimizes overall variance. Extensive experiments demonstrate that DYPO significantly outperforms traditional sequential pipelines, achieving an average improvement of 4.8% on complex reasoning benchmarks and 13.3% on out-of-distribution tasks. Our code is publicly available at https://github.com/Tocci-Zhu/DYPO.

Taojie Zhu, Dongyang Xu, Ding Zou +4

Shenzhen International Graduate School, Tsinghua University · Intelligent System Department, Zhongxing Telecom Equipment (ZTE) · Institute of Advanced Interdisciplinary Studies, Chongqing University of Posts and Telecommunications

LLM Fine-Tuning RL for Language Model Reasoning RL Fine-Tuning Language Model Robustness

Apr 10, 2026

StaRPO: Stability-Augmented Reinforcement Policy Optimization

Reinforcement learning (RL) is effective in enhancing the accuracy of large language models in complex reasoning tasks. Existing RL policy optimization frameworks rely on final-answer correctness as feedback signals and rarely capture the internal logical structure of the reasoning process. Consequently, the models would generate fluent and semantically relevant responses but logically inconsistent, structurally erratic, or redundant. To this end, we propose StaRPO, a stability-augmented reinforcement learning framework that explicitly incorporates reasoning stability into the optimization objective. Our StaRPO decomposes stability into two computable lightweight metrics: the Autocorrelation Function (ACF) to evaluate local step-to-step coherence, and Path Efficiency (PE) to evaluate global goal-directedness of the reasoning trajectory. These stability rewards are combined with task rewards to provide complementary and process-aware feedback. We validate the effectiveness of using ACF and PE rewards by showing their correlation with logic errors on two backbone models. Experiments on four reasoning benchmarks show that StaRPO consistently outperforms compared baselines and can enhance both final-answer accuracy and logical stability.

Jinghan Zhang, Fengran Mo, Tharindu Cyril Weerasooriya +5

Clemson University · Université de Montréal · Accenture (United States) +2

RL for Language Model Reasoning Reasoning Consistency in Language Models Reward Shaping

Apr 10, 2026

SPPO: Sequence-Level PPO for Long-Horizon Reasoning Tasks

Proximal Policy Optimization (PPO) is central to aligning Large Language Models (LLMs) in reasoning tasks with verifiable rewards. However, standard token-level PPO struggles in this setting due to the instability of temporal credit assignment over long Chain-of-Thought (CoT) horizons and the prohibitive memory cost of the value model. While critic-free alternatives like GRPO mitigate these issues, they incur significant computational overhead by requiring multiple samples for baseline estimation, severely limiting training throughput. In this paper, we introduce Sequence-Level PPO (SPPO), a scalable algorithm that harmonizes the sample efficiency of PPO with the stability of outcome-based updates. SPPO reformulates the reasoning process as a Sequence-Level Contextual Bandit problem, employing a decoupled scalar value function to derive low-variance advantage signals without multi-sampling. Extensive experiments on mathematical benchmarks demonstrate that SPPO significantly surpasses standard PPO and matches the performance of computation-heavy group-based methods, offering a resource-efficient framework for aligning reasoning LLMs.

Tianyi Wang, Yixia Li, Long Li +6

Southern University of Science and Technology · Beijing University of Posts and Telecommunications · INFLY TECH +3

RL for Language Model Reasoning Proximal Policy Optimization LLM Reasoning

Apr 9, 2026

ExecTune: Effective Steering of Black-Box LLMs with Guide Models

For large language models deployed through black-box APIs, recurring inference costs often exceed one-time training costs. This motivates composed agentic systems that amortize expensive reasoning into reusable intermediate representations. We study a broad class of such systems, termed Guide-Core Policies (GCoP), in which a guide model generates a structured strategy that is executed by a black-box core model. This abstraction subsumes base, supervised, and advisor-style approaches, which differ primarily in how the guide is trained. We formalize GCoP under a cost-sensitive utility objective and show that end-to-end performance is governed by guide-averaged executability: the probability that a strategy generated by the guide can be faithfully executed by the core. Our analysis shows that existing GCoP instantiations often fail to optimize executability under deployment constraints, resulting in brittle strategies and inefficient computation. Motivated by these insights, we propose ExecTune, a principled training recipe that combines teacher-guided acceptance sampling, supervised fine-tuning, and structure-aware reinforcement learning to directly optimize syntactic validity, execution success, and cost efficiency. Across mathematical reasoning and code-generation benchmarks, GCoP with ExecTune improves accuracy by up to 9.2% over prior state-of-the-art baselines while reducing inference cost by up to 22.4%. It enables Claude Haiku 3.5 to outperform Sonnet 3.5 on both math and code tasks, and to come within 1.7% absolute accuracy of Sonnet 4 at 38% lower cost. Beyond efficiency, GCoP also supports modular adaptation by updating the guide without retraining the core.

