Generalization over different cellular automata rules learned by a deep feed-forward neural network

TL;DR

This study demonstrates that a deep neural network can learn and generalize the rules of complex cellular automata, such as Conway's Game of Life, to unseen configurations and rule sets, indicating strong predictive capabilities.

Contribution

The paper introduces a neural network approach that successfully learns and generalizes cellular automata rules across different configurations and neighborhood sizes.

Findings

Network learns complex CA rules effectively.

Generalizes to unseen rule sets and neighborhood sizes.

Code is publicly available for reproducibility.

Abstract

To test generalization ability of a class of deep neural networks, we randomly generate a large number of different rule sets for 2-D cellular automata (CA), based on John Conway's Game of Life. Using these rules, we compute several trajectories for each CA instance. A deep convolutional encoder-decoder network with short and long range skip connections is trained on various generated CA trajectories to predict the next CA state given its previous states. Results show that the network is able to learn the rules of various, complex cellular automata and generalize to unseen configurations. To some extent, the network shows generalization to rule sets and neighborhood sizes that were not seen during the training at all. Code to reproduce the experiments is publicly available at: https://github.com/SLAMPAI/generalization-cellular-automata