# Hopfield Networks as Models of Emergent Function in Biology

arXiv: https://arxiv.org/abs/2506.13076 · HTML: https://mlsanity.com/paper/2506.13076/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2025.

## Built on by (most cited first, 2 of 2)

- [Free energy landscape of Dense Associative Memory](https://mlsanity.com/paper/2607.19195/) (2026)
- [Boolean threshold functions, neuron capacity, and memory retrieval](https://mlsanity.com/paper/2609.29756/) (2026)

## Abstract (arXiv)

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.