# GRPO-λ: Credit Assignment improves LLM Reasoning

arXiv: https://arxiv.org/abs/2510.00194 · HTML: https://mlsanity.com/paper/2510.00194/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 37 of its 75 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 37)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Instruction Tuning for Large Language Models: A Survey](https://mlsanity.com/paper/2308.10792/) (2023)
- [Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models](https://mlsanity.com/paper/2305.04091/) (2023)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)
- [KTO: Model Alignment as Prospect Theoretic Optimization](https://mlsanity.com/paper/2402.01306/) (2024)
- [VinePPO: Refining Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2410.01679/) (2024)
- [Token-level Direct Preference Optimization](https://mlsanity.com/paper/2404.11999/) (2024)
- [Back to Basics: Revisiting REINFORCE Style Optimization for Learning from Human Feedback in LLMs](https://mlsanity.com/paper/2402.14740/) (2024)
- [LiPO: Listwise Preference Optimization through Learning-to-Rank](https://mlsanity.com/paper/2402.01878/) (2024)

## Built on by (most cited first, 23 of 23)

- [Unifying Group-Relative and Self-Distillation Policy Optimization via Sample Routing](https://mlsanity.com/paper/2604.02288/) (2026)
- [DASH: Divergence-Adaptive Supervision Horizons for On-Policy Self-Distillation of Reasoning Models](https://mlsanity.com/paper/2608.06243/) (2026)
- [Thinking with Deltas: Incentivizing Reinforcement Learning via Differential Visual Reasoning Policy](https://mlsanity.com/paper/2601.06801/) (2026)
- [Beyond Uniform Credit Assignment: Selective Eligibility Traces for RLVR](https://mlsanity.com/paper/2605.05965/) (2026)
- [Efficient Paths and Dense Rewards: Probabilistic Flow Reasoning for Large Language Models](https://mlsanity.com/paper/2601.09260/) (2026)
- [Modularized Reinforcement Learning on LLMs: From MDP Creation to Exploration and Learning](https://mlsanity.com/paper/2606.21943/) (2026)
- [DRIFT: Difficulty Routing Self-DIstillation with Rhythm-Gated Exploration and Success BuFfer Training](https://mlsanity.com/paper/2606.30345/) (2026)
- [Breaking Failure Cascades: Step-Aware Reinforcement Learning for Medical Multimodal Reasoning](https://mlsanity.com/paper/2606.31825/) (2026)
- [MoRSE: Task-Oriented Multi-Agent System with Mixture of Role-Subtask Experts](https://mlsanity.com/paper/2608.09251/) (2026)
- [Learning When to Think: Adaptive Reasoning for Test-Time Compute Allocation](https://mlsanity.com/paper/2608.20256/) (2026)
- [Learning CLI Agents with Structured Action Credit under Selective Observation](https://mlsanity.com/paper/2605.08013/) (2026)
- [Trait-Aware Policy Optimization for Autoregressive Multi-Trait Essay Scoring](https://mlsanity.com/paper/2605.25731/) (2026)
- [A First-Principles Derivation of LLM Policy Optimization: From Expected Reward to GRPO and Its Structural Extensions](https://mlsanity.com/paper/2606.16733/) (2026)
- [When Implausible Tokens Get Reinforced: Tail-Aware Credit Calibration for LLM Reinforcement Learning](https://mlsanity.com/paper/2607.07976/) (2026)
- [IAPO: Influence-Aware Policy Optimization for Credit Assignment in Multi-Turn Service Agents](https://mlsanity.com/paper/2608.24588/) (2026)
- [TISD: On-Policy Self-Distillation with Trajectory Intervention](https://mlsanity.com/paper/2609.30878/) (2026)
- [Not All Tokens Deserve Equal Credit: Counterfactual Sensitivity Credit Reallocation for Long-CoT Reasoning](https://mlsanity.com/paper/2607.27888/) (2026)
- [Let Credit Follow Computation: Architecture-Aware Credit Transport for Large Language Model Reinforcement Learning](https://mlsanity.com/paper/2608.21501/) (2026)
- [Reinforcement Learning with Decomposed Subtasks](https://mlsanity.com/paper/2609.27035/) (2026)
- [Advancing Entropy-Level Credit Assignment in RLVR via Proximal Entropy Policy Optimization](https://mlsanity.com/paper/2609.39402/) (2026)
- [Characterizing a Configuration Where Inference-Time PRM-Pruned Fragment Grafting Is Inert: Evidence from Three Reasoning LMs](https://mlsanity.com/paper/2610.00047/) (2026)
- [Agentic RCA for Internet-Scale Services Using Constrained Creativity](https://mlsanity.com/paper/2610.08622/) (2026)
- [BoT-GRPO: Efficient Process-Reward RL for Reasoning via Bag-of-Token Aggregation](https://mlsanity.com/paper/2610.09804/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are increasingly deployed for tasks requiring complex reasoning, prompting significant interest in improving their reasoning abilities through post-training. Especially RL based methods using verifiable reward, like the state-of-the-art GRPO, have shown to tremendously improve reasoning behaviors when applied as post-training methods. However, the lack of an explicit reward or critic model limits GRPO's ability to assign fine-grained credit across token sequences. In this work, we present GRPO-λ, a novel extension to GRPO that enhances credit assignment in RL finetuning of LLMs for complex reasoning tasks. We approximate learning from λ-return with a reformulation of eligibility traces using token-level log-probabilities applied after each sequence generation, and a novel critic-free approximation of the temporal-difference error. We introduce a few variations for the weighting of the λ-return, and their applications to the eligibility-trace, where all the variations provide significant gains over GRPO. We compare GRPO-λ against GRPO by training models from 1.5B to 7B parameters on 4 different math reasoning datasets. The training plots demonstrate 30-40% improved performance during RL training on both LLaMA-3.1 and Qwen-2.5 architectures. Finally, we show that with GRPO-λ, the resulting average performance on AIME24, Math500, OlympiadMath, MinervaMath, and AMC improves over GRPO by over 3 points and a 4.5 points improvement on the 7B model.