Vijay Lingam, Aditya Golatkar, Anwesan Pal +6

AWS AI

Language Model Steering LLM Inference Efficiency Cost-Aware Inference RL for Language Model Reasoning

Apr 9, 2026

Decomposing the Delta: What Do Models Actually Learn from Preference Pairs?

Preference optimization methods such as DPO and KTO are widely used for aligning language models, yet little is understood about what properties of preference data drive downstream reasoning gains. We ask: what aspects of a preference pair improve a reasoning model's performance on general reasoning tasks? We investigate two distinct notions of quality delta in preference data: generator-level delta, arising from the differences in capability between models that generate chosen and rejected reasoning traces, and sample-level delta, arising from differences in judged quality differences within an individual preference pair. To study generator-level delta, we vary the generator's scale and model family, and to study sample-level delta, we employ an LLM-as-a-judge to rate the quality of generated traces along multiple reasoning-quality dimensions. We find that increasing generator-level delta steadily improves performance on out-of-domain reasoning tasks and filtering data by sample-level delta can enable more data-efficient training. Our results suggest a twofold recipe for improving reasoning performance through preference optimization: maximize generator-level delta when constructing preference pairs and exploit sample-level delta to select the most informative training examples.

Chia-Hsuan Lee, Mingyang Zhou, Renkun Ni +6

Capital One

Preference Optimization Pairwise Preference Learning Efficient Language Model Reasoning RL for Language Model Reasoning Data Selection

Apr 9, 2026

Skip-Connected Policy Optimization for Implicit Advantage

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

Fengwei Teng, Jinyi Bai, Xinhao Yao +3

Mohamed bin Zayed University of Artificial Intelligence · Renmin University of China · Carnegie Mellon University +1

RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Group Relative Policy Optimization Dense Reward RL

Apr 9, 2026

SUPERNOVA: Eliciting General Reasoning in LLMs with Reinforcement Learning on Natural Instructions

Reinforcement Learning with Verifiable Rewards (RLVR) has substantially improved reasoning in formal domains such as mathematics and code, but extending these gains beyond STEM remains challenging. Extending RLVR beyond STEM is fundamentally constrained by the lack of high-quality verifiable training data. In this work, we introduce SUPERNOVA, a framework for curating RLVR data from natural instruction datasets, which are a rich source of expert-annotated data but are underexplored for RLVR training. Through 100+ controlled RL experiments, we systematically study how to utilize these dataset for RLVR and how data curation decisions affect downstream reasoning performance . In particular, we investigate three data designs: (a) source task selection, (b) task mixing, and (c) synthetic interventions. Our analysis reveals that source task selection has a significant impact on downstream reasoning performance. Moreover, selecting tasks based on their performance for individual target tasks outperforms strategies based on overall average performance and synthetic interventions do not improve reasoning. Guided by these insights, we construct SUPERNOVA, a high-quality RLVR dataset of 25K instances curated from natural instruction datasets. We show that training Qwen3-0.6B on SUPERNOVA outperforms the base Qwen3-0.6B, yielding a relative gain of 64.4pp on BigBench Extra Hard (BBEH), a challenging benchmark comprising 23 complex reasoning tasks. Importantly, we find that gains from SUPERNOVA generalize to unseen benchmarks, larger model scales, and newer model families. Overall, our findings provide practical insights for curating human-annotated resources to extend RLVR to general reasoning. Models, Data, Code at https://github.com/asuvarna31/supernova.

Ashima Suvarna, Kendrick Phan, Mehrab Beikzadeh +2

University of California, Los Angeles

RL for Language Model Reasoning LLM Reasoning Reinforcement Learning with Verifiable Rewards

Apr 9, 2026

TTVS: Boosting Self-Exploring Reinforcement Learning via Test-time Variational Synthesis

Despite significant advances in Large Reasoning Models (LRMs) driven by reinforcement learning with verifiable rewards (RLVR), this paradigm is fundamentally limited in specialized or novel domains where such supervision is prohibitively expensive or unavailable, posing a key challenge for test-time adaptation. While existing test-time methods offer a potential solution, they are constrained by learning from static query sets, risking overfitting to textual patterns. To address this gap, we introduce Test-Time Variational Synthesis (TTVS), a novel framework that enables LRMs to self-evolve by dynamically augmenting the training stream from unlabeled test queries. TTVS comprises two synergistic modules: (1) Online Variational Synthesis, which transforms static test queries into a dynamic stream of diverse, semantically-equivalent variations, enforcing the model to learn underlying problem logic rather than superficial patterns; (2) Test-time Hybrid Exploration, which balances accuracy-driven exploitation with consistency-driven exploration across synthetic variants. Extensive experiments show TTVS yields superior performance across eight model architectures. Notably, using only unlabeled test-time data, TTVS not only surpasses other test-time adaptation methods but also outperforms state-of-the-art supervised RL-based techniques trained on vast, high-quality labeled data.

