Neuronal diversity can improve machine learning for physics and beyond

TL;DR

This paper demonstrates that neural networks with neurons that learn their own activation functions and diversify can outperform traditional homogeneous networks in tasks like image classification and physics-based modeling.

Contribution

It introduces a method for neurons to meta-learn their activation functions, leading to effective diversity that enhances performance in various tasks.

Findings

Neurons that learn their activation functions quickly diversify.

Diverse neural networks outperform homogeneous ones in classification and regression.

Learned diversity models dynamical systems selecting for variety.

Abstract

Diversity conveys advantages in nature, yet homogeneous neurons typically comprise the layers of artificial neural networks. Here we construct neural networks from neurons that learn their own activation functions, quickly diversify, and subsequently outperform their homogeneous counterparts on image classification and nonlinear regression tasks. Sub-networks instantiate the neurons, which meta-learn especially efficient sets of nonlinear responses. Examples include conventional neural networks classifying digits and forecasting a van der Pol oscillator and physics-informed Hamiltonian neural networks learning H\'enon-Heiles stellar orbits and the swing of a video recorded pendulum clock. Such \textit{learned diversity} provides examples of dynamical systems selecting diversity over uniformity and elucidates the role of diversity in natural and artificial systems.