Neural Cellular Automata for ARC-AGI

TL;DR

This work investigates gradient-trained Neural Cellular Automata as decentralized agents for ARC-AGI tasks, focusing on learning local update rules that transform inputs to outputs under a highly constrained, few-shot regime. By enabling asynchronous, stochastic updates and supervising at every step, the approach emphasizes stability and generalization over raw performance, revealing both the strengths of local interactions and the limitations imposed by lack of long-range coordination. Key findings include size-generalizable spirals, regularization benefits from update randomness, and notable failure modes such as memorization and orientation gaps, guiding future directions in adaptive computation and probabilistic NCAs. The study provides a compact, efficient alternative perspective on ARC-like reasoning tasks and highlights design considerations for broader self-organizing neural systems.

Abstract

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 transformations and few-shot generalization, using the Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI) as a domain that challenges their capabilities in ways not previously explored. Specifically, this paper uses gradient-based training to learn iterative update rules that transform input grids into their outputs from the training examples and apply them to the test inputs. Results suggest that gradient-trained NCA models are a promising and efficient approach to a range of abstract grid-based tasks from ARC. Along with discussing the impacts of various design modifications and training constraints, this work examines the behavior and properties of NCAs applied to ARC to give insights for broader applications of self-organizing systems.

Figures (5)

• Figure 1: An example ARC-AGI task, ID: 00d62c1b. On the top are the input grids, with the bottom grids being their corresponding outputs. The task is to fill the insides of enclosed structures with yellow pixels.
• Figure 2: Task ID: 28e73c20. The input-output training pairs of the spiral task, used to learn the iterative update rule to construct any sized spiral.
• Figure 3: Spiral pattern generalized to 100$\times$100 grid, shown at three stages of the update process (t=0, 50, 110). The model was trained only on the small examples from \ref{['fg:spiral']} and tested with asynchronous updates on, yet maintains structural coherence across space and time, indicating strong generalization and stability.
• Figure 4: Task ID: 3aa6fb7a. Input-output pairs. The left two are training pairs, and the right pair is the test task. This task is structurally simple, filling in the corner of 2$\times$2 squares, but one of four orientations does not appear in the training examples, which is a problem for Neural Cellular Automata.
• Figure 5: Task ID: 00d62c1b. The test input for the task in \ref{['fg:arc']} is on the left, correct solution in the middle, and a trained model's output on the right. This case demonstrates a failure to learn the correct transformation and structural interpretation.