2D Spatial Reasoning with Adaptive Neural Cellular Automata

2026-10-06

AI Summary

This study addresses the challenge that existing models struggle to effectively leverage geometric information and spatial relationships in two-dimensional spatial reasoning. To this end, we propose an adaptive neural cellular automaton architecture that integrates deformable convolutions into the cellular automaton framework. By dynamically adjusting receptive fields, this method enables iterative reasoning over spatial relationships on grid-structured data. The core innovation lies in synergizing the local adaptivity of deformable convolutions with the global iterative capacity of cellular automata to achieve efficient spatial representation learning. Experimental results demonstrate that the proposed model achieves state-of-the-art performance on benchmark tasks, including Sudoku solving and shortest-path maze navigation, while exhibiting superior generalization capabilities.

Abstract

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.

Problem

• Spatial Reasoning
• Neural Cellular Automata
• 2D Spatial Relations
• Image-based Puzzles
• Generalization

Innovation

• Adaptive Neural Cellular Automata
• Spatial Reasoning
• Deformable Convolutions
• Iterative Reasoning
• Generalization