  Spatial reasoning is a crucial component of both biological and artificial
intelligence. In this work, we present a comprehensive study of the capability
of current state-of-the-art large language models (LLMs) on spatial reasoning.
To support our study, we created and contribute a novel Spatial Reasoning
Characterization (SpaRC) framework and Spatial Reasoning Paths (SpaRP)
datasets, to enable an in-depth understanding of the spatial relations and
compositions as well as the usefulness of spatial reasoning chains. We found
that all the state-of-the-art LLMs do not perform well on the datasets -- their
performances are consistently low across different setups. The spatial
reasoning capability improves substantially as model sizes scale up. Finetuning
both large language models (e.g., Llama-2-70B) and smaller ones (e.g.,
Llama-2-13B) can significantly improve their F1-scores by 7--32 absolute
points. We also found that the top proprietary LLMs still significantly
outperform their open-source counterparts in topological spatial understanding
and reasoning.
