链式思维异质性如何影响高效可学习性：从多个“思考者”学习的理论研究
Learning to Think from Multiple Thinkers: How Chain-of-Thought Heterogeneity Affects Efficient Learnability
AI 导读
arXiv 论文从学习理论视角研究多来源异构 CoT 监督的可学习性问题：各来源给出相同最终答案但中间推理步骤不同。论文证明，从被动收集的多来源思维链中学习具有密码学难度，尽管从任一单一来源的同构 CoT 学习是易处理的；来源贡献偏差或未过滤混合都可能导致这种困难。受迭代式自适应微调启发，论文提出一种主动、自适应收集多来源 CoT 的高效学习算法，其每来源 CoT 预算与目标误差 ε 完全无关。
正文 · 原文
Abstract:Chain-of-thought (CoT) supervision makes computationally hard learning problems tractable by exposing intermediate steps that are easy to learn via next-token prediction. However, in practice, CoT datasets draw on heterogeneous sources with different reasoning styles, and substantial effort goes into curating supervision suitable for next-token training. What role does this curation play in enabling the computational advantage of CoT supervision? In this work, we take a first step toward understanding this question from a learning-theoretic perspective. We introduce several models of $heterogeneous$ $CoT$ $supervision$ from multiple sources, each providing correct traces with the same final answer but different intermediate steps. Assuming that fitting a next-token predictor to $homogeneous$ traces from any single source is computationally tractable, we ask when this suffices for efficient learning from heterogeneous supervision.
We show $cryptographic$ $hardness$ of learning from $passively$ collected traces from multiple sources, even though learning from homogeneous CoTs is easy. This hardness can stem either from $hard$-$to$-$learn$ $contribution$ $biases$ determining which sources contribute traces on different parts of the domain, or from receiving an $unfiltered$ heterogeneous mixture (though a filtered subset of homogeneous traces is sufficient for efficient learning). On the positive side, inspired by iterative and adaptive fine-tuning of language models, we give a computationally efficient learning algorithm that $actively$ and $adaptively$ collects CoTs from multiple sources with a per-source CoT budget completely independent of the target error $\varepsilon$. We argue that our results illuminate data collection and curation practices central to making CoT supervision effective for learning.
| Comments: | Comments are welcome. Revised the presentation to highlight the connections of the main theorems to practice with conceptual messages |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computational Complexity (cs.CC); Machine Learning (stat.ML) |
| Cite as: | arXiv:2604.24737 [cs.LG] |
| (or arXiv:2604.24737v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2604.24737 arXiv-issued DOI via DataCite |
Submission history
From: Nirmit Joshi [view email]
[v1]
Mon, 27 Apr 2026 17:43:44 UTC (166 KB)
[v2]
Thu, 5 Nov 2026 10:27:14 UTC (321 KB)
来源：arXiv cs.AI · arxiv.org