English
Related papers

Related papers: Generalization over different cellular automata ru…

200 papers

Cellular Automata (CA) have long been foundational in simulating dynamical systems computationally. With recent innovations, this model class has been brought into the realm of deep learning by parameterizing the CA's update rule using an…

Neural and Evolutionary Computing · Computer Science 2023-11-29 Magnus Petersen

We define and study a few properties of a class of random automata networks. While regular finite one-dimensional cellular automata are defined on periodic lattices, these automata networks, called randomized cellular automata, are defined…

Cellular Automata and Lattice Gases · Physics 2009-11-13 Nino Boccara

We investigate a special class of cellular automata (CA) evolving in a environment filled by an electromagnetic wave. The rules of the Conway's Game of Life are modified to account for the ability to retrieve life-sustenance from the field…

Optics · Physics 2010-03-29 Claudio Conti

Very recently, the Neural Cellular Automata (NCA) has been proposed to simulate the morphogenesis process with deep networks. NCA learns to grow an image starting from a fixed single pixel. In this work, we show that the neural network (NN)…

Neural and Evolutionary Computing · Computer Science 2021-03-03 Alejandro Hernandez Ruiz , Armand Vilalta , Francesc Moreno-Noguer

Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial…

Cellular Automata and Lattice Gases · Physics 2014-07-11 Theodore P. Pavlic , Alyssa M. Adams , Paul C. W. Davies , Sara Imari Walker

Cellular automata and their differentiable counterparts, Neural Cellular Automata (NCA), are highly expressive and capable of surprisingly complex behaviors. This paper explores how NCAs perform when applied to tasks requiring precise…

Neural and Evolutionary Computing · Computer Science 2025-12-03 Kevin Xu , Risto Miikkulainen

Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and PDE trajectories. Our method is designed to identify underlying…

Pattern Formation and Solitons · Physics 2024-04-23 Alex D. Richardson , Tibor Antal , Richard A. Blythe , Linus J. Schumacher

Neural Cellular Automata (NCA) represent a powerful framework for modeling biological self-organization, extending classical rule-based systems with trainable, differentiable (or evolvable) update rules that capture the adaptive…

Artificial Intelligence · Computer Science 2025-09-16 Benedikt Hartl , Michael Levin , Léo Pio-Lopez

This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…

Computational Complexity · Computer Science 2007-05-23 Maxim Makatchev

It is frequently observed that overparameterized neural networks generalize well. Regarding such phenomena, existing theoretical work mainly devotes to linear settings or fully-connected neural networks. This paper studies the learning…

Machine Learning · Statistics 2023-08-17 Tian-Yi Zhou , Xiaoming Huo

Cellular automata (CA) have been utilized for decades as discrete models of many physical, mathematical, chemical, biological, and computing systems. The most widely known form of CA, the elementary cellular automaton (ECA), has been…

Cellular Automata and Lattice Gases · Physics 2013-10-15 Lucas Kang

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…

Discrete Mathematics · Computer Science 2017-09-01 Carlos Martin

Neural Cellular Automata (NCA) have shown a remarkable ability to learn the required rules to "grow" images, classify morphologies, segment images, as well as to do general computation such as path-finding. We believe the inductive prior…

Artificial Intelligence · Computer Science 2021-05-18 Alexander Mordvintsev , Eyvind Niklasson , Ettore Randazzo

Inspired by cellular growth and self-organization, Neural Cellular Automata (NCAs) have been capable of "growing" artificial cells into images, 3D structures, and even functional machines. NCAs are flexible and robust computational systems…

Neural and Evolutionary Computing · Computer Science 2022-05-16 Shyam Sudhakaran , Elias Najarro , Sebastian Risi

Efforts to improve the learning abilities of neural networks have focused mostly on the role of optimization methods rather than on weight initializations. Recent findings, however, suggest that neural networks rely on lucky random initial…

Machine Learning · Computer Science 2020-09-04 Jacob M. Springer , Garrett T. Kenyon

We propose a method for deriving networks from one-dimensional binary cellular automata. The derived networks are usually directed and have structural properties corresponding to the dynamical behaviors of their cellular automata. Network…

Cellular Automata and Lattice Gases · Physics 2010-09-28 Yoshihiko Kayama

Neural cellular automata (Neural CA) are a recent framework used to model biological phenomena emerging from multicellular organisms. In these systems, artificial neural networks are used as update rules for cellular automata. Neural CA are…

Neural and Evolutionary Computing · Computer Science 2021-07-13 Alexandre Variengien , Stefano Nichele , Tom Glover , Sidney Pontes-Filho

Deep learning models have lately shown great performance in various fields such as computer vision, speech recognition, speech translation, and natural language processing. However, alongside their state-of-the-art performance, it is still…

Machine Learning · Computer Science 2019-04-09 Daniel Jakubovitz , Raja Giryes , Miguel R. D. Rodrigues

A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain…

Cellular Automata and Lattice Gases · Physics 2025-05-30 Rolf Hoffmann , Mariusz Białecki

It has been shown that uniform as well as non-uniform cellular automata (CA) can be evolved to perform certain computational tasks. Random Boolean networks are a generalization of two-state cellular automata, where the interconnection…

Disordered Systems and Neural Networks · Physics 2007-05-23 Bertrand Mesot , Christof Teuscher