arXiv cs.AI· Lars Simon, Holger Eble, Manuel Radons·· 9 天前AI 评分27
通过回望来学习规划：用事后分层训练推理模型
Learning to Plan by Looking Back: Hindsight Hierarchies for Training Reasoning Models
AI 导读
研究者提出一种推理模型自我改进循环：即使问题难度超出模型当前能力，额外提供的解答也能让模型事后提取有用的解题思路。该方法联合训练同一模型的三项能力——仅从问题预测解题思路、从问题与已知解答反向推导思路、以及利用给定思路解题，并在 Lean 定理证明器中给出交互式定理证明的具体实例。该工作目前仅给出形式化规范，实证评估留待未来完成。
正文 · 原文
Abstract:We introduce a self-improvement loop for reasoning models based on the following observation: Even when the difficulty of a problem exceeds the model's current solving abilities, an additionally supplied solution might enable the model to extract useful solution ideas in hindsight. We operationalize this by jointly training the same model to exhibit the following three capabilities: predicting solution ideas from problems alone, reverse-engineering ideas from problems and known solutions, and solving problems using provided ideas. The loop alternates between reverse engineering such ideas from problems with supplied solutions and using these ideas as additional supervision for joint training of all three capabilities. We give a formal specification of our method and a concrete instantiation for interactive theorem proving in the Lean theorem prover; empirical evaluation remains future work.
| Comments: | 21 Pages, 4 Figures |
| Subjects: | Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Logic in Computer Science (cs.LO) |
| MSC classes: | 68V15, 68T05, 68V20, 68T20 |
| Cite as: | arXiv:2610.12168 [cs.AI] |
| (or arXiv:2610.12168v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2610.12168 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Manuel Radons [view email]
[v1]
Thu, 8 Oct 2026 15:42:27 UTC (35 KB)
来源：arXiv cs.AI · arxiv.org