Cellular automata can classify data by inducing trajectory phase coexistence

TL;DR

This paper demonstrates that cellular automata can be used to classify data by inducing dynamical phase coexistence, acting as nonlinear activation functions similar to spiking neurons, through a Monte Carlo search for effective automata.

Contribution

It introduces a method to identify cellular automata that classify images based on activity, revealing a new way to emulate neural activation functions using automata.

Findings

Automata generate trajectories with high or low activity based on initial conditions.

The automata act as nonlinear activation functions with binary-like outputs.

The approach uses Monte Carlo methods to discover classification automata.

Abstract

We show that cellular automata can classify data by inducing a form of dynamical phase coexistence. We use Monte Carlo methods to search for general two-dimensional deterministic automata that classify images on the basis of activity, the number of state changes that occur in a trajectory initiated from the image. When the number of timesteps of the automaton is a trainable parameter, the search scheme identifies automata that generate a population of dynamical trajectories displaying high or low activity, depending on initial conditions. Automata of this nature behave as nonlinear activation functions with an output that is effectively binary, resembling an emergent version of a spiking neuron.