Ising models of deep neural networks

TL;DR

This paper maps deep neural networks to Ising spin models, revealing how training induces structural changes in weights that correlate with network performance and exhibit thermodynamic phase transitions.

Contribution

It introduces a novel approach to analyze neural networks using statistical thermodynamics by mapping them to Ising models, uncovering emergent structures and phase transition behaviors.

Findings

Trained networks span a wider energy range than untrained ones.

Network performance correlates with energy values.

Trained networks show higher critical temperatures in thermodynamic analysis.

Abstract

This work maps deep neural networks to classical Ising spin models, allowing them to be described using statistical thermodynamics. The density of states shows that structures emerge in the weights after they have been trained -- well-trained networks span a much wider range of realizable energies compared to poorly trained ones. These structures propagate throughout the entire network and are not observed in individual layers. The energy values correlate to performance on tasks, making it possible to distinguish networks based on quality without access to data. Thermodynamic properties such as specific heat are also studied, revealing a higher critical temperature in trained networks.