组合学习的谱理论
A Spectral Theory of Compositional Learning
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中文总结 AI 辅助
本文通过数学分析深度线性网络的学习动态，提出组合学习的谱理论，预测组合推理的出现条件、可识别性及新证据的解锁作用，并解释人类认知中的相关现象。
中文摘要 AI 辅助
组合推理是如何在学习过程中出现的？我们通过数学分析深度线性网络的学习动态来回答这个问题。我们在结构化的合成环境中训练这些网络，并推导出一个将经验结构与组合学习联系起来的理论。我们的理论预测了组合推理何时出现，它们是否能从现有证据中被识别出来，以及新的连接证据如何能迅速解锁先前不可用的推理。这些结果为人类认知中观察到的几种现象提供了定性解释。它们解释了为什么一个组合即使在知道其前提的情况下也可能失败，为什么相似的组合可能在不同时间出现，以及一个单一的联系事实如何能突然启用许多新的推理。综合来看，这些发现建立了经验的统计结构与组合推理发展之间的数学联系。
英文摘要
How does compositional reasoning emerge during learning? We address this question by mathematically analyzing the learning dynamics of deep linear networks. We train these networks in structured synthetic environments and derive a theory linking the structure of experience to compositional learning. Our theory predicts when compositional inferences emerge, whether they are identifiable from the available evidence, and how new linking evidence can rapidly unlock previously unavailable inferences. These results provide a qualitative explanation for several phenomena observed in human cognition. They account for why a composition can fail despite knowing its premises, why similar compositions can emerge at different times, and how a single linking fact can suddenly enable many new inferences. Taken together, these findings establish a mathematical link between the statistical structure of experience and the development of compositional reasoning.
发表机构
- University of Manchester（曼彻斯特大学）
机构由 AI 辅助整理，请以论文原文为准。
