Lattice physics approaches for neural networks

TL;DR

This paper summarizes a lattice field theory framework for modeling neural networks, connecting physics-based methods with neuroscience to better understand neural interactions and facilitate experimental data analysis.

Contribution

It introduces a concise, accessible summary of lattice physics methods applied to neural networks, bridging theoretical physics and neuroscience.

Findings

Provides a foundational overview of lattice field theory in neural modeling

Connects theoretical parameters to experimental variables using renormalization

Highlights the potential of physics-inspired methods for neural data analysis

Abstract

Modern neuroscience has evolved into a frontier field that draws on numerous disciplines, resulting in the flourishing of novel conceptual frames primarily inspired by physics and complex systems science. Contributing in this direction, we recently introduced a mathematical framework to describe the spatiotemporal interactions of systems of neurons using lattice field theory, the reference paradigm for theoretical particle physics. In this note, we provide a concise summary of the basics of the theory, aiming to be intuitive to the interdisciplinary neuroscience community. We contextualize our methods, illustrating how to readily connect the parameters of our formulation to experimental variables using well-known renormalization procedures. This synopsis yields the key concepts needed to describe neural networks using lattice physics. Such classes of methods are attention-worthy in an era of blistering improvements in numerical computations, as they can facilitate relating the observation of neural activity to generative models underpinned by physical principles.