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Main Authors: Ju, Feng, Qin, Zeyu, Min, Rui, He, Zhitao, Kong, Lingpeng, Fung, Yi R.
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2510.26122
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author Ju, Feng
Qin, Zeyu
Min, Rui
He, Zhitao
Kong, Lingpeng
Fung, Yi R.
author_facet Ju, Feng
Qin, Zeyu
Min, Rui
He, Zhitao
Kong, Lingpeng
Fung, Yi R.
contents 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 .
format Preprint
id arxiv_https___arxiv_org_abs_2510_26122
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Reasoning Path Divergence: A New Metric and Curation Strategy to Unlock LLM Diverse Thinking
Ju, Feng
Qin, Zeyu
Min, Rui
He, Zhitao
Kong, Lingpeng
Fung, Yi R.
Computation and Language
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 .
title Reasoning Path Divergence: A New Metric and Curation Strategy to Unlock LLM Diverse Thinking
topic Computation and Language
url https://arxiv.org/abs/2510.26122