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arXiv · 2311.01575

On the Convergence of Encoder-only Shallow Transformers

Yongtao Wu·Fanghui Liu·Grigorios G Chrysos·Volkan Cevher
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Abstract

In this paper, we aim to build the global convergence theory of encoder-only shallow Transformers under a realistic setting from the perspective of architectures, initialization, and scaling under a finite width regime. The difficulty lies in how to tackle the softmax in self-attention mechanism, the core ingredient of Transformer. In particular, we diagnose the scaling scheme, carefully tackle the input/output of softmax, and prove that quadratic overparameterization is sufficient for global convergence of our shallow Transformers under commonly-used He/LeCun initialization in practice. Besides, neural tangent kernel (NTK) based analysis is also given, which facilitates a comprehensive comparison. Our theory demonstrates the separation on the importance of different scaling schemes and initialization. We believe our results can pave the way for a better understanding of modern Transformers, particularly on training dynamics.

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Yongtao Wu, Fanghui Liu, Grigorios G Chrysos, Volkan Cevher. 2023-11-02. On the Convergence of Encoder-only Shallow Transformers. https://arxiv.org/abs/2311.01575

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