Sikai Bai, Haoxi Li, Jie Zhang +2

The Hong Kong University of Science and Technology

Test-Time Adaptation Test-Time RL RL for Language Model Reasoning Test-Time Augmentation

Apr 9, 2026

Beyond Stochastic Exploration: What Makes Training Data Valuable for Agentic Search

Reinforcement learning (RL) has become an effective approach for advancing the reasoning capabilities of large language models (LLMs) through the strategic integration of external search engines. However, current RL-based search agents often rely on a process of stochastic exploration guided by carefully crafted outcome rewards, leading to inefficient reasoning trajectories and unstable training. To address these issues, we propose a novel framework, Hierarchical Experience (HiExp), to enhance the performance and training stability of search agents. Specifically, we extract empirical knowledge through contrastive analysis and a multi-level clustering mechanism, transforming raw reasoning trajectories into hierarchical experience knowledge. By leveraging experience-aligned training, we effectively regularize stochastic exploration, evolving it into a strategic and experience-driven search process. Extensive evaluations on multiple complex agentic search and mathematical reasoning benchmarks demonstrate that our approach not only achieves substantial performance gains but also exhibits strong cross-task and cross-algorithm generalization.

Chuzhan Hao, Wenfeng Feng, Guochao Jiang +3

Alibaba Cloud Computing

Agentic Search RL for Language Model Reasoning RL for LLM Agents Reinforcement Learning

Apr 9, 2026

QaRL: Rollout-Aligned Quantization-Aware RL for Fast and Stable Training under Training--Inference Mismatch

Large language model (LLM) reinforcement learning (RL) pipelines are often bottlenecked by rollout generation, making end-to-end training slow. Recent work mitigates this by running rollouts with quantization to accelerate decoding, which is the most expensive stage of the RL loop. However, these setups destabilize optimization by amplifying the training-inference gap: rollouts are operated at low precision, while learning updates are computed at full precision. To address this challenge, we propose QaRL (Rollout Alignment Quantization-Aware RL), which aligns training-side forward with the quantized rollout to minimize mismatch. We further identify a failure mode in quantized rollouts: long-form responses tend to produce repetitive, garbled tokens (error tokens). To mitigate these problems, we introduce TBPO (Trust-Band Policy Optimization), a sequence-level objective with dual clipping for negative samples, aimed at keeping updates within the trust region. On Qwen3-30B-A3B MoE for math problems, QaRL outperforms quantized-rollout training by +5.5 while improving stability and preserving low-bit throughput benefits.

Hao Gu, Hao Wang, Jiacheng Liu +9

The Hong Kong University of Science and Technology · City University of Hong Kong · Zhejiang University

Reinforcement Learning RL Fine-Tuning RL for Language Model Reasoning Quantization-Aware Training

Apr 9, 2026

ReRec: Reasoning-Augmented LLM-based Recommendation Assistant via Reinforcement Fine-tuning

With the rise of LLMs, there is an increasing need for intelligent recommendation assistants that can handle complex queries and provide personalized, reasoning-driven recommendations. LLM-based recommenders show potential but face challenges in multi-step reasoning, underscoring the need for reasoning-augmented systems. To address this gap, we propose ReRec, a novel reinforcement fine-tuning (RFT) framework designed to improve LLM reasoning in complex recommendation tasks. Our framework introduces three key components: (1) Dual-Graph Enhanced Reward Shaping, integrating recommendation metrics like NDCG@K with Query Alignment and Preference Alignment Scores to provide fine-grained reward signals for LLM optimization; (2) Reasoning-aware Advantage Estimation, which decomposes LLM outputs into reasoning segments and penalizes incorrect steps to enhance reasoning of recommendation; and (3) Online Curriculum Scheduler, dynamically assess query difficulty and organize training curriculum to ensure stable learning during RFT. Experiments demonstrate that ReRec outperforms state-of-the-art baselines and preserves core abilities like instruction-following and general knowledge. Our codes are available at https://github.com/jiani-huang/ReRec.

Jiani Huang, Shijie Wang, Liangbo Ning +2

The Hong Kong Polytechnic University

Large Language Model-Based Recommendation RL Fine-Tuning RL for Language Model Reasoning Reward Shaping

Apr 8, 2026

Reason in Chains, Learn in Trees: Self-Rectification and Grafting for Multi-turn Agent Policy Optimization

Reinforcement learning for Large Language Model agents is often hindered by sparse rewards in multi-step reasoning tasks. Existing approaches like Group Relative Policy Optimization treat sampled trajectories as independent chains, assigning uniform credit to all steps in each chain and ignoring the existence of critical steps that may disproportionally impact reasoning outcome. In this paper, we propose T-STAR(Tree-structured Self-Taught Agent Rectification), a framework that recovers the latent correlated reward structure across seemingly independent trajectories. Specifically, we consolidate trajectories into a unified Cognitive Tree by identifying and merging functionally similar steps/nodes. It enables an Introspective Valuation mechanism that back-propagates trajectory-level rewards through the tree to obtain a new notion of variance-reduced relative advantage at step-level. Using the Cognitive Tree, we also develop In-Context Thought Grafting to synthesize corrective reasoning by contrasting successful and failed branches at critical divergence points/steps. Our proposed Surgical Policy Optimization then capitalizes on the rich policy gradient information concentrated at these critical points/steps through a Bradley-Terry type of surgical loss. Extensive experiments across embodied, interactive, reasoning, and planning benchmarks demonstrate that T-STAR achieves consistent improvements over strong baselines, with gains most pronounced on tasks requiring extended reasoning chains.

