title: Inductive Biases and Variable Creation in Self-Attention Mechanisms
abstract: Self-attention, an architectural motif designed to model long-range interactions in sequential data, has driven numerous recent breakthroughs in natural language processing and beyond. This work provides a theoretical analysis of the inductive biases of self-attention modules, where our focus is to rigorously establish which functions and long-range dependencies self-attention blocks prefer to represent. We show that bounded-norm Transformer layers create sparse variables: they can represent sparse Lipschitz functions of the input sequence, with sample complexity scaling only logarithmically with the context length. We propose new experimental protocols to support the analysis and guide the practice of training Transformers, built around the rich theory of learning sparse Boolean functions.
authors: Benjamin L. Edelman Surbhi Goel Sham M. Kakade Cyril Zhang
hIndex: Sham M. Kakade 76