mlsanityData to 7 Oct 2026

Learning Graph Cellular Automata

arXiv 2110.14237 ↗First posted 27 Oct 2021cs.LG cs.AIcited by 33

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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.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). Builds on 11 of its 50 references that are in the map. First posted on arXiv 27 Oct 2021.

Builds on

11 of 50 references.

References · 11

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2018The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networkscited by 2,250
  3. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,220
  4. 2017Deep Setscited by 1,394
  5. 2018Relational inductive biases, deep learning, and graph networkscited by 1,341
  6. 2017Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphscited by 307
  7. 2020Design Space for Graph Neural Networkscited by 182
  8. 2018Cellular automata as convolutional neural networkscited by 45
  9. 2018Lenia - Biology of Artificial Lifecited by 41
  10. 2020It's Hard for Neural Networks To Learn the Game of Lifecited by 13
  11. 2021Generalization over different cellular automata rules learned by a deep feed-forward neural networkcited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 5; 2024: 9; 2025: 7; 2026: 10.

33 papers.

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  1. 2022Attention-based Neural Cellular Automatacited by 26
  2. 2023Towards Self-Assembling Artificial Neural Networks through Neural Developmental Programscited by 17
  3. 2023Mesh Neural Cellular Automatacited by 10
  4. 2023E(n)-equivariant Graph Neural Cellular Automatacited by 9
  5. 2024CAX: Cellular Automata Accelerated in JAXcited by 8
  6. 2023Growing Steerable Neural Cellular Automatacited by 6
  7. 2022Learning stochastic dynamics and predicting emergent behavior using transformerscited by 5
  8. 2024Learning Locally Interacting Discrete Dynamical Systems: Towards Data-Efficient and Scalable Predictioncited by 5
  9. 2025Learning Individual Behavior in Agent-Based Models with Graph Diffusion Networkscited by 4
  10. 2025Beyond Memorization: Extending Reasoning Depth with Recurrence, Memory and Test-Time Compute Scalingcited by 4
  11. 2023Pathfinding Neural Cellular Automatacited by 3
  12. 2024Learning Elementary Cellular Automata with Transformerscited by 3
21 more
  1. 2024CoRe-GD: A Hierarchical Framework for Scalable Graph Visualization with GNNscited by 2
  2. 2024Graph Neural Networks Gone Hogwildcited by 2
  3. 2025Growing Reservoirs with Developmental Graph Cellular Automatacited by 2
  4. 2026Neural Particle Automata: Learning Self-Organizing Particle Dynamicscited by 2
  5. 2026A New Kind of Network? Review and Reference Implementation of Neural Cellular Automatacited by 2
  6. 2024The Complexity of Sequential Prediction in Dynamical Systemscited by 1
  7. 2026BraiNCA: brain-inspired neural cellular automata and applications to morphogenesis and motor controlcited by 1
  8. 2026Self-Organising Digital Circuitscited by 1
  9. 2024A Sensitivity Analysis of Cellular Automata and Heterogeneous Topology Networks: Partially-Local Cellular Automata and Homogeneous Homogeneous Random Boolean Networkscited by 0
  10. 2024GraphFSA: A Finite State Automaton Framework for Algorithmic Learning on Graphscited by 0
  11. 2024A Computational Model of Learning and Memory Using Structurally Dynamic Cellular Automatacited by 0
  12. 2025Mixtures of Neural Cellular Automata: A Stochastic Framework for Growth Modelling and Self-Organizationcited by 0
  13. 2025The Generalist Brain Module: Module Repetition in Neural Networks in Light of the Minicolumn Hypothesiscited by 0
  14. 2025A Framework Based on Graph Cellular Automata for Similarity Evaluation in Urban Spatial Networkscited by 0
  15. 2025DiffeoMorph: Learning to Morph 3D Shapes Using Differentiable Agent-Based Simulationscited by 0
  16. 2026Communication Heterogeneity and Collective Consensus in Neural Cellular Automatacited by 0
  17. 2026Emulating Cosmic Structure Formation with a Lagrangian Neural Cellular Automatoncited by 0
  18. 2026Recurrent Graph Neural Networks with Set-Based Aggregationcited by 0
  19. 2026Applications of Neural Cellular Automata: State of the Art, Challenges and Opportunitiescited by 0
  20. 2026G-NAC: Graph Neural Automata Clustering via Emergent Domain Formationcited by 0
  21. 2026Where Does Randomness Matter in Neural Cellular Automata?cited by 0