Unraveling the Gradient Descent Dynamics of Transformers

• URL: http://arxiv.org/abs/2411.07538v1
• Date: Tue, 12 Nov 2024 04:33:56 GMT
• Title: Unraveling the Gradient Descent Dynamics of Transformers
• Authors: Bingqing Song, Boran Han, Shuai Zhang, Jie Ding, Mingyi Hong,
• Abstract summary: Gradient Descent (GD) can train a Transformer model to achieve a global optimal solution, especially when the input embedding dimension is large. We analyze the loss landscape of a single Transformer layer using Softmax and Gaussian attention kernels.
• Score: 37.096572564254515
• License:
• Abstract: While the Transformer architecture has achieved remarkable success across various domains, a thorough theoretical foundation explaining its optimization dynamics is yet to be fully developed. In this study, we aim to bridge this understanding gap by answering the following two core questions: (1) Which types of Transformer architectures allow Gradient Descent (GD) to achieve guaranteed convergence? and (2) Under what initial conditions and architectural specifics does the Transformer achieve rapid convergence during training? By analyzing the loss landscape of a single Transformer layer using Softmax and Gaussian attention kernels, our work provides concrete answers to these questions. Our findings demonstrate that, with appropriate weight initialization, GD can train a Transformer model (with either kernel type) to achieve a global optimal solution, especially when the input embedding dimension is large. Nonetheless, certain scenarios highlight potential pitfalls: training a Transformer using the Softmax attention kernel may sometimes lead to suboptimal local solutions. In contrast, the Gaussian attention kernel exhibits a much favorable behavior. Our empirical study further validate the theoretical findings.

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