Infinite Limits of Multi-head Transformer Dynamics

24 May 2024  ·  Blake Bordelon, Hamza Tahir Chaudhry, Cengiz Pehlevan ·

In this work, we analyze various scaling limits of the training dynamics of transformer models in the feature learning regime. We identify the set of parameterizations that admit well-defined infinite width and depth limits, allowing the attention layers to update throughout training--a relevant notion of feature learning in these models. We then use tools from dynamical mean field theory (DMFT) to analyze various infinite limits (infinite key/query dimension, infinite heads, and infinite depth) which have different statistical descriptions depending on which infinite limit is taken and how attention layers are scaled. We provide numerical evidence of convergence to the limits and discuss how the parameterization qualitatively influences learned features.

PDF Abstract
No code implementations yet. Submit your code now

Tasks


Datasets


Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods