# GPO: Learning from Critical Steps to Improve LLM Reasoning

arXiv: https://arxiv.org/abs/2509.16456 · HTML: https://mlsanity.com/paper/2509.16456/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 40 of its 72 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 40)

- [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)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [WebArena: A Realistic Web Environment for Building Autonomous Agents](https://mlsanity.com/paper/2307.13854/) (2023)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [ORPO: Monolithic Preference Optimization without Reference Model](https://mlsanity.com/paper/2403.07691/) (2024)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [KTO: Model Alignment as Prospect Theoretic Optimization](https://mlsanity.com/paper/2402.01306/) (2024)
- [ReFT: Reasoning with Reinforced Fine-Tuning](https://mlsanity.com/paper/2401.08967/) (2024)
- [VinePPO: Refining Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2410.01679/) (2024)
- [DistiLLM: Towards Streamlined Distillation for Large Language Models](https://mlsanity.com/paper/2402.03898/) (2024)
- [MiniLLM: On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2306.08543/) (2023)
- [BIG-Bench Extra Hard](https://mlsanity.com/paper/2502.19187/) (2025)
- [Q*: Improving Multi-step Reasoning for LLMs with Deliberative Planning](https://mlsanity.com/paper/2406.14283/) (2024)
- [Planning In Natural Language Improves LLM Search For Code Generation](https://mlsanity.com/paper/2409.03733/) (2024)
- [Satori: Reinforcement Learning with Chain-of-Action-Thought Enhances LLM Reasoning via Autoregressive Search](https://mlsanity.com/paper/2502.02508/) (2025)

## Built on by (most cited first, 10 of 10)

- [The Debate on RLVR Reasoning Capability Boundary: Shrinkage, Expansion, or Both? A Two-Stage Dynamic View](https://mlsanity.com/paper/2510.04028/) (2025)
- [TRIM: Hybrid Inference via Targeted Stepwise Routing in Multi-Step Reasoning Tasks](https://mlsanity.com/paper/2601.10245/) (2026)
- [AIR: Post-training Data Selection for Reasoning via Attention Head Influence](https://mlsanity.com/paper/2512.13279/) (2025)
- [Stabilizing Unsupervised Self-Evolution of MLLMs via Continuous Softened Retracing reSampling](https://mlsanity.com/paper/2604.03647/) (2026)
- [Believe Your Model: Distribution-Guided Confidence Calibration](https://mlsanity.com/paper/2603.03872/) (2026)
- [Skip-Connected Policy Optimization for Implicit Advantage](https://mlsanity.com/paper/2604.08690/) (2026)
- [IsoSci: A Benchmark of Isomorphic Cross-Domain Science Problems for Evaluating Reasoning versus Knowledge Retrieval in LLMs](https://mlsanity.com/paper/2607.01431/) (2026)
- [Learning Where Outcomes Change:Credit-Addressable Reasoning for Multimodal Geometry](https://mlsanity.com/paper/2608.30457/) (2026)
- [Tracking the Moving Frontier: Long-Short Term Advantage Estimator](https://mlsanity.com/paper/2609.06671/) (2026)
- [Reflective Recovery: A Self-Supervised Method for Reasoning by Learning from Mistakes](https://mlsanity.com/paper/2609.19156/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are increasingly used in various domains, showing impressive potential on different tasks. Recently, reasoning LLMs have been proposed to improve the textitreasoning or textitthinking capabilities of LLMs to solve complex problems. Despite the promising results of reasoning LLMs, enhancing the multi-step reasoning capabilities of LLMs still remains a significant challenge. While existing optimization methods have advanced the LLM reasoning capabilities, they often treat reasoning trajectories as a whole, without considering the underlying critical steps within the trajectory. In this paper, we introduce Guided Pivotal Optimization (GPO), a novel fine-tuning strategy that dives into the reasoning process to enable more effective improvements. GPO first identifies the `critical step' within a reasoning trajectory - a point that the model must carefully proceed to succeed at the problem. We locate the critical step by estimating the advantage function. GPO then resets the policy to the critical step, samples the new rollout and prioritizes the learning process on those rollouts. This focus allows the model to learn more effectively from pivotal moments within the reasoning process to improve the reasoning performance. We demonstrate that GPO is a general strategy that can be integrated with various optimization methods to improve reasoning performance. Besides theoretical analysis, our experiments across challenging reasoning benchmarks show that GPO can consistently and significantly enhance the performance of existing optimization methods, showcasing its effectiveness and generalizability in improving LLM reasoning by concentrating on pivotal moments within the generation process.