Convolutional Neural Networks for Automated Cellular Automaton Classification

TL;DR

This paper develops a convolutional neural network approach to classify cellular automata into behavioral classes based on their spacetime diagrams, enabling automated analysis beyond elementary cases.

Contribution

It introduces a CNN-based method that focuses on mesoscopic patterns for classifying cellular automata, avoiding the need to identify local update rules.

Findings

Nearly perfect classification accuracy achieved.

Deep learning models previously focused on local rules, not behavioral classes.

Method generalizes to non-elementary cellular automata.

Abstract

The emergent dynamics in spacetime diagrams of cellular automata (CAs) is often organised by means of a number of behavioural classes. Whilst classification of elementary CAs is feasible and well-studied, non-elementary CAs are generally too diverse and numerous to exhaustively classify manually. In this chapter we treat the spacetime diagram as a digital image, and implement simple computer vision techniques to perform an automated classification of elementary cellular automata into the five Li-Packard classes. In particular, we present a supervised learning task to a convolutional neural network, in such a way that it may be generalised to non-elementary CAs. If we want to do so, we must divert the algorithm's focus away from the underlying 'microscopic' local updates. We first show that previously developed deep learning approaches have in fact been trained to identify the local update rule, rather than directly focus on the mesoscopic patterns that are associated with the particular behavioural classes. By means of a well-argued neural network design, as well as a number of data augmentation techniques, we then present a convolutional neural network that performs nearly perfectly at identifying the behavioural class, without necessarily first identifying the underlying microscopic dynamics.