# Reasoning Path Divergence: A New Metric and Curation Strategy to Unlock LLM Diverse Thinking

arXiv: https://arxiv.org/abs/2510.26122 · HTML: https://mlsanity.com/paper/2510.26122/

## 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 36 of its 38 references that are in the map.
- First posted on arXiv 30 Oct 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 36)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [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)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [Understanding the Effects of RLHF on LLM Generalisation and Diversity](https://mlsanity.com/paper/2310.06452/) (2023)
- [What Makes Good Data for Alignment? A Comprehensive Study of Automatic Data Selection in Instruction Tuning](https://mlsanity.com/paper/2312.15685/) (2023)
- [SemDeDup: Data-efficient learning at web-scale through semantic deduplication](https://mlsanity.com/paper/2303.09540/) (2023)
- [A Survey on Data Selection for Language Models](https://mlsanity.com/paper/2402.16827/) (2024)
- [When More is Less: Understanding Chain-of-Thought Length in LLMs](https://mlsanity.com/paper/2502.07266/) (2025)
- [The Good, The Bad, and The Greedy: Evaluation of LLMs Should Not Ignore Non-Determinism](https://mlsanity.com/paper/2407.10457/) (2024)
- [Self-Training Elicits Concise Reasoning in Large Language Models](https://mlsanity.com/paper/2502.20122/) (2025)
- [Inference-Aware Fine-Tuning for Best-of-N Sampling in Large Language Models](https://mlsanity.com/paper/2412.15287/) (2024)
- [Preserving Diversity in Supervised Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2408.16673/) (2024)
- [AdaCtrl: Towards Adaptive and Controllable Reasoning via Difficulty-Aware Budgeting](https://mlsanity.com/paper/2505.18822/) (2025)
- [Scaling Laws of Synthetic Data for Language Models](https://mlsanity.com/paper/2503.19551/) (2025)
- [Diversity-Aware Policy Optimization for Large Language Model Reasoning](https://mlsanity.com/paper/2505.23433/) (2025)
- [Weight Ensembling Improves Reasoning in Language Models](https://mlsanity.com/paper/2504.10478/) (2025)
- [Self-Correction is More than Refinement: A Learning Framework for Visual and Language Reasoning Tasks](https://mlsanity.com/paper/2410.04055/) (2024)

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

- [RebuttalAgent: Strategic Persuasion in Academic Rebuttal via Theory of Mind](https://mlsanity.com/paper/2601.15715/) (2026)
- [FrontierSmith: Synthesizing Open-Ended Coding Problems at Scale](https://mlsanity.com/paper/2605.14445/) (2026)
- [The Homogenization Problem in LLMs: Towards Meaningful Diversity in AI Safety](https://mlsanity.com/paper/2601.06116/) (2026)
- [Are We Measuring Strategy or Phrasing? The Gap Between Surface- and Approach-Level Diversity in LLM Math Reasoning](https://mlsanity.com/paper/2606.29985/) (2026)
- [Beyond Accuracy: Evaluating Strategy Diversity in LLM Mathematical Reasoning](https://mlsanity.com/paper/2605.09292/) (2026)
- [Fork-Think with Confidence](https://mlsanity.com/paper/2606.31484/) (2026)
- [Adversarial Moral Stress Testing of Large Language Models](https://mlsanity.com/paper/2604.01108/) (2026)
- [Locked at the Entrance, Open Inside: Where RLVR Narrows the Solution Space](https://mlsanity.com/paper/2608.29188/) (2026)
- [Selecting Diverse SFT Traces Improves Post-RL Generalization](https://mlsanity.com/paper/2609.33780/) (2026)
- [On-Policy Parameter Update Direction Underlies Generalization in LLM Post-Training](https://mlsanity.com/paper/2609.36659/) (2026)

## Abstract (arXiv)

While Test-Time Scaling (TTS) has proven effective in improving the reasoning ability of large language models (LLMs), low diversity in model outputs often becomes a bottleneck; this is partly caused by the common "one problem, one solution" (1P1S) training practice, which provides a single canonical answer and can push models toward a narrow set of reasoning paths. This homogenization not only limits sampling effectiveness but also restricts the exploration space for subsequent Reinforcement Learning (RL) stages. To address this, we propose a "one problem, multiple solutions" (1PNS) training paradigm that exposes the model to a variety of valid reasoning trajectories and thus increases inference diversity. A core challenge for 1PNS is reliably measuring semantic differences between multi-step chains of thought, so we introduce Reasoning Path Divergence (RPD), a step-level metric that aligns and scores Long Chain-of-Thought solutions to capture differences in intermediate reasoning. Using RPD, we curate maximally diverse solution sets per problem and fine-tune Qwen3-4B-Base. Experiments show that RPD-selected training yields more varied outputs and higher pass@k, with an average +2.80% gain in pass@16 over a strong 1P1S baseline and a +4.99% gain on AIME24, demonstrating that 1PNS further amplifies the effectiveness of TTS. Our code is available at https://github.com/fengjujf/Reasoning-Path-Divergence .