An Efficient Algorithm for Tensor Learning

TL;DR

This paper introduces a highly efficient algorithm for tensor learning that accurately recovers paths from third-order signature tensors, significantly outperforming existing methods through advanced algebraic and randomized techniques.

Contribution

The paper presents a novel algorithm leveraging symbolic multilinear algebra and group action stabilizers, offering exact solutions and improved efficiency in tensor path recovery.

Findings

Exact recovery of paths from third-order signature tensors

Algorithm improves efficiency by an order of magnitude

Implementation in OSCAR demonstrates practical applicability

Abstract

We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this learning problem and improves upon current approaches by an order of magnitude. It relies on symbolic multilinear algebra and stabilizers of group actions via matrix-tensor congruence. We apply randomized transformation techniques that avoid the task of solving nonlinear polynomial systems associated to degenerate paths, and accompany our methods with an efficient implementation in the computer algebra system OSCAR.