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Mind the Gap: Bridging Thought Leap for Improved Chain-of-Thought Tuning

Haolei Xu, Yuchen Yan, Yongliang Shen, Wenqi Zhang, Guiyang Hou, Shengpei Jiang, Kaitao Song, Weiming Lu, Jun Xiao, Yueting Zhuang

TL;DR

This work identifies Thought Leaks as gaps in Chain-of-Thought reasoning and proposes a bridging task to restore completeness. It introduces ScaleQM+ as a training corpus and CoT-Bridge, a model that detects leaps and generates missing intermediate steps, improving mathematical reasoning across benchmarks by notable margins. The method also shows positive transfer to data distillation, reinforcement learning, and out-of-domain reasoning, establishing a plug-and-play approach to enhance multi-step reasoning. The results argue for broader applicability of reasoning-completeness augmentation beyond math, with robust generalization and practical integration potential.

Abstract

Large language models (LLMs) have achieved remarkable progress on mathematical tasks through Chain-of-Thought (CoT) reasoning. However, existing mathematical CoT datasets often suffer from Thought Leaps due to experts omitting intermediate steps, which negatively impacts model learning and generalization. We propose the CoT Thought Leap Bridge Task, which aims to automatically detect leaps and generate missing intermediate reasoning steps to restore the completeness and coherence of CoT. To facilitate this, we constructed a specialized training dataset called ScaleQM+, based on the structured ScaleQuestMath dataset, and trained CoT-Bridge to bridge thought leaps. Through comprehensive experiments on mathematical reasoning benchmarks, we demonstrate that models fine-tuned on bridged datasets consistently outperform those trained on original datasets, with improvements of up to +5.87% on NuminaMath. Our approach effectively enhances distilled data (+3.02%) and provides better starting points for reinforcement learning (+3.1%), functioning as a plug-and-play module compatible with existing optimization techniques. Furthermore, CoT-Bridge demonstrate improved generalization to out-of-domain logical reasoning tasks, confirming that enhancing reasoning completeness yields broadly applicable benefits.

Mind the Gap: Bridging Thought Leap for Improved Chain-of-Thought Tuning

TL;DR

This work identifies Thought Leaks as gaps in Chain-of-Thought reasoning and proposes a bridging task to restore completeness. It introduces ScaleQM+ as a training corpus and CoT-Bridge, a model that detects leaps and generates missing intermediate steps, improving mathematical reasoning across benchmarks by notable margins. The method also shows positive transfer to data distillation, reinforcement learning, and out-of-domain reasoning, establishing a plug-and-play approach to enhance multi-step reasoning. The results argue for broader applicability of reasoning-completeness augmentation beyond math, with robust generalization and practical integration potential.

Abstract

Large language models (LLMs) have achieved remarkable progress on mathematical tasks through Chain-of-Thought (CoT) reasoning. However, existing mathematical CoT datasets often suffer from Thought Leaps due to experts omitting intermediate steps, which negatively impacts model learning and generalization. We propose the CoT Thought Leap Bridge Task, which aims to automatically detect leaps and generate missing intermediate reasoning steps to restore the completeness and coherence of CoT. To facilitate this, we constructed a specialized training dataset called ScaleQM+, based on the structured ScaleQuestMath dataset, and trained CoT-Bridge to bridge thought leaps. Through comprehensive experiments on mathematical reasoning benchmarks, we demonstrate that models fine-tuned on bridged datasets consistently outperform those trained on original datasets, with improvements of up to +5.87% on NuminaMath. Our approach effectively enhances distilled data (+3.02%) and provides better starting points for reinforcement learning (+3.1%), functioning as a plug-and-play module compatible with existing optimization techniques. Furthermore, CoT-Bridge demonstrate improved generalization to out-of-domain logical reasoning tasks, confirming that enhancing reasoning completeness yields broadly applicable benefits.

Paper Structure

This paper contains 53 sections, 3 equations, 4 figures, 15 tables.

Table of Contents

  1. Introduction
  2. Method
  3. Task Formalization
  4. Thought Leap Bridging Dataset Construction and Bridge Model Training
  5. Data Augmentation with Bridge Model
  6. Experiments
  7. Setup
  8. Evaluation
  9. Baselines
  10. Main Results
  11. Bridging Thought Leaps consistently improves reasoning performance.
  12. Accurate leap identification is crucial for effective bridging.
  13. Zero-shot bridging shows promise but lacks consistency.
  14. Analysis
  15. Plug-and-Play Integration
  16. ...and 38 more sections

Figures (4)

  • Figure 1: Overview of the Thought Leap phenomenon and our bridging approach. (a) Thought Leaps in CoT; (b) Negative impact on training; (c) Bridging leaps improves reasoning performance.
  • Figure 2: Illustration of our work. The left panel shows data construction for training, where we strategically remove intermediate steps (e.g., between Step 0 and Step 1, or Step 2 and Step 3) from complete reasoning chains in ScaleQuestMath to create ScaleQM+ with Thought Leaps. The right panel demonstrates inference, where CoT-Bridge identifies gaps and generates appropriate intermediate steps to restore coherence in reasoning.
  • Figure 3: Model accuracy over training steps on MATH500.
  • Figure 4: PRM scores of Qwen2.5-Instruct-7B/72B on CoT-Bridge for MetaMathQA and NuminaMath.