# Reasoning with Neural Cellular Automata

arXiv: https://arxiv.org/abs/2609.36126 · HTML: https://mlsanity.com/paper/2609.36126/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 36 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 22 of 22)

- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks](https://mlsanity.com/paper/2106.04537/) (2021)
- [Recurrent Relational Networks](https://mlsanity.com/paper/1711.08028/) (2017)
- [Artificial Kuramoto Oscillatory Neurons](https://mlsanity.com/paper/2410.13821/) (2024)
- [Updates of Equilibrium Prop Match Gradients of Backprop Through Time in an RNN with Static Input](https://mlsanity.com/paper/1905.13633/) (2019)
- [End-to-end Algorithm Synthesis with Recurrent Networks: Logical Extrapolation Without Overthinking](https://mlsanity.com/paper/2202.05826/) (2022)
- [Addressing the Abstraction and Reasoning Corpus via Procedural Example Generation](https://mlsanity.com/paper/2404.07353/) (2024)
- [ARC Is a Vision Problem!](https://mlsanity.com/paper/2511.14761/) (2025)
- [Generative Recursive Reasoning](https://mlsanity.com/paper/2605.19376/) (2026)
- [Probabilistic Tiny Recursive Model](https://mlsanity.com/paper/2605.19943/) (2026)
- [Towards self-organized control: Using neural cellular automata to robustly control a cart-pole agent](https://mlsanity.com/paper/2106.15240/) (2021)
- [Image segmentation via Cellular Automata](https://mlsanity.com/paper/2008.04965/) (2020)
- [LoopViT: Scaling Visual ARC with Looped Transformers](https://mlsanity.com/paper/2602.02156/) (2026)
- [ARC-NCA: Towards Developmental Solutions to the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2505.08778/) (2025)
- [Thinking with Looped Flows](https://mlsanity.com/paper/2609.11801/) (2026)
- [Flow Reasoning Models: Turning Flows Into Efficient Recurrent Reasoners](https://mlsanity.com/paper/2606.29150/) (2026)
- [Pathfinding Neural Cellular Automata](https://mlsanity.com/paper/2301.06820/) (2023)
- [Neural Particle Automata: Learning Self-Organizing Particle Dynamics](https://mlsanity.com/paper/2601.16096/) (2026)
- [Learning Multi-Agent Coordination via Sheaf-ADMM](https://mlsanity.com/paper/2605.31005/) (2026)
- [Diffusion as a Training Curriculum for Timestep-Free Iterative Reasoning](https://mlsanity.com/paper/2609.01449/) (2026)
- [Fractal basins trap latent reasoning](https://mlsanity.com/paper/2609.04963/) (2026)

## Abstract (arXiv)

Modern AI architectures used to solve visual reasoning tasks typically rely heavily on global connectivity and synchronization. As biological systems demonstrate, though, sophisticated computation can be performed in a more decentralized fashion. In this work, we test the reasoning capabilities of Neural Cellular Automata (NCAs), networks of recurrent cells that use strictly local connectivity and asynchronous updates. NCAs have been extensively studied in artificial life experiments, but it is unclear whether they can perform complex multi-step reasoning. We show that NCAs produce spatio-temporal dynamics capable of solving challenging visual reasoning tasks, including large mazes, Sudoku, and ARC-AGI-1. Furthermore, we provide evidence that NCAs generalize out-of-distribution when running with larger grids, longer rollouts, or parallel trials; and that the latter can be made more efficient via pruning of redundant trajectories. We find that these generalization capabilities depend on training with sample replay and stochastic perturbations, and that stochasticity remains beneficial at test time. Finally, we show that NCAs are robust reasoners capable of dynamically modulating compute to recover efficiently from damage, and that they can scale to solve reasoning in raw pixel space.