# Pathfinding Neural Cellular Automata

arXiv: https://arxiv.org/abs/2301.06820 · HTML: https://mlsanity.com/paper/2301.06820/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 23 references that are in the map.
- First posted on arXiv 17 Jan 2023.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Evolving Curricula with Regret-Based Environment Design](https://mlsanity.com/paper/2203.01302/) (2022)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [Illuminating Diverse Neural Cellular Automata for Level Generation](https://mlsanity.com/paper/2109.05489/) (2021)
- [Learning Graph Cellular Automata](https://mlsanity.com/paper/2110.14237/) (2021)
- [Texture Generation with Neural Cellular Automata](https://mlsanity.com/paper/2105.07299/) (2021)
- [Towards Scale-Invariant Graph-related Problem Solving by Iterative Homogeneous Graph Neural Networks](https://mlsanity.com/paper/2010.13547/) (2020)
- [Generation of Paths in a Maze using a Deep Network without Learning](https://mlsanity.com/paper/2004.00540/) (2020)

## Built on by (most cited first, 3 of 3)

- [Neural cellular automata: applications to biology and beyond classical AI](https://mlsanity.com/paper/2509.11131/) (2025)
- [Autoverse: An Evolvable Game Language for Learning Robust Embodied Agents](https://mlsanity.com/paper/2407.04221/) (2024)
- [Reasoning with Neural Cellular Automata](https://mlsanity.com/paper/2609.36126/) (2026)

## Abstract (arXiv)

Pathfinding makes up an important sub-component of a broad range of complex tasks in AI, such as robot path planning, transport routing, and game playing. While classical algorithms can efficiently compute shortest paths, neural networks could be better suited to adapting these sub-routines to more complex and intractable tasks. As a step toward developing such networks, we hand-code and learn models for Breadth-First Search (BFS), i.e. shortest path finding, using the unified architectural framework of Neural Cellular Automata, which are iterative neural networks with equal-size inputs and outputs. Similarly, we present a neural implementation of Depth-First Search (DFS), and outline how it can be combined with neural BFS to produce an NCA for computing diameter of a graph. We experiment with architectural modifications inspired by these hand-coded NCAs, training networks from scratch to solve the diameter problem on grid mazes while exhibiting strong generalization ability. Finally, we introduce a scheme in which data points are mutated adversarially during training. We find that adversarially evolving mazes leads to increased generalization on out-of-distribution examples, while at the same time generating data-sets with significantly more complex solutions for reasoning tasks.