Differentiable cellular automata

TL;DR

This paper introduces differentiable cellular automata (DCAs), enabling gradient-based optimization of CA rules for desired behaviors by interpolating traditional CAs through probabilistic rules.

Contribution

The paper presents a novel class of differentiable cellular automata that allow end-to-end gradient computation for optimizing CA rules.

Findings

Gradient of DCA can be computed via iterative propagation

DCAs interpolate ordinary CAs through probabilistic rules

Potential for optimizing CA properties using gradient methods

Abstract

We describe a class of cellular automata (CAs) that are end-to-end differentiable. DCAs interpolate the behavior of ordinary CAs through rules that act on distributions of states. The gradient of a DCA with respect to its parameters can be computed with an iterative propagation scheme that uses previously-computed gradients and values. Gradient-based optimization over DCAs could be used to find ordinary CAs with desired properties.