GeoGR^2:Zero-Shot Geospatial Inference via Geostatistically-Guided Iterative Refinement with LLMs

Standard large language model prompting treats geospatial inference as independent, instance-wise prediction, ignoring the fundamental spatial dependencies that govern geographic reality. Consequently, even advanced models struggle with spatial consistency and exhibit severe biases toward populous regions. To bridge this gap, we propose GeoGR^2 (Geospatial Graph Refine Reasoning), a framework that formalizes zero-shot geospatial prediction as an iterative message-passing process on a dynamically constructed graph. Unlike static retrieval methods, GeoGR^2 instantiates three dynamic operators via collaborating operators: (1) a Topology Operator that constructs graph topology to enforce the Spatial Markov property; (2) a Feature Operator that enriches nodes with task-relevant semantic covariates; and (3) an Update Operator that performs natural language message passing to iteratively minimize spatial discrepancy. Theoretically, we frame this refinement as a contraction mapping that approximates the fixed point of a global consistency equation. Empirically, we validate GeoGR^2 on diverse physical and socioeconomic tasks. Results demonstrate that by explicitly embedding geostatistical inductive biases, GeoGR^2 significantly outperforms standard prompting baselines, while effectively mitigating systematic geographic bias. Our framework leverages large language models' intrinsic capacity for understanding spatial correlations through explicit topological scaffolding, without resorting to general graph reasoning paradigms. The code of GeoGR^2 is available at https://github.com/JinfanTang/GeoGRR.