Yu Li, Sizhe Tang, Tian Lan

Department of Electrical and Computer Engineering, George Washington University

RL for Language Model Reasoning RL for LLM Agents Step-Level Credit Assignment in RL Sparse-Reward RL

Apr 8, 2026

SubSearch: Intermediate Rewards for Unsupervised Guided Reasoning in Complex Retrieval

Large language models (LLMs) are probabilistic in nature and perform more reliably when augmented with external information. As complex queries often require multi-step reasoning over the retrieved information, with no clear or predetermined reasoning path, they remain challenging. Recent approaches train models using reinforcement learning on the model's outcome, showing promise in improving how models handle complex information. We introduce SubSearch, a specialized framework that shifts from outcome-only supervision to intermediate reward signals that incentivize planning high-quality reasoning. Unlike previous work on process reward modeling, which focuses on training a separate reward model with annotated trajectories by either human annotators or large LLM judges, SubSearch directly optimizes the generator using intrinsic process rewards, which we define as internally-derived rewards, eliminating the need for external supervision, and moving towards autonomous information-intensive reasoning. Experiments on seven benchmarks show that rewarding intermediate reasoning steps with intrinsic rewards leads to more robust reasoning traces in both QA and multi-hop QA datasets over using only outcome rewards. SubSearch can help in building reasoning traces that allow agents to better integrate search engines for complex query answering, while offering a data-efficient alternative to supervised process modeling.

Roxana Petcu, Evangelos Kanoulas, Maarten de Rijke

IRLab, University of Amsterdam

RL for Language Model Reasoning Process Reward Models RL for IR Multi-Hop QA Retrieval-Augmented Generation

Apr 8, 2026

SHAPE: Stage-aware Hierarchical Advantage via Potential Estimation for LLM Reasoning

Process supervision has emerged as a promising approach for enhancing LLM reasoning, yet existing methods fail to distinguish meaningful progress from mere verbosity, leading to limited reasoning capabilities and unresolved token inefficiency. To address this, we propose Stage-aware Hierarchical Advantage via Potential Estimation (SHAPE), a framework that formalizes reasoning as a trajectory through a state space of empirical solvability. SHAPE introduces a hierarchical credit assignment mechanism: at the segment level, it employs a stage-aware advantage function to prioritize efficient breakthroughs in low-potential states; at the token level, it utilizes entropy-driven redistribution to sharpen execution signals. Extensive experiments in math reasoning across three base models and five benchmarks demonstrate that SHAPE achieves an average accuracy gain of 3% with 30% reduced token consumption.

Zhengyang Ai, Zikang Shan, Xiaodong Ai +3

Huawei Taylor Lab · Center for Data Science, Peking University · Shanghai University of Finance and Economics

LLM Reasoning Efficient Language Model Reasoning Process Supervision RL for Language Model Reasoning

Apr 8, 2026

Generate, Filter, Control, Replay: A Comprehensive Survey of Rollout Strategies for LLM Reinforcement Learning

Reinforcement learning (RL) has become a central post-training tool for improving the reasoning abilities of large language models (LLMs). In these systems, the rollout, the trajectory sampled from a prompt to termination, including intermediate reasoning steps and optional tool or environment interactions, determines the data the optimizer learns from, yet rollout design is often underreported. This survey provides an optimizer-agnostic view of rollout strategies for RL-based post-training of reasoning LLMs. We formalize rollout pipelines with unified notation and introduce Generate-Filter-Control-Replay (GFCR), a lifecycle taxonomy that decomposes rollout pipelines into four modular stages: Generate proposes candidate trajectories and topologies; Filter constructs intermediate signals via verifiers, judges, critics; Control allocates compute and makes continuation/branching/stopping decisions under budgets; and Replay retains and reuses artifacts across rollouts without weight updates, including self-evolving curricula that autonomously generate new training tasks. We complement GFCR with a criterion taxonomy of reliability, coverage, and cost sensitivity that characterizes rollout trade-offs. Using this framework, we synthesize methods spanning RL with verifiable rewards, process supervision, judge-based gating, guided and tree/segment rollouts, adaptive compute allocation, early-exit and partial rollouts, throughput optimization, and replay/recomposition for self-improvement. We ground the framework with case studies in math, code/SQL, multimodal reasoning, tool-using agents, and agentic skill benchmarks that evaluate skill induction, reuse, and cross-task transfer. Finally, we provide a diagnostic index that maps common rollout pathologies to GFCR modules and mitigation levers, alongside open challenges for building reproducible, compute-efficient, and trustworthy rollout pipelines.

