Two failure modes of deep transformers and how to avoid them: a unified theory of signal propagation at initialisation

TL;DR

This paper develops an analytical theory for initializing deep transformers, identifying two failure modes—rank and entropy collapse—and provides a method to choose hyperparameters that ensure trainability.

Contribution

It offers a unified theoretical framework for understanding and avoiding failure modes in transformer initializations, including a practical algorithm for optimal hyper-parameter selection.

Findings

Identifies two failure modes: rank collapse and entropy collapse.

Provides a simple algorithm for computing trainability diagrams.

Quantitatively predicts initialization scales for stable training.

Abstract

Finding the right initialisation for neural networks is crucial to ensure smooth training and good performance. In transformers, the wrong initialisation can lead to one of two failure modes of self-attention layers: rank collapse, where all tokens collapse into similar representations, and entropy collapse, where highly concentrated attention scores lead to training instability. While previous work has studied different scaling regimes for transformers, an asymptotically exact, down-to-the constant prescription for how to initialise transformers has so far been lacking. Here, we provide an analytical theory of signal propagation through deep transformers with self-attention, layer normalisation, skip connections and MLP. Our theory yields a simple algorithm to compute trainability diagrams that identify the correct choice of initialisation hyper-parameters for a given architecture. We overcome the key challenge, an exact treatment of the self-attention layer, by establishing a formal parallel with the Random Energy Model from statistical physics. We also analyse gradients in the backward path and determine the regime where gradients vanish at initialisation. We demonstrate the versatility of our framework through three case studies. Our theoretical framework gives a unified perspective on the two failure modes of self-attention and gives quantitative predictions on the scale of both weights and residual connections that guarantee smooth training.