Flow markers improve reasoning in large language models
Aha-Flow Distillation: Flow Markers Matter in LLM Reasoning
Computation and LanguageArtificial IntelligenceMachine Learning
Summary
This paper explores two ways that language models talk through their reasoning: the 'Aha Moment,' where the model backtracks and revises its ideas, and the 'Flow Moment,' where it steadily explains its thought process confidently. The authors create new training methods using these 'Flow Markers' to help models learn better reasoning patterns. By training models with this dual approach, they improve performance on math problem benchmarks. The improvements happen without changing how the model is prompted when used normally.
What this means in practice
- •For ai developers: Train large language models with dual reasoning signals to improve problem-solving accuracy on math tasks.
- •For chatbot builders: Enhance conversational systems with training methods that encourage clearer, more confident reasoning chains.
Authors
Xiaodong Wang, Peixi Peng
Abstract
We identify the Flow Moment, a reasoning pattern characterized by sustained, process-confirming verbalizations such as I'm doing, in contrast to the revision- and backtracking-oriented Aha Moment. We refer to their corresponding linguistic expressions as Flow Markers and Aha Markers, respectively. Based on this observation, we construct Flow-CoT by rewriting the discourse markers of original reasoning traces while preserving their underlying reasoning content, and use it as auxiliary supervision for on-policy self-distillation (OPSD). We further propose \textbf{Aha-Flow Distillation (AFD)}, a dual-mode extension of OPSD that pairs different forms of privileged information with corresponding reasoning instructions. The Aha branch retains concise solution-based supervision, while the Flow branch introduces rewritten Flow-CoT under a direct and confident reasoning instruction. At inference time, the model uses only the standard reflective instruction, so Flow-style reasoning serves purely as a training signal. Experiments on AIME25 and HMMT25 show consistent improvements across Qwen3-8B and Qwen3-4B: AFD improves Avg@12 from 60.8 to 61.3 on Qwen3-8B and from 57.5 to 58.6 on Qwen3-4B over our reproduced OPSD baselines. Controlled ablations further show that, with the same Flow-CoT/Aha-CoT composition, dual-mode training improves Avg@12 from 59.5 to 60.1, indicating that the benefit comes not only from introducing heterogeneous reasoning supervision, but also from how it is organized during self-distillation. The code is available at https://github.com/Wang-Xiaodong1899/Aha-Flow-Distillation.