Rohan Surana, Gagan Mundada, Xunyi Jiang +19

University of California, San Diego · University of Toronto · UIUC +3

RL for Language Model Reasoning RL for Language Models LLM Post-Training

Apr 7, 2026

Target Policy Optimization

In RL, given a prompt, we sample a group of completions from a model and score them. Two questions follow: which completions should gain probability mass, and how should the parameters move to realize that change? Standard policy-gradient methods answer both at once, so the update can overshoot or undershoot depending on the learning rate, clipping, and other optimizer choices. We introduce Target Policy Optimization (TPO), which separates the two questions. Given scored completions, TPO constructs a target distribution

q_i \propto p_i^{\,\mathrm{old}} \exp(u_i)

and fits the policy to it by cross-entropy. The loss gradient on sampled-completion logits is

p^θ- q

, which vanishes once the policy matches the target. On tabular bandits, transformer sequence tasks, and billion-parameter LLM RLVR, TPO matches PG, PPO, GRPO, and DG on easy tasks and substantially outperforms them under sparse reward. Code is available at https://github.com/JeanKaddour/tpo.

Jean Kaddour

Policy Optimization RL Post-Training RL for Language Model Reasoning

Apr 7, 2026

Limits of Difficulty Scaling: Hard Samples Yield Diminishing Returns in GRPO-Tuned SLMs

Recent alignment work on Large Language Models (LLMs) suggests preference optimization can improve reasoning by shifting probability mass toward better solutions. We test this claim in a resource-constrained setting by applying GRPO with LoRA to SLMs (up to 3B) for math reasoning on GSM8K and MATH datasets with difficulty-stratified analyses. As problem difficulty increases, accuracy plateaus, revealing a capacity boundary: GRPO primarily reshapes output preferences without reliably improving hardest-tier solving. Consistent with this, training GRPO only on lower-difficulty problems matches full-dataset accuracy across difficulty tiers while using only ~45% training steps, indicating diminishing returns from harder samples in this regime. We also find a cross-dataset generalization effect: GSM8K-trained GRPO achieves higher accuracy on the numeric subset of MATH than MATH-trained GRPO, exceeding it by ~5% at 1.5B and by ~3% at 3B. We show that the best achievable gains depend strongly on the base model's prior reasoning competence and the dataset's difficulty profile.

Suraj Yadav, Siddharth Yadav, Parth Goyal

IIIT Delhi

RL for Language Model Reasoning Small Language Models Group Relative Policy Optimization Numerical Reasoning in Language Models

Apr 7, 2026

Graph-Based Chain-of-Thought Pruning for Reducing Redundant Reflections in Reasoning LLMs

Extending CoT through RL has been widely used to enhance the reasoning capabilities of LLMs. However, due to the sparsity of reward signals, it can also induce undesirable thinking patterns such as overthinking, i.e., generating redundant intermediate reasoning content. In this work, we argue that a major source of such redundancy is inefficient reflection, which often manifests in two problematic patterns: Indiscriminate Reflection, where the model performs broad, low-impact checks throughout reasoning, and Repetitive Reflection, where it repeatedly re-verifies an already established conclusion. To address this, we introduce a graph-based CoT optimization framework. Specifically, we convert each linear CoT into a directed acyclic graph (DAG) with explicit dependency edges, and design a dual pruning strategy: branch-level pruning removes weakly contributing reflection branches, while depth-level pruning eliminates late-stage re-verification. We distill this behavior via a three-stage pipeline: (1) SFT to initialize the policy on pruned concise traces, (2) DPO to prefer correct but less redundant trajectories, and (3) GRPO with length penalty to jointly optimize answer correctness and efficiency. Experiments show that our approach reduces the average reasoning tokens by 42% while maintaining or improving accuracy.

Hongyuan Yuan, Xinran He, Run Shao +6

School of Geosciences and Info-Physics, Central South University, Changsha, China · Baidu Inc., Beijing, China

Efficient Language Model Reasoning Overthinking in Language Models RL for Language Model Reasoning

Apr 7, 2026

ETR: Entropy Trend Reward for Efficient Chain-of-Thought Reasoning

Chain-of-thought (CoT) reasoning improves large language model performance on complex tasks, but often produces excessively long and inefficient reasoning traces. Existing methods shorten CoTs using length penalties or global entropy reduction, implicitly assuming that low uncertainty is desirable throughout reasoning. We show instead that reasoning efficiency is governed by the trajectory of uncertainty. CoTs with dominant downward entropy trends are substantially shorter. Motivated by this insight, we propose Entropy Trend Reward (ETR), a trajectory-aware objective that encourages progressive uncertainty reduction while allowing limited local exploration. We integrate ETR into Group Relative Policy Optimization (GRPO) and evaluate it across multiple reasoning models and challenging benchmarks. ETR consistently achieves a superior accuracy-efficiency tradeoff, improving DeepSeek-R1-Distill-7B by 9.9% in accuracy while reducing CoT length by 67% across four benchmarks. Code is available at https://github.com/Xuan1030/ETR

