TimeHSG: Hierarchical Semantic Guidance with Frozen LLM Embeddings for Multivariate Time Series Forecasting

Accurate multivariate time-series forecasting requires jointly modeling variablespeciffc local dynamics, cross-variable inffuences, and long-range periodic structures. However, existing forecasting methods often fail to capture these complementary factors within a uniffed framework. Recent large language model (LLM)-based approaches typically rely on model ffne-tuning or direct feature fusion without assigning distinct forecasting roles to frozen LLM embeddings. We use frozen LLM-derived embeddings as hierarchical guidance rather than as prediction features for direct fusion. Based on this insight, we propose TimeHSG, a multivariate forecasting framework that combines embedding-guided local and relