# Reasoning Paths Optimization: Learning to Reason and Explore From Diverse Paths

arXiv: https://arxiv.org/abs/2410.10858 · HTML: https://mlsanity.com/paper/2410.10858/

## Key facts

- Cited by 6 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 21 of its 63 references that are in the map.
- First posted on arXiv 7 Oct 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, 21 of 21)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [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)
- [ORPO: Monolithic Preference Optimization without Reference Model](https://mlsanity.com/paper/2403.07691/) (2024)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Orca: Progressive Learning from Complex Explanation Traces of GPT-4](https://mlsanity.com/paper/2306.02707/) (2023)
- [Iterative Reasoning Preference Optimization](https://mlsanity.com/paper/2404.19733/) (2024)
- [Secrets of RLHF in Large Language Models Part I: PPO](https://mlsanity.com/paper/2307.04964/) (2023)
- [Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future](https://mlsanity.com/paper/2309.15402/) (2023)
- [Evaluation of OpenAI o1: Opportunities and Challenges of AGI](https://mlsanity.com/paper/2409.18486/) (2024)
- [Boosting Language Models Reasoning with Chain-of-Knowledge Prompting](https://mlsanity.com/paper/2306.06427/) (2023)
- [Multi-step Problem Solving Through a Verifier: An Empirical Analysis on Model-induced Process Supervision](https://mlsanity.com/paper/2402.02658/) (2024)
- [Flacuna: Unleashing the Problem Solving Power of Vicuna using FLAN Fine-Tuning](https://mlsanity.com/paper/2307.02053/) (2023)
- [PathFinder: Guided Search over Multi-Step Reasoning Paths](https://mlsanity.com/paper/2312.05180/) (2023)

## Built on by (most cited first, 6 of 6)

- [The Danger of Overthinking: Examining the Reasoning-Action Dilemma in Agentic Tasks](https://mlsanity.com/paper/2502.08235/) (2025)
- [SciReplicate-Bench: Benchmarking LLMs in Agent-driven Algorithmic Reproduction from Research Papers](https://mlsanity.com/paper/2504.00255/) (2025)
- [FROST: Filtering Reasoning Outliers with Attention for Efficient Reasoning](https://mlsanity.com/paper/2601.19001/) (2026)
- [Putting on the Thinking Hats: A Survey on Chain of Thought Fine-tuning from the Perspective of Human Reasoning Mechanism](https://mlsanity.com/paper/2510.13170/) (2025)
- [Beyond Entropy: Correctness-Aware Advantage Shaping via Contrastive Policy Optimization](https://mlsanity.com/paper/2607.14614/) (2026)
- [It Takes 8 Tokens: Weak-to-Strong Off-Policy RL via Auxiliary Branches](https://mlsanity.com/paper/2607.16205/) (2026)

## Abstract (arXiv)

Advanced models such as OpenAI o1 exhibit impressive problem-solving capabilities through step-by-step reasoning. However, they may still falter on more complex problems, making errors that disrupt their reasoning paths. We attribute this to the expansive solution space, where each step has the risk of diverging into mistakes. To enhance language model reasoning, we introduce a specialized training framework called Reasoning Paths Optimization (RPO), which enables learning to reason and explore from diverse paths. Our approach encourages favorable branches at each reasoning step while penalizing unfavorable ones, enhancing the model's overall problem-solving performance. Reasoning Paths Optimization does not rely on large-scale human-annotated rationales or outputs from closed-source models, making it scalable and data-efficient. We focus on multi-step reasoning tasks, such as math word problems and science-based exam questions. The experiments demonstrate that our framework significantly enhances the reasoning performance of large language models, with up to 3.1% and 4.3% improvement on GSM8K and MMLU (STEM) respectively. Our data and code can be found at https://reasoning-paths.github.io.