Xuan Xiong, Huan Liu, Li Gu +4

University of Toronto · McMaster University · Concordia University +1

Efficient Language Model Reasoning CoT Reasoning RL for Language Model Reasoning Reward Shaping

Apr 6, 2026

Not All Turns Are Equally Hard: Adaptive Thinking Budgets For Efficient Multi-Turn Reasoning in Agents

As LLM reasoning performance plateaus, improving inference-time compute efficiency is crucial to mitigate overthinking and long thinking traces even for simple queries. Prior approaches including length regularization, adaptive routing, and difficulty-based budget allocation primarily focus on single-turn settings and fail to address the sequential dependencies inherent in multi-turn reasoning. In this work, we formulate multi-turn reasoning as a sequential compute allocation problem and model it as a multi-objective Markov Decision Process. We propose TAB: Turn-Adaptive Budgets, a budget allocation policy trained via Group Relative Policy Optimization (GRPO) that learns to maximize task accuracy while respecting global per-problem token constraints. Consequently, TAB takes as input the conversation history and learns to adaptively allocate smaller budgets to easier turns and save appropriate number of tokens for the crucial harder reasoning steps. Our experiments on diverse agentic benchmarks demonstrate that TAB achieves a superior accuracy-cost tradeoff saving up to 35% tokens and reducing latency up to 30% while maintaining accuracy over static and off-the-shelf LLM budget baselines. Further, for systems where a plan of all turns is available apriori, we propose TAB All-SubQ, a budget allocation policy that budgets tokens based on the conversation history and entire plan saving up to 40% tokens over baselines.

Neharika Jali, Anupam Nayak, Gauri Joshi

Carnegie Mellon University

Multi-Turn Language Model Reasoning Efficient Language Model Reasoning Inference-Time Compute Allocation LLM Inference Scheduling RL for Language Model Reasoning

Apr 6, 2026

How Reasoning Evolves from Post-Training Data: An Empirical Study Using Chess

We study how reasoning evolves in a language model -- from supervised fine-tuning (SFT) to reinforcement learning (RL) -- by analyzing how a set of theoretically-inspired datasets influences language model performance in chess. We find that fine-tuning a model to directly predict the best move leads to effective RL and the strongest downstream performance -- however, the RL stage elicits unfaithful reasoning (reasoning inconsistent with the chosen move). Alternatively, training on multi-move trajectories yields comparable downstream performance with faithful reasoning and more stable RL. We analyze multiple qualitative and quantitative measures and highlight how these evolve from SFT through RL; we find several SFT-checkpoint metrics -- spanning evaluation performance, hallucination rates, and reasoning quality -- to be predictive of post-RL model performance. Finally, we ground our results with an experiment measuring chess information density in our custom datasets. We release models as well as training data, evaluations, and code that allowed us to surpass leading open-source reasoning models in chess with a 7B-parameter model. Code, models, and data are available at https://github.com/lucasdino/lang-chess.

Lucas Dionisopoulos, Nicklas Majamaki, Prithviraj Ammanabrolu

Department of Computer Science and Engineering, University of California San Diego, San Diego, United States.

Language Model Post-Training RL for Language Model Reasoning Reasoning Consistency in Language Models

Apr 6, 2026

QED-Nano: Teaching a Tiny Model to Prove Hard Theorems

Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO). However, the training pipelines behind these systems remain largely undisclosed, and their reliance on large "internal" models and scaffolds makes them expensive to run, difficult to reproduce, and hard to study or improve upon. This raises a central question: can small, open models also be trained to achieve competitive reasoning performance on difficult Olympiad-level math? In this paper, we answer this question by building QED-Nano, a 4B model post-trained for Olympiad-level proofs. Our training recipe has three stages: (1) supervised fine-tuning to imbue good proof-writing styles by distilling from DeepSeek-Math-V2, (2) reinforcement learning (RL) with rubric-based rewards, and (3) expanding RL with a reasoning cache, which decomposes long proofs into iterative summarize-and-refine cycles and enables stronger test-time reasoning. QED-Nano surpasses the proof-generation performance of much larger open models, including Nomos-1 and GPT-OSS-120B, and approaches the performance of proprietary models like Gemini 3 Pro, at a fraction of the inference cost. To support further research on open mathematical reasoning, we release the full QED-Nano pipeline, including the QED-Nano and QED-Nano-SFT models, the FineProofs-SFT and FineProofs-RL datasets, and the training and evaluation code.

