JoMA: Demystifying Multilayer Transformers via JOint Dynamics of MLP and Attention

• URL: http://arxiv.org/abs/2310.00535v3
• Date: Fri, 15 Mar 2024 02:03:21 GMT
• Title: JoMA: Demystifying Multilayer Transformers via JOint Dynamics of MLP and Attention
• Authors: Yuandong Tian, Yiping Wang, Zhenyu Zhang, Beidi Chen, Simon Du,
• Abstract summary: We propose Joint/Attention (JoMA) dynamics, a novel mathematical framework to understand the training procedure of multilayer Transformers. JoMA predicts that the attention first becomes sparse (to learn salient tokens), then dense (to learn less salient tokens) in the presence of nonlinear activations. We leverage JoMA to explain how tokens are combined to form hierarchies in multilayer Transformers, when the input tokens are generated by a latent hierarchical generative model.
• Score: 36.737750120893516
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose Joint MLP/Attention (JoMA) dynamics, a novel mathematical framework to understand the training procedure of multilayer Transformer architectures. This is achieved by integrating out the self-attention layer in Transformers, producing a modified dynamics of MLP layers only. JoMA removes unrealistic assumptions in previous analysis (e.g., lack of residual connection) and predicts that the attention first becomes sparse (to learn salient tokens), then dense (to learn less salient tokens) in the presence of nonlinear activations, while in the linear case, it is consistent with existing works that show attention becomes sparse over time. We leverage JoMA to qualitatively explains how tokens are combined to form hierarchies in multilayer Transformers, when the input tokens are generated by a latent hierarchical generative model. Experiments on models trained from real-world dataset (Wikitext2/Wikitext103) and various pre-trained models (OPT, Pythia) verify our theoretical findings. Code can be found in https://github.com/facebookresearch/luckmatters/tree/yuandong3.

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