How Transformers Get Rich: Approximation and Dynamics Analysis

• URL: http://arxiv.org/abs/2410.11474v3
• Date: Wed, 29 Jan 2025 10:27:40 GMT
• Title: How Transformers Get Rich: Approximation and Dynamics Analysis
• Authors: Mingze Wang, Ruoxi Yu, Weinan E, Lei Wu,
• Abstract summary: We provide both approximation and dynamics analyses of how transformers implement induction heads. In the em approximation analysis, we formalize both standard and generalized induction head mechanisms. For the em dynamics analysis, we study the training dynamics on a synthetic mixed target, composed of a 4-gram and an in-context 2-gram component.
• Score: 11.789846138681359
• License:
• Abstract: Transformers have demonstrated exceptional in-context learning capabilities, yet the theoretical understanding of the underlying mechanisms remains limited. A recent work (Elhage et al., 2021) identified a ``rich'' in-context mechanism known as induction head, contrasting with ``lazy'' $n$-gram models that overlook long-range dependencies. In this work, we provide both approximation and dynamics analyses of how transformers implement induction heads. In the {\em approximation} analysis, we formalize both standard and generalized induction head mechanisms, and examine how transformers can efficiently implement them, with an emphasis on the distinct role of each transformer submodule. For the {\em dynamics} analysis, we study the training dynamics on a synthetic mixed target, composed of a 4-gram and an in-context 2-gram component. This controlled setting allows us to precisely characterize the entire training process and uncover an {\em abrupt transition} from lazy (4-gram) to rich (induction head) mechanisms as training progresses.

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