Related papers: Neural Cellular Automata for ARC-AGI
Training generative adversarial networks (GANs) often suffers from cyclic behaviors of iterates. Based on a simple intuition that the direction of centripetal acceleration of an object moving in uniform circular motion is toward the center…
Models of areas of physics in terms of cellular automata have become increasingly popular. Cellular automata (CAs) support the modeling of systems with discrete state component values and enforce the comprehensive specification of the…
A method for studying the qualitative dynamical properties of abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm is presented. It is shown that the…
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…
We study structured abstraction-based reasoning for the Abstraction and Reasoning Corpus (ARC) and compare its generalization to test-time approaches. Purely neural architectures lack reliable combinatorial generalization, while strictly…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
This study focuses on an extended model of a standard cellular automaton (CA) that includes an extra index consisting of a radius that defines a perception area for each cell in addition to the radius defined by the CA rule. Extended…
Discretizing spacetime is often a natural step towards modelling physical systems. For quantum systems, if we also demand a strict bound on the speed of information propagation, we get quantum cellular automata (QCAs). These originally…
Cellular automata are a fundamental computational model with applications in mathematics, computer science, and physics. In this work, we explore the study of cellular automata to cases where the universe is a group, introducing the concept…
Identification of different neuronal cell types is critical for understanding their contribution to brain functions. Yet, automated and reliable classification of neurons remains a challenge, primarily because of their biological…
A quantum cellular automaton (QCA) is an abstract model consisting of an array of finite-dimensional quantum systems that evolves in discrete time by local unitary operations. Here we propose a simple coarse-graining map, where the spatial…
Cellular automaton (CA) approach is an important theoretical framework for studying complex system behavior and has been widely applied in various research field. CA traffic flow models have the advantage of flexible evolution rules and…
Neural Cellular Automata (NCAs) offer a way to study the growth of two-dimensional artificial organisms from a single seed cell. From the outset, NCA-grown organisms have had issues with stability, their natural boundary often breaking down…
Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the…
Graph neural networks (GNNs) have emerged as a powerful tool for learning software engineering tasks including code completion, bug finding, and program repair. They benefit from leveraging program structure like control flow graphs, but…
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on…
The Abstraction and Reasoning Corpus (ARC-AGI) poses a significant challenge for large language models (LLMs), exposing limitations in their abstract reasoning abilities. In this work, we leverage task-specific data augmentations throughout…
Information-theoretic fitness functions are becoming increasingly popular to produce generally useful, task-independent behaviors. One such universal function, dubbed empowerment, measures the amount of control an agent exerts on its…
Saliency detection, finding the most important parts of an image, has become increasingly popular in computer vision. In this paper, we introduce Hierarchical Cellular Automata (HCA) -- a temporally evolving model to intelligently detect…
One of the challenges facing artificial intelligence research today is designing systems capable of utilizing systematic reasoning to generalize to new tasks. The Abstraction and Reasoning Corpus (ARC) measures such a capability through a…