Loss of material trainability through an unusual transition

TL;DR

This paper investigates how the trainability of materials diminishes at a critical transition point, revealing a link between training complexity, vibrational modes, and material degradation.

Contribution

It uncovers the critical threshold where training becomes ineffective, showing how low frequency vibrational modes proliferate and cause material failure.

Findings

Training error decays as a power-law with a vanishing exponent at the critical point.

Low frequency modes increase and approach zero frequency near the transition.

Atypical local structures with nearly aligned bonds cause excess low frequency spectrum.

Abstract

Material training is a method to endow materials with specific responses through external driving. We study the complexity of attainable responses, as expressed in the number of sites that are simultaneously controlled. With increased complexity, convergence to the desired response becomes very slow. The training error decays as a power-law with an exponent that varies continuously and vanishes at a critical threshold, marking the limit of trainable responses. We study how the transition affects the vibrational properties. Approaching the critical threshold, low frequency modes proliferate, approaching zero frequency. This implies that training causes material degradation and that training fails due to competing spurious low frequency modes. We propose that the excess low frequency spectrum is due to atypical local structures with bonds that nearly align. Our work explains how the presence of an exotic critical point affects the convergence of training, and could be relevant for understanding learning in physical systems.