PlanarBench: Evaluating LLM Spatial Reasoning via Planar Graph Drawing

When faced with complex spatial problems, humans naturally sketch layouts to organize their thinking, and the act of drawing further sharpens their understanding. In this work, we ask whether a similar principle holds for Large Language Models (LLMs): can learning to construct explicit visual layouts from spatial descriptions instill genuine spatial understanding? We introduce Text2Space, a dataset that pairs natural language descriptions with ground-truth ASCII grid layouts and spatial QA pairs, enabling us to separate failures in constructing spatial representations from failures in reasoning over them. We adopt ASCII because it is human-readable, operates entirely within the token space of language models, and encodes spatial relations in a structurally verifiable form. Our evaluation reveals a pronounced "Read-Write Asymmetry": LLMs interpret ASCII representations effectively but struggle to produce them from text, and these construction errors propagate to incorrect answers downstream. To address this limitation, we train models on layout construction (Text$\rightarrow$ASCII) and find that it significantly improves spatial reasoning from text alone, even without producing any ASCII at inference time. Combining construction with comprehension training further amplifies these gains. Crucially, these improvements transfer to three external spatial reasoning benchmarks, demonstrating that, much as sketching sharpens human spatial thinking, learning to construct explicit layouts instills spatial understanding that generalizes beyond the training format.

There have been many recent improvements in the ability of Large Language Models (LLMs) to perform complex tasks and answer domain-specific questions through techniques like Retrieval Augmented Generation (RAG). However, reasoning abilities of LLMs, including spatial reasoning abilities, are still lacking. Spatial reasoning is a key component required to answer questions in a variety of domains that are grounded in the physical world, including urban planning, civil engineering, travel, and many others. To advance the development of LLMs and facilitate an impact in these domains, new research techniques must be developed to enable LLMs to reason over spatial data, which is commonly stored in the form of a graph. In this paper we outline the challenges associated with spatial reasoning through LLMs and envision a future in which search engines integrate with LLMs to answer complex spatial questions through graph-enhanced reasoning.

Large Language Models (LLMs) are increasingly asked to reason over structured data such as graphs, yet how reliably they can carry out multi-step graph algorithms in language remains unclear. Existing evaluations tend to use simple tasks on small graphs, to score code generation rather than reasoning over the graph itself, or to fix a single input format. We introduce Graph Theory Bench (GT Bench), a benchmark covering 24 classical graph problems in 44 task-structure settings, with over 100,000 examples across four representations: natural language, structured language, adjacency list, and adjacency matrix. Evaluating eight LLMs on GT Bench shows that accuracy is strongly tied to the input representation, that the best representation shifts with graph density, size, and topology as well as with the model, and that this sensitivity persists, attenuated, in the strongest reasoning models. Building on these observations, we propose the Graph Theory Agent (GTA), which pairs a preference-trained representation selector with plan-and-decompose scaffolding around a frozen executor LLM. GTA lifts Phi-4 from 53.5% to 69.1% on the benchmark's easy split and from 33.0% to 41.5% on its hard split, outperforming eight prompting and agent baselines, and transfers without retraining to GraCoRe and NLGraph. Code for benchmark generation and evaluation: https://github.com/xzx34/GTA. The project homepage is available at https://xzx34.github.io/gta/.