# 2D Spatial Reasoning with Adaptive Neural Cellular Automata

arXiv: https://arxiv.org/abs/2610.08518 · HTML: https://mlsanity.com/paper/2610.08518/

## 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 14 of its 47 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Placed in

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

## Builds on (most cited first, 14 of 14)

- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Deformable ConvNets v2: More Deformable, Better Results](https://mlsanity.com/paper/1811.11168/) (2018)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [OmniSpatial: Towards Comprehensive Spatial Reasoning Benchmark for Vision Language Models](https://mlsanity.com/paper/2506.03135/) (2025)
- [Less is More: Recursive Reasoning with Tiny Networks](https://mlsanity.com/paper/2510.04871/) (2025)
- [Variational Neural Cellular Automata](https://mlsanity.com/paper/2201.12360/) (2022)
- [Image segmentation via Cellular Automata](https://mlsanity.com/paper/2008.04965/) (2020)
- [Generative Adversarial Neural Cellular Automata](https://mlsanity.com/paper/2108.04328/) (2021)
- [Frequency-Time Diffusion with Neural Cellular Automata](https://mlsanity.com/paper/2401.06291/) (2024)
- [Spatial-DISE: A Unified Benchmark for Evaluating Spatial Reasoning in Vision-Language Models](https://mlsanity.com/paper/2510.13394/) (2025)
- [SpatiaLQA: A Benchmark for Evaluating Spatial Logical Reasoning in Vision-Language Models](https://mlsanity.com/paper/2602.20901/) (2026)
- [TESGNN: Temporal Equivariant Scene Graph Neural Networks for Efficient and Robust Multi-View 3D Scene Understanding](https://mlsanity.com/paper/2411.10509/) (2024)
- [A New Kind of Network? Review and Reference Implementation of Neural Cellular Automata](https://mlsanity.com/paper/2604.24990/) (2026)

## Abstract (arXiv)

Many modern learning approaches are still struggling with spatial reasoning tasks, i.e. they lack the ability to utilize geometric information of perceived entities and their spatial relation to each other to solve problems. We introduce a novel Adaptive Neural Cellular Automata (aNCA) architecture which uses deformable convolutions to dynamically adapt the perceptive field and iteratively reason over 2D spatial relations on grid-like data structures (e.g. images). Empirical results on public benchmarks show state of the art comprehensible results with high generalization abilities for solving image based puzzles like Sudoku or finding the shortest path in a maze.