Spatio-temporal time series (STTS) play a crucial role in domains such as traffic forecasting, energy scheduling, and financial analysis. However, accurate and efficient prediction remains challenging due to the complex dynamic dependencies across temporal and spatial dimensions. Existing Graph Neural Networks (GNNs) often struggle to balance effectiveness and efficiency when modeling dynamic spatio-temporal relations. Meanwhile, Large Language Models (LLMs) exhibit strong capabilities in modeling long-range dependencies and generalization under few-shot and zero-shot conditions, yet their ability to capture spatio-temporal structures remains limited. To address this, we propose LAD-SGNN, a unified framework that integrates the advantages of graph-based and language-based modeling. Specifically, LAD-SGNN employs Spectral Graph Convolution on the Stiefel manifold (SGSC) together with Linear Dynamic Graph Optimization (LDGOSM) to efficiently extract dynamic spatio-temporal features with nearly linear complexity. Structured prompts and a spatio-temporal alignment mechanism are then designed to fuse the extracted dynamic spectral information with task semantics, which are fed into a lightweight LLM to achieve unified modeling of spatio-temporal structures and semantic reasoning. In this framework, SGSC efficiently represents dynamic spatial dependencies in the spectral domain, while the prompt-based alignment strategy explicitly injects spatio-temporal information into the LLM, thereby enhancing generalization across datasets. Extensive experiments on multiple real-world spatio-temporal datasets demonstrate that LAD-SGNN significantly improves prediction accuracy in both zero-shot and few-shot scenarios.

Spatio-temporal time series (STTS) have been widely used in many applications. However, accurately forecasting STTS is challenging due to complex dynamic correlations in both time and space dimensions. Existing graph neural networks struggle to balance effectiveness and efficiency in modeling dynamic spatio-temporal relations. To address this problem, we propose the Dynamic Spatio-Temporal Stiefel Graph Neural Network (DST-SGNN) to efficiently process STTS. For DST-SGNN, we first introduce the novel Stiefel Graph Spectral Convolution (SGSC) and Stiefel Graph Fourier Transform (SGFT). The SGFT matrix in SGSC is constrained to lie on the Stiefel manifold, and SGSC can be regarded as a filtered graph spectral convolution. We also propose the Linear Dynamic Graph Optimization on Stiefel Manifold (LDGOSM), which can efficiently learn the SGFT matrix from the dynamic graph and significantly reduce the computational complexity. Finally, we propose a multi-layer SGSC (MSGSC) that efficiently captures complex spatio-temporal correlations. Extensive experiments on seven spatio-temporal datasets show that DST-SGNN outperforms state-of-the-art methods while maintaining relatively low computational costs.