Chemical Reaction Networks Learn Better than Spiking Neural Networks

TL;DR

This paper proves that chemical reaction networks without hidden layers can outperform spiking neural networks in learning tasks, providing theoretical insights and empirical evidence for their superior efficiency and capacity.

Contribution

It introduces a mathematical proof that certain chemical reaction networks can learn complex tasks without hidden layers, unlike spiking neural networks, and demonstrates their effectiveness through experiments.

Findings

Chemical reaction networks can learn classification tasks without hidden layers.

They achieve higher accuracy and efficiency than spiking neural networks with hidden layers.

Theoretical bounds and biological implications are analyzed.

Abstract

We mathematically prove that chemical reaction networks without hidden layers can solve tasks for which spiking neural networks require hidden layers. Our proof uses the deterministic mass-action kinetics formulation of chemical reaction networks. Specifically, we prove that a certain reaction network without hidden layers can learn a classification task previously proved to be achievable by a spiking neural network with hidden layers. We provide analytical regret bounds for the global behavior of the network and analyze its asymptotic behavior and Vapnik-Chervonenkis dimension. In a numerical experiment, we confirm the learning capacity of the proposed chemical reaction network for classifying handwritten digits in pixel images, and we show that it solves the task more accurately and efficiently than a spiking neural network with hidden layers. This provides a motivation for machine learning in chemical computers and a mathematical explanation for how biological cells might exhibit more efficient learning behavior within biochemical reaction networks than neuronal networks.