Work

Inductive Biases and Variable Creation in Self-Attention Mechanisms

Year: 2021

Type: preprint

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. 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2110.10090

Authors: Edelman, Benjamin L., Goel, Surbhi, Kakade, Sham, Zhang, Cyril

Institutions: Harvard University, Microsoft Research New York City (United States)

Language: English

Topic: Topic Modeling

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Office of Naval Research

Awards: AF: Medium: Collaborative Research: Estimation, Learning, and Memory: The Quest for Statistically Optimal Algorithms, G4720003262, G8876996369

OpenAlex ID: W3206006178

Cites: 61

Cited by: 39

Related to: 10