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Inductive Biases and Variable Creation in Self-Attention Mechanisms
Benjamin Edelman · Surbhi Goel · Sham Kakade · Cyril Zhang

Tue Jul 19 02:30 PM -- 02:35 PM (PDT) @ Hall G
in T: Learning/Deep Learning Theory »

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. Our focus is to rigorously establish which functions and long-range dependencies self-attention blocks prefer to represent. Our main result shows that bounded-norm Transformer networks "create sparse variables": a single self-attention head can represent a sparse function of the input sequence, with sample complexity scaling only logarithmically with the context length. To support our analysis, we present synthetic experiments to probe the sample complexity of learning sparse Boolean functions with Transformers.

Keywords: DL: Attention Mechanisms · DL: Theory · DL: Sequential Models, Time series · T: Deep Learning · T: Learning Theory

Author Information

Benjamin Edelman (Harvard University)
Surbhi Goel (Microsoft Research)
Sham Kakade (Harvard University)
Cyril Zhang (Microsoft Research)

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