Stuck in the Matrix: Probing Spatial Reasoning in Large Language Models

This paper explores the spatial reasoning capability of large language models (LLMs) over textual input through a suite of five tasks aimed at probing their spatial understanding and computational abilities. The models were tested on both fundamental spatial reasoning and multi-step problem-solving within structured grid-based environments using tasks such as quadrant identification, geometric transformations, distance evaluation, word searches, and tile sliding. Each task was scaled in complexity through increasing grid dimensions, requiring models to extend beyond simple pattern recognition into abstract spatial reasoning. Our results reveal that while LLMs demonstrate moderate success in all tasks with small complexity and size, performance drops off rapidly as scale increases, with an average loss in accuracy of 42.7%, and reaching as high as 84%. Every test that began with over 50% accuracy showed a loss of at least 48%, illustrating the consistent nature of the deterioration. Furthermore, their struggles with scaling complexity hint at a lack of robust spatial representations in their underlying architectures. This paper underscores the gap between linguistic and spatial reasoning in LLMs, offering insights into their current limitations, and laying the groundwork for future integrative benchmarks at the intersection of language and geometry.