这篇论文用数学方法搞清楚了Transformer在归纳推理任务中怎么学习不同策略，还解释了in-context和in-weights学习谁赢跟数据统计有关，挺有启发性。
这篇论文提出了一个理论框架，解释Transformer语言模型如何涌现归纳推理能力。它统一了包括in-context n-grams和多跳推理在内的多种合成任务。作者证明，注意力模型的训练动力学可以限制在高度可解释的低维不变流形上，该流形用少量坐标而非数百万参数描述学习过程。利用该框架，他们分析了数据统计如何决定in-context学习与in-weights学习的竞争，并展示了流形坐标可自动检测模型学到的电路。这为预测Transformer学习行为提供了理论步骤。
Invariant Learning Dynamics of Transformers in Inductive Reasoning Tasks
We present a theoretical framework to explain the emergence of inductive reasoning abilities in Transformer language models. While previous works on Transformer learning dynamics have so far been mostly tied to specific tasks, we study a generalized class of inductive tasks that unifies several synthetic tasks known in the literature, including in-context n-grams and multi-hop reasoning. In this class, we theoretically prove that the training dynamics of attention models can be confined to a highly interpretable, low-dimensional invariant manifold. On this manifold, the learning dynamics are captured by a handful of interpretable coordinates rather than millions of parameters, making both theoretical and empirical analysis more tractable. Using this framework, we characterize how data statistics govern the competition between in-context and in-weights learning, we study how random initializations determine the `winning' circuit when multiple solutions are possible, and we demonstrate that the coordinate frame associated with the manifold can be used to automatically detect which circuits have been learned in trained models. By casting circuit formation as a low-dimensional dynamical phenomenon, we take a step toward a predictive theory of how Transformers learn.