Guanyu Chen

Shuyang Hou, Haoyue Jiao, Ziqi Liu et al.

Large language models (LLMs) have shown strong performance in natural language to SQL (NL2SQL) tasks within general databases. However, extending to GeoSQL introduces additional complexity from spatial data types, function invocation, and coordinate systems, which greatly increases generation and execution difficulty. Existing benchmarks mainly target general SQL, and a systematic evaluation framework for GeoSQL is still lacking. To fill this gap, we present GeoSQL-Eval, the first end-to-end automated evaluation framework for PostGIS query generation, together with GeoSQL-Bench, a benchmark for assessing LLM performance in NL2GeoSQL tasks. GeoSQL-Bench defines three task categories-conceptual understanding, syntax-level SQL generation, and schema retrieval-comprising 14,178 instances, 340 PostGIS functions, and 82 thematic databases. GeoSQL-Eval is grounded in Webb's Depth of Knowledge (DOK) model, covering four cognitive dimensions, five capability levels, and twenty task types to establish a comprehensive process from knowledge acquisition and syntax generation to semantic alignment, execution accuracy, and robustness. We evaluate 24 representative models across six categories and apply the entropy weight method with statistical analyses to uncover performance differences, common error patterns, and resource usage. Finally, we release a public GeoSQL-Eval leaderboard platform for continuous testing and global comparison. This work extends the NL2GeoSQL paradigm and provides a standardized, interpretable, and extensible framework for evaluating LLMs in spatial database contexts, offering valuable references for geospatial information science and related applications.

Guan-Yu Chen, Xi Yang

We propose a novel randomized framework for the estimation problem of large-scale linear statistical models, namely Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), which integrates Sketch-and-Solve and Iterative-Sketching methods for the first time. By iteratively constructing and solving sketched least-squares (LS) subproblems with increasing sketch sizes to achieve better precisions, SLSE-FRS gradually refines the estimators of the true parameter vector, ultimately producing high-precision estimators. We analyze the convergence properties of SLSE-FRS, and provide its efficient implementation. Numerical experiments show that SLSE-FRS outperforms the state-of-the-art methods, namely the Preconditioned Conjugate Gradient (PCG) method, and the Iterative Double Sketching (IDS) method.