Geometric Dynamics of Signal Propagation Predict Trainability of Transformers

arXiv:2403.02579v1 Announce Type: cross
Abstract: We investigate forward signal propagation and gradient back propagation in deep, randomly initialized transformers, yielding simple necessary and sufficient conditions on initialization hyperparameters that ensure trainability of deep transformers. Our approach treats the evolution of the representations of $n$ tokens as they propagate through the transformer layers in terms of a discrete time dynamical system of $n$ interacting particles. We derive simple update equations for the evolving geometry of this particle system, starting from a …

abstract arxiv back propagation cond-mat.dis-nn cs.lg dynamics evolution gradient propagation signal simple through tokens transformer transformers type