LM-Provers, Yuxiao Qu, Amrith Setlur +6

CMU · Hugging Face · ETH Zurich +1

Mathematical Reasoning LLM Mathematical Reasoning Efficient Language Model Reasoning Automated Theorem Proving RL for Language Model Reasoning

Apr 6, 2026

Asymmetric Advantage Modulation Calibrates Entropy Dynamics in RLVR

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning ability of large language models (LLMs), but it often suffers from restricted exploration, where the policy rapidly concentrates on a narrow set of solutions. A common remedy is entropy regularization, which attempts to preserve exploration by increasing policy entropy. However, for LLM-RL, this intervention is highly sensitive to its coefficient, can introduce semantically weak uncertainty, and often yields limited accuracy gains. This motivates a more precise question: which entropy helps reasoning, and which entropy should be reduced? To study this, we parameterize the advantage estimator in Group Relative Policy Optimization (GRPO) into positive and negative outcome-conditioned channels and analyze their entropy dynamics. Our results show that positive-channel modulation raises productive entropy associated with successful reasoning trajectories, while negative-channel modulation removes noisy entropy associated with failed rollouts and reduces interference with correct paths. Guided by this channel-wise view, we propose AsymGRPO, which decouples the modulation strengths of positive and negative advantages. This enables flexible control over how the model updates across prompt difficulty levels, allowing stronger reinforcement of rare successes on harder prompts or stronger suppression of residual failures on easier prompts without forcing the two channels to share the same modulation strength. Experiments on five mathematical reasoning benchmarks show that AsymGRPO outperforms strong RLVR baselines, with consistent gains across model backbones.

Hengrui Gu, Xiaotian Han, Yujing Bian +2

North Carolina State University · Case Western Reserve University · Oak Ridge National Laboratory

RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Group Relative Policy Optimization Entropy Regularization

Apr 6, 2026

Cog-DRIFT: Exploration on Adaptively Reformulated Instances Enables Learning from Hard Reasoning Problems

Reinforcement learning from verifiable rewards (RLVR) has improved the reasoning abilities of LLMs, yet a fundamental limitation remains: models cannot learn from problems that are too difficult to solve under their current policy, as these yield no meaningful reward signal. We propose a simple yet effective solution based on task reformulation. We transform challenging open-ended problems into cognitively simpler variants -- such as multiple-choice and cloze formats -- that preserve the original answer while reducing the effective search space and providing denser learning signals. These reformulations span a spectrum from discriminative to generative tasks, which we exploit to bootstrap learning: models first learn from structured, easier formats, and this knowledge transfers back to improve performance on the original open-ended problems. Building on this insight, we introduce Cog-DRIFT, a framework that constructs reformulated variants and organizes them into an adaptive curriculum based on difficulty. Training progresses from easier to harder formats, enabling the model to learn from problems that previously yielded zero signal under standard RL post-training. Cog-DRIFT not only improves on the originally unsolvable hard problems (absolute +10.11% for Qwen and +8.64% for Llama) but also generalizes well to other held-out datasets. Across 2 models and 6 reasoning benchmarks, our method consistently outperforms standard GRPO and strong guided-exploration baselines. On average, Cog-DRIFT shows +4.72% (Qwen) and +3.23% (Llama) improvements over the second-best baseline. We further show that Cog-DRIFT improves pass@k at test time, and the curriculum improves sample efficiency. Overall, our results highlight task reformulation and curriculum learning as an effective paradigm for overcoming the exploration barrier in LLM post-training.

Justin Chih-Yao Chen, Archiki Prasad, Zaid Khan +4

UNC Chapel Hill

RL for Language Model Reasoning LLM Reasoning Reinforcement Learning with Verifiable Rewards Curriculum RL

Apr 6, 2026

Delay, Plateau, or Collapse: Evaluating the Impact of Systematic Verification Error on RLVR

Reinforcement Learning with Verifiable Rewards (RLVR) has become a powerful approach for improving the reasoning capabilities of large language models (LLMs). While RLVR is designed for tasks with verifiable ground-truth answers, real-world verifiers (e.g., static code checkers) can introduce errors into the reward signal. Prior analyses have largely treated such errors as random and independent across samples, concluding that errors merely slow training with limited effect on final performance. However, practical verifiers tend to exhibit systematic errors. This introduces a risk of models learning unwanted consistent behavior from a structurally incorrect reward signal. In this work, we study the impact of such systematic verification errors on RLVR. Through controlled experiments on arithmetic tasks, we show that systematic false negatives lead to similar effects as random noise. On the other hand, systematic false positives can cause a wide range of behaviors from sub-optimal plateaus to performance collapse. Crucially, these outcomes are not determined by the overall error rate but by the specific pattern of introduced errors, making pre-hoc mitigation difficult. Our results show that, in contrast to prior conclusions, realistic verification errors can critically shape RLVR outcomes and that verifier quality has to be understood beyond its sample-level error rate.

