Hopfield Networks as Models of Emergent Function in Biology

TL;DR

This paper reviews how Hopfield networks, originally for neural memory, serve as versatile models for emergent biological functions, highlighting their mathematical foundations and recent biological applications.

Contribution

It provides a comprehensive pedagogical overview of classical and modern Hopfield networks from a biophysical perspective, connecting theory with biological phenomena.

Findings

Hopfield networks can model cellular differentiation and epigenetic memory.

They are useful for understanding molecular self-assembly.

Applications include modeling spatial neural representations.

Abstract

Hopfield models, originally developed to study memory retrieval in neural networks, have become versatile tools for modeling diverse biological systems in which function emerges from collective dynamics. In this review, we provide a pedagogical introduction to both classical and modern Hopfield networks from a biophysical perspective. After presenting the underlying mathematics, we build physical intuition through three complementary interpretations of Hopfield dynamics: as noise discrimination, as a geometric construction defining a natural coordinate system in pattern space, and as gradient-like descent on an energy landscape. We then survey recent applications of Hopfield networks a variety of biological setting including cellular differentiation and epigenetic memory, molecular self-assembly, and spatial neural representations.