Algebraic Invariants of Lightning Self-Attention

TL;DR

This paper explores the algebraic structure of lightning self-attention by identifying various polynomial invariants and constraints that characterize its behavior.

Contribution

It introduces new algebraic invariants and constraints for lightning self-attention, advancing the understanding of its polynomial coefficient structure.

Findings

Identified linear and nonlinear algebraic invariants of lightning self-attention.

Established Chow-type, low-rank, Veronese-type, and Sylvester resultant-based constraints.

Provided a framework for analyzing self-attention through algebraic geometry.

Abstract

We study the polynomial coefficients of lightning self-attention as coordinates of an algebraic variety. We identify linear and nonlinear families of algebraic invariants, including Chow-type, low-rank, Veronese-type, and Sylvester resultant-based constraints.