Distortions in Judged Spatial Relations in Large Language Models

We present a benchmark for assessing the capability of large language models (LLMs) to discern intercardinal directions between geographic locations and apply it to three prominent LLMs: GPT-3.5, GPT-4, and Llama-2. This benchmark specifically evaluates whether LLMs exhibit a hierarchical spatial bias similar to humans, where judgments about individual locations' spatial relationships are influenced by the perceived relationships of the larger groups that contain them. To investigate this, we formulated fourteen questions focusing on well-known U.S. cities. Seven questions were designed to challenge the LLMs with scenarios potentially influenced by the orientation of larger geographical units, such as states or countries, whereas the remaining seven targeted locations were less susceptible to such hierarchical categorization. Among the tested models, GPT-4 exhibited superior performance with 55 percent accuracy, followed by GPT-3.5 at 47 percent and Llama-2 at 45 percent. The models showed significantly reduced accuracy on tasks with suspected hierarchical bias. For example, GPT-4's accuracy dropped to 33 percent on these tasks, compared to 86 percent on others. The models identified the nearest cardinal direction in most cases, however, reflecting their associative learning mechanism, thereby embodying human-like misconceptions. We discuss avenues for improving the spatial reasoning capabilities of LLMs.