# Learning Graph Cellular Automata arXiv: https://arxiv.org/abs/2110.14237 ยท HTML: https://mlsanity.com/paper/2110.14237/ ## Key facts - Cited by 33 papers in the map (data through 14 Oct 2026). - Builds on 11 of its 50 references that are in the map. - First posted on arXiv 27 Oct 2021. ## Builds on (most cited first, 11 of 11) - [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014) - [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018) - [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018) - [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017) - [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018) - [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017) - [Design Space for Graph Neural Networks](https://mlsanity.com/paper/2011.08843/) (2020) - [Cellular automata as convolutional neural networks](https://mlsanity.com/paper/1809.02942/) (2018) - [Lenia - Biology of Artificial Life](https://mlsanity.com/paper/1812.05433/) (2018) - [It's Hard for Neural Networks To Learn the Game of Life](https://mlsanity.com/paper/2009.01398/) (2020) - [Generalization over different cellular automata rules learned by a deep feed-forward neural network](https://mlsanity.com/paper/2103.14886/) (2021) ## Built on by (most cited first, 30 of 33) - [Attention-based Neural Cellular Automata](https://mlsanity.com/paper/2211.01233/) (2022) - [Towards Self-Assembling Artificial Neural Networks through Neural Developmental Programs](https://mlsanity.com/paper/2307.08197/) (2023) - [Mesh Neural Cellular Automata](https://mlsanity.com/paper/2311.02820/) (2023) - [E(n)-equivariant Graph Neural Cellular Automata](https://mlsanity.com/paper/2301.10497/) (2023) - [CAX: Cellular Automata Accelerated in JAX](https://mlsanity.com/paper/2410.02651/) (2024) - [Growing Steerable Neural Cellular Automata](https://mlsanity.com/paper/2302.10197/) (2023) - [Learning stochastic dynamics and predicting emergent behavior using transformers](https://mlsanity.com/paper/2202.08708/) (2022) - [Learning Locally Interacting Discrete Dynamical Systems: Towards Data-Efficient and Scalable Prediction](https://mlsanity.com/paper/2404.06460/) (2024) - [Learning Elementary Cellular Automata with Transformers](https://mlsanity.com/paper/2412.01417/) (2024) - [Learning Individual Behavior in Agent-Based Models with Graph Diffusion Networks](https://mlsanity.com/paper/2505.21426/) (2025) - [Beyond Memorization: Extending Reasoning Depth with Recurrence, Memory and Test-Time Compute Scaling](https://mlsanity.com/paper/2508.16745/) (2025) - [Pathfinding Neural Cellular Automata](https://mlsanity.com/paper/2301.06820/) (2023) - [A New Kind of Network? Review and Reference Implementation of Neural Cellular Automata](https://mlsanity.com/paper/2604.24990/) (2026) - [CoRe-GD: A Hierarchical Framework for Scalable Graph Visualization with GNNs](https://mlsanity.com/paper/2402.06706/) (2024) - [Graph Neural Networks Gone Hogwild](https://mlsanity.com/paper/2407.00494/) (2024) - [Growing Reservoirs with Developmental Graph Cellular Automata](https://mlsanity.com/paper/2508.08091/) (2025) - [Neural Particle Automata: Learning Self-Organizing Particle Dynamics](https://mlsanity.com/paper/2601.16096/) (2026) - [The Complexity of Sequential Prediction in Dynamical Systems](https://mlsanity.com/paper/2402.06614/) (2024) - [BraiNCA: brain-inspired neural cellular automata and applications to morphogenesis and motor control](https://mlsanity.com/paper/2604.01932/) (2026) - [Self-Organising Digital Circuits](https://mlsanity.com/paper/2608.02606/) (2026) - [A Sensitivity Analysis of Cellular Automata and Heterogeneous Topology Networks: Partially-Local Cellular Automata and Homogeneous Homogeneous Random Boolean Networks](https://mlsanity.com/paper/2407.18017/) (2024) - [GraphFSA: A Finite State Automaton Framework for Algorithmic Learning on Graphs](https://mlsanity.com/paper/2408.11042/) (2024) - [A Computational Model of Learning and Memory Using Structurally Dynamic Cellular Automata](https://mlsanity.com/paper/2501.06192/) (2024) - [Mixtures of Neural Cellular Automata: A Stochastic Framework for Growth Modelling and Self-Organization](https://mlsanity.com/paper/2506.20486/) (2025) - [The Generalist Brain Module: Module Repetition in Neural Networks in Light of the Minicolumn Hypothesis](https://mlsanity.com/paper/2507.12473/) (2025) - [A Framework Based on Graph Cellular Automata for Similarity Evaluation in Urban Spatial Networks](https://mlsanity.com/paper/2511.00768/) (2025) - [DiffeoMorph: Learning to Morph 3D Shapes Using Differentiable Agent-Based Simulations](https://mlsanity.com/paper/2512.17129/) (2025) - [Communication Heterogeneity and Collective Consensus in Neural Cellular Automata](https://mlsanity.com/paper/2606.21202/) (2026) - [Emulating Cosmic Structure Formation with a Lagrangian Neural Cellular Automaton](https://mlsanity.com/paper/2607.27320/) (2026) - [Recurrent Graph Neural Networks with Set-Based Aggregation](https://mlsanity.com/paper/2609.15932/) (2026) ## Abstract (arXiv) 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.