让AI学会在推理失败后回溯重来，提升复杂问题求解能力。
Search, Fail, Recover: A Training Framework for Correction-Aware Reasoning
- 通过搜索树建模推理过程，明确区分继续、完成和回溯动作。
- 在隐藏图任务上解决率提升72.7个百分点，显著优于传统监督训练。
- 适合需要错误恢复与多路径探索的复杂推理场景，如数学证明、逻辑谜题。
许多推理任务无法用单一的左到右链描述：求解器可能需探索一个合理分支，发现延迟失败后，返回仍可继续的最新前缀。我们提出Pyligent，一种受Diligent Learner启发的训练与推理框架，将推理视为对部分解链的验证性搜索。任务验证器标记生成的延续与失败，生成的搜索树转化为三种动作的监督目标：继续、完成、回溯，并可选包含被放弃分支的摘要。我们在设计用于隔离延迟失败恢复的隐藏有向图任务，以及具备精确验证器的结构化推理领域上评估Pyligent，包括4×4 Sudoku、带推理轨迹的Sudoku、Blocksworld。相比仅使用黄金标准的监督微调，Pyligent在隐藏图上解决率提升72.7个百分点，在混合与专家级Sudoku上分别提升17和18个百分点，在带轨迹的Sudoku上提升27和14个百分点，在Blocksworld上提升13个百分点。结果表明，显式失败分支监督可教会模型超越模仿完美解链的实用恢复行为。
原文摘要 · Abstract (English)
Many reasoning tasks are not well described by a single left-to-right chain: a solver may need to pursue a plausible branch, observe delayed failure, and return to the latest prefix that can still be completed. We introduce Pyligent, a training and inference framework inspired by the Diligent Learner formulation that represents reasoning as validated search over partial solution chains. A task validator labels generated continuations and failures, and the resulting search trees are converted into supervised targets for three actions: continue, finish, and backtrack, with optional traces that summarize abandoned branches. We evaluate Pyligent on a hidden directed graph task designed to isolate delayed-failure recovery, and on structured reasoning domains with exact validators, including $4{\times}4$ Sudoku, Sudoku with reasoning traces, and Blocksworld. Compared with gold-only supervised fine-tuning, Pyligent improves solve rate by $72.7$ percentage points on hidden graphs, by $17$ and $18$ points on mixed and expert Sudoku, by $27$ and $14$ points on mixed and expert Sudoku with reasoning traces, and by $13$ points on Blocksworld. These results suggest that explicit failed-branch supervision can teach useful recovery behavior beyond imitation of polished solution chains.
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