Learning Graph Cellular Automata

Daniele Grattarola, Lorenzo Livi, Cesare Alippi

Keywords: cellular automata, graph neural networks

TL;DR: We study the application of graph neural networks to learn the transition rule of graph cellular automata.

Abstract:

Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice.
In this work we focus on a generalised version of typical CA, called graph cellular automata (GCA), in which the lattice structure is replaced by an arbitrary graph.
In particular, we extend previous work that used convolutional neural networks to learn the transition rule of conventional CA and we use graph neural networks to learn a variety of transition rules for GCA.
First, we present a general-purpose architecture for learning GCA, and we show that it can represent any arbitrary GCA with finite and discrete state space.
Then, we test our approach on three different tasks: 1) learning the transition rule of a GCA on a Voronoi tessellation; 2) imitating the behaviour of a group of flocking agents; 3) learning a rule that converges to a desired target state.

Code Of Conduct: I certify that all co-authors of this work have read and commit to adhering to the NeurIPS Statement on Ethics, Fairness, Inclusivity, and Code of Conduct.

Code: https://github.com/danielegrattarola/GNCA

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2110.14237/code)