# Self-Explore: Enhancing Mathematical Reasoning in Language Models with Fine-grained Rewards

arXiv: https://arxiv.org/abs/2404.10346 · HTML: https://mlsanity.com/paper/2404.10346/

## Key facts

- Cited by 31 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 57 of its 60 references that are in the map.
- First posted on arXiv 16 Apr 2024.

## 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 57)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [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)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (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)
- [Zephyr: Direct Distillation of LM Alignment](https://mlsanity.com/paper/2310.16944/) (2023)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision](https://mlsanity.com/paper/2312.09390/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)

## Built on by (most cited first, 30 of 31)

- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models](https://mlsanity.com/paper/2501.09686/) (2025)
- [From r to Q^*: Your Language Model is Secretly a Q-Function](https://mlsanity.com/paper/2404.12358/) (2024)
- [SWEET-RL: Training Multi-Turn LLM Agents on Collaborative Reasoning Tasks](https://mlsanity.com/paper/2503.15478/) (2025)
- [Concise Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2504.05185/) (2025)
- [1.4 Million Open-Source Distilled Reasoning Dataset to Empower Large Language Model Training](https://mlsanity.com/paper/2503.19633/) (2025)
- [Ignore the KL Penalty! Boosting Exploration on Critical Tokens to Enhance RL Fine-Tuning](https://mlsanity.com/paper/2502.06533/) (2025)
- [Topology of Reasoning: Understanding Large Reasoning Models through Reasoning Graph Properties](https://mlsanity.com/paper/2506.05744/) (2025)
- [Exploiting Tree Structure for Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2509.18314/) (2025)
- [Thinking Machines: A Survey of LLM based Reasoning Strategies](https://mlsanity.com/paper/2503.10814/) (2025)
- [GRPO-λ: Credit Assignment improves LLM Reasoning](https://mlsanity.com/paper/2510.00194/) (2025)
- [The Role of Deductive and Inductive Reasoning in Large Language Models](https://mlsanity.com/paper/2410.02892/) (2024)
- [Stepwise Guided Policy Optimization: Coloring your Incorrect Reasoning in GRPO](https://mlsanity.com/paper/2505.11595/) (2025)
- [Generative AI Act II: Test Time Scaling Drives Cognition Engineering](https://mlsanity.com/paper/2504.13828/) (2025)
- [Don't Pass@k: A Bayesian Framework for Large Language Model Evaluation](https://mlsanity.com/paper/2510.04265/) (2025)
- [Enhancing Reasoning through Process Supervision with Monte Carlo Tree Search](https://mlsanity.com/paper/2501.01478/) (2025)
- [MPBench: A Comprehensive Multimodal Reasoning Benchmark for Process Errors Identification](https://mlsanity.com/paper/2503.12505/) (2025)
- [CPL: Critical Plan Step Learning Boosts LLM Generalization in Reasoning Tasks](https://mlsanity.com/paper/2409.08642/) (2024)
- [ClinicalGPT-R1: Pushing reasoning capability of generalist disease diagnosis with large language model](https://mlsanity.com/paper/2504.09421/) (2025)
- [RATIONALYST: Mining Implicit Rationales for Process Supervision of Reasoning](https://mlsanity.com/paper/2410.01044/) (2024)
- [Self-Training Meets Consistency: Improving LLMs' Reasoning with Consistency-Driven Rationale Evaluation](https://mlsanity.com/paper/2411.06387/) (2024)
- [A Short Survey on Small Reasoning Models: Training, Inference, Applications and Research Directions](https://mlsanity.com/paper/2504.09100/) (2025)
- [AQuilt: Weaving Logic and Self-Inspection into Low-Cost, High-Relevance Data Synthesis for Specialist LLMs](https://mlsanity.com/paper/2507.18584/) (2025)
- [Self-Verified Distillation: Your Language Model Is Secretly Its Own Synthetic Data Pipeline](https://mlsanity.com/paper/2605.26132/) (2026)
- [Large Language Models Are Self-Taught Reasoners: Enhancing LLM Applications via Tailored Problem-Solving Demonstrations](https://mlsanity.com/paper/2408.12315/) (2024)
- [p2-TQA: A Process-based Preference Learning Framework for Self-Improving Table Question Answering Models](https://mlsanity.com/paper/2505.17565/) (2025)
- [Datarus-R1: An Adaptive Multi-Step Reasoning LLM for Automated Data Analysis](https://mlsanity.com/paper/2508.13382/) (2025)
- [TORSO: Template-Oriented Reasoning Towards General Tasks](https://mlsanity.com/paper/2509.09448/) (2025)
- [From Implicit to Explicit: Token-Efficient Logical Supervision for Mathematical Reasoning in LLMs](https://mlsanity.com/paper/2601.03682/) (2026)
- [CoTZero: Annotation-Free Human-Like Vision Reasoning via Hierarchical Synthetic CoT](https://mlsanity.com/paper/2602.08339/) (2026)

## Abstract (arXiv)

Training on large amounts of rationales (i.e., CoT Fine-tuning) is effective at improving the reasoning capabilities of large language models (LLMs). However, acquiring human-authored rationales or augmenting rationales from proprietary models is costly and not scalable. In this paper, we study the problem of whether LLMs could self-improve their reasoning capabilities. To this end, we propose Self-Explore, where the LLM is tasked to explore the first wrong step (i.e., the first pit) within the rationale and use such signals as fine-grained rewards for further improvement. On the GSM8K and MATH test set, Self-Explore achieves 11.57% and 2.89% improvement on average across three LLMs compared to supervised fine-tuning (SFT). Our code is available at https://github.com/hbin0701/Self-Explore.