A Probabilistic Interpretation of Transformers

TL;DR

This paper offers a probabilistic perspective on transformer attention, linking it to exponential families and Hopfield networks, and discusses theoretical limitations and future directions.

Contribution

It introduces a probabilistic interpretation of transformer attention as a gradient ascent process within exponential families, connecting it to Hopfield theory.

Findings

Attention corresponds to gradient ascent on the log-normalizer.

Layer normalization balances point expansion during attention.

Theoretical limitations of the current interpretation are identified.

Abstract

We propose a probabilistic interpretation of exponential dot product attention of transformers and contrastive learning based off of exponential families. The attention sublayer of transformers is equivalent to a gradient ascent step of the log normalizer, which is the log-sum-exp term in the Hopfield theory of attention. This ascent step induces a parallel expansion of points, which is counterbalanced by a contraction from layer normalization. We also state theoretical limitations of our theory and the Hopfield theory and suggest directions for resolution.