Kazuki Egashira, Mark Vero, Jasper Dekoninck +3

ETH Zurich · Max Planck Institute for Intelligent Systems, Tübingen

Reinforcement Learning with Verifiable Rewards RL for Language Model Reasoning

Apr 6, 2026

When Rewards Disagree: Reward Weighting for Token-Efficient Video Reasoning

Human perception interprets video dynamics by constructing structured mental representations of entities, actions, and temporal boundaries before engaging in high-level reasoning. In contrast, current Video-LLMs typically rely on unstructured Chain-of-Thought (CoT), where crucial visual cues are obscured by verbose narration. While recent efforts ground reasoning in intermediate visual evidence, they rely on task-specific schemas that fail to generalize across diverse video understanding tasks. To address this, we introduce Structured Event Evidence, a unified, temporally ordered schema designed for general video reasoning. However, post-training a model to extract structured evidence while reasoning introduces a severe multi-objective optimization bottleneck, as candidate rollouts must simultaneously satisfy schema compliance, task accuracy, and reasoning budget. Standard reinforcement learning (RL) algorithms attempt to balance these objectives via static scalarization, enforcing a rigid accuracy-length trade-off across training and obscuring fine-grained reward signals. We resolve this by proposing Group-Relative Advantage Balancing (GRAB), which dynamically computes Pareto-optimal objective weights within each rollout group via a minimum-norm criterion over centered rewards. Operating strictly in reward space, GRAB incurs virtually zero computational overhead (<0.002% relative runtime to GRPO) and eliminates brittle weight tuning. Supported by our new PARSE-60K dataset (60K annotations across 35K videos) and a three-stage progressive curriculum, we train PARSE-4B. Across temporal grounding and video question-answering benchmarks, GRAB generates 13% to 39% fewer tokens while maintaining competitive accuracy with exhaustively hand-tuned static weights -- without requiring hyperparameter weight sweeps.

Zinuo Li, Yongxin Guo, Jun Liu +6

University of Western Australia · Tencent Youtu Lab · CUHKSZ +2

Video Reasoning VLM Reasoning Temporal Video Understanding RL for Video Reasoning RL for Language Model Reasoning Multi-Objective Reinforcement Learning

Apr 4, 2026

Design Conditions for Intra-Group Learning of Sequence-Level Rewards: Token Gradient Cancellation

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.

Fei Ding, Yongkang Zhang, youwei wang +1

Alibaba Group · Tsinghua University

RL for Language Model Reasoning Step-Level Credit Assignment in RL Sparse-Reward RL Counterfactual Credit Assignment

Apr 3, 2026

BioAlchemy: Distilling Biological Literature into Reasoning-Ready Reinforcement Learning Training Data

Despite the large corpus of biology training text, the impact of reasoning models on biological research generally lags behind math and coding. In this work, we show that biology questions from current large-scale reasoning datasets do not align well with modern research topic distributions in biology, and that this topic imbalance may negatively affect performance. In addition, we find that methods for extracting challenging and verifiable research problems from biology research text are a critical yet underdeveloped ingredient in applying reinforcement learning for better performance on biology research tasks. We introduce BioAlchemy, a pipeline for sourcing a diverse set of verifiable question-and-answer pairs from a scientific corpus of biology research text. We curate BioAlchemy-345K, a training dataset containing over 345K scientific reasoning problems in biology. Then, we demonstrate how aligning our dataset to the topic distribution of modern scientific biology can be used with reinforcement learning to improve reasoning performance. Finally, we present BioAlchemist-8B, which improves over its base reasoning model by 9.12% on biology benchmarks. These results demonstrate the efficacy of our approach for developing stronger scientific reasoning capabilities in biology. The BioAlchemist-8B model is available at: https://huggingface.co/BioAlchemy.

Brian Hsu, Ozan Gökdemir, Carlo Siebenschuh +7

Department of Computer Science, University of Chicago, Chicago, IL 60637 · Data Science and Learning Division, Argonne National Laboratory, Lemont, IL 60439

Scientific Reasoning in Language Models Scientific QA RL for Language Model Reasoning

Apr 3, 2026

Vocabulary Dropout for Curriculum Diversity in LLM Co-Evolution

Co-evolutionary self-play, where one language model generates problems and another solves them, promises curriculum learning without human supervision. The promise breaks down early in practice. The proposer converges to a narrow distribution of problems that satisfy the reward function, and the collapsed curriculum teaches the solver little, stalling the loop. We introduce vocabulary dropout, a lightweight intervention that randomly masks the proposer's output logits during both policy training and curriculum generation. The mask is hard and non-stationary, so the proposer cannot lock into fixed token sequences. Training Qwen3-4B and Qwen3-8B on mathematical reasoning via R-Zero, vocabulary dropout sustains proposer diversity throughout training across lexical, semantic, and functional measures, and improves the solver by an average of +4.4 points at 8B with the largest gains on competition-level benchmarks. Explicit action-space constraints, filling the structural role that game rules fill in classical self-play, can keep co-evolution in language productive. Vocabulary dropout is one simple way to impose them.

Jacob Dineen, Aswin RRV, Zhikun Xu +1

Arizona State University

Curriculum RL RL for Language Model Reasoning LLM Reasoning