# Learning Graph Cellular Automata

@inproceedings{Grattarola2021LearningGC, title={Learning Graph Cellular Automata}, author={Daniele Grattarola and Lorenzo Francesco Livi and Cesare Alippi}, booktitle={NeurIPS}, year={2021} }

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…

## 8 Citations

### Variational Neural Cellular Automata

- Computer ScienceICLR
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This work proposes a generative model, the Variational Neural Cellular Automata (VNCA), which is loosely inspired by the biological processes of cellular growth and differentiation, and shows that the VNCA can learn a purely self-organizing generative process of data.

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- Computer ScienceICONS
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Experiments under low-shot conditions demonstrate that the cellular automata-integrated CNN outperforms compact state-of-the-art CNN models by 6-10% on static image datasets and 8-12% on temporal image sequence datasets.

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- Computer ScienceCollective Intelligence
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## References

SHOWING 1-10 OF 48 REFERENCES

### Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics

- Computer ScienceEntropy
- 2012

This work extends the investigation towards graphs obtained in a simulated-evolution procedure, starting from Erdő s–Renyi (ER) graphs and selecting for low entropies of the CA dynamics, finding a strong association of low Shannon entropy with a broadening of the graph’s degree distribution.

### Evolving Self-organizing Cellular Automata Based on Neural Network Genotypes

- Computer ScienceIWSOS
- 2011

The application of a genotypical template for all cells in the automaton greatly reduces the search space for the evolutionary algorithm, which makes the presented morphogenetic approach a promising and innovative method for overcoming the complexity limits of evolutionary design approaches.

### Cellular automata as convolutional neural networks

- Computer SciencePhysical review. E
- 2019

This work shows that any CA may readily be represented using a convolutional neural network with a network-in-network architecture, and investigates how the trained networks internally represent the CA rules using an information-theoretic technique based on distributions of layer activation patterns.

### A survey of cellular automata: types, dynamics, non-uniformity and applications

- Computer ScienceNatural Computing
- 2018

This survey tours to the various types of CAs introduced till date, the different characterization tools, the global behavior ofCAs, like universality, reversibility, dynamics etc, and special attention is given to non-uniformity in CAs and especially to non -uniform elementary CAs, which have been very useful in solving several real-life problems.

### Statistical mechanics of cellular automata

- Computer Science
- 1983

Analysis is given of ''elementary'' cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to p definite rules involving the values of its nearest neighbors.

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

- Computer ScienceArXiv
- 2021

To test generalization ability of a class of deep neural networks, a large number of different rule sets for 2-D cellular automata (CA) are generated based on John Conway’s Game of Life to show generalization to rule sets and neighborhood sizes that were not seen during the training at all.

### CA-NEAT: Evolved Compositional Pattern Producing Networks for Cellular Automata Morphogenesis and Replication

- BiologyIEEE Transactions on Cognitive and Developmental Systems
- 2018

This paper proposes a new principle of morphogenesis based on compositional pattern producing networks (CPPNs), an abstraction of development that has been able to produce complex structural motifs without local interactions to provide a valuable mapping for morphogenetic systems, beyond CA systems, where development through local interactions is desired.

### Learning Cellular Automation Dynamics with Neural Networks

- Computer ScienceNIPS
- 1992

We have trained networks of Σ - II units with short-range connections to simulate simple cellular automata that exhibit complex or chaotic behaviour. Three levels of learning are possible (in…