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ARC-NCA: Towards Developmental Solutions to the Abstraction and Reasoning Corpus

Etienne Guichard, Felix Reimers, Mia Kvalsund, Mikkel Lepperød, Stefano Nichele

TL;DR

ARC-NCA introduces a developmental framework that uses Neural Cellular Automata and EngramNCA to tackle the ARC-AGI benchmark, emphasizing emergent, morphogenesis-inspired reasoning from minimal examples. By mapping 2D ARC grids into a 3D real-valued NCA lattice and applying ARC-specific augmentations, the approach achieves competitive solve rates while dramatically reducing computational cost compared with large language models. Key contributions include per-problem test-time training of NCAs, a suite of architectural augmentations (torus handling, local/global focus, learnable sensing), and evidence of partial solutions that reveal strong iterative refinement capabilities. The work suggests that developmental computation in NCAs can yield robust abstraction and reasoning with potential synergy with LLMs, offering a promising direction for scalable, low-cost ARC-like generalization.

Abstract

The Abstraction and Reasoning Corpus (ARC), later renamed ARC-AGI, poses a fundamental challenge in artificial general intelligence (AGI), requiring solutions that exhibit robust abstraction and reasoning capabilities across diverse tasks, while only few (with median count of three) correct examples are presented. While ARC-AGI remains very challenging for artificial intelligence systems, it is rather easy for humans. This paper introduces ARC-NCA, a developmental approach leveraging standard Neural Cellular Automata (NCA) and NCA enhanced with hidden memories (EngramNCA) to tackle the ARC-AGI benchmark. NCAs are employed for their inherent ability to simulate complex dynamics and emergent patterns, mimicking developmental processes observed in biological systems. Developmental solutions may offer a promising avenue for enhancing AI's problem-solving capabilities beyond mere training data extrapolation. ARC-NCA demonstrates how integrating developmental principles into computational models can foster adaptive reasoning and abstraction. We show that our ARC-NCA proof-of-concept results may be comparable to, and sometimes surpass, that of ChatGPT 4.5, at a fraction of the cost.

ARC-NCA: Towards Developmental Solutions to the Abstraction and Reasoning Corpus

TL;DR

ARC-NCA introduces a developmental framework that uses Neural Cellular Automata and EngramNCA to tackle the ARC-AGI benchmark, emphasizing emergent, morphogenesis-inspired reasoning from minimal examples. By mapping 2D ARC grids into a 3D real-valued NCA lattice and applying ARC-specific augmentations, the approach achieves competitive solve rates while dramatically reducing computational cost compared with large language models. Key contributions include per-problem test-time training of NCAs, a suite of architectural augmentations (torus handling, local/global focus, learnable sensing), and evidence of partial solutions that reveal strong iterative refinement capabilities. The work suggests that developmental computation in NCAs can yield robust abstraction and reasoning with potential synergy with LLMs, offering a promising direction for scalable, low-cost ARC-like generalization.

Abstract

The Abstraction and Reasoning Corpus (ARC), later renamed ARC-AGI, poses a fundamental challenge in artificial general intelligence (AGI), requiring solutions that exhibit robust abstraction and reasoning capabilities across diverse tasks, while only few (with median count of three) correct examples are presented. While ARC-AGI remains very challenging for artificial intelligence systems, it is rather easy for humans. This paper introduces ARC-NCA, a developmental approach leveraging standard Neural Cellular Automata (NCA) and NCA enhanced with hidden memories (EngramNCA) to tackle the ARC-AGI benchmark. NCAs are employed for their inherent ability to simulate complex dynamics and emergent patterns, mimicking developmental processes observed in biological systems. Developmental solutions may offer a promising avenue for enhancing AI's problem-solving capabilities beyond mere training data extrapolation. ARC-NCA demonstrates how integrating developmental principles into computational models can foster adaptive reasoning and abstraction. We show that our ARC-NCA proof-of-concept results may be comparable to, and sometimes surpass, that of ChatGPT 4.5, at a fraction of the cost.
Paper Structure (23 sections, 5 equations, 12 figures, 8 tables)

This paper contains 23 sections, 5 equations, 12 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Models and Methods
  4. NCA models
  5. From ARC to NCA Space
  6. From $2D$ Integer grid to $3D$ real-valued lattice.
  7. Dealing with changing grid sizes.
  8. ARC Specific Augmentations
  9. Toroidal versus Non-Toroidal Problems
  10. Local versus Global Solutions
  11. Inappropriate Sensing
  12. Training
  13. Determining the Quality of Solutions
  14. Model Training
  15. Results
  16. ...and 8 more sections

Figures (12)

  • Figure 1: Example ARC task, adapted from chollet2019measure.
  • Figure 2: Diagram depicting one pass of the Growing NCA update step and its neural network model. Adapted from mordvintsev2020growing.
  • Figure 3: Diagram depicting one pass of the EngramNCA GeneCA update step and its neural network model. Adapted from guichard2025engramnca.
  • Figure 4: Diagram depicting one pass of the EngramNCA GenePropCA update step and its neural network model. Adapted from guichard2025engramnca.
  • Figure 5: One backpropagation step of training EngramNCA for solving ARC problems.
  • ...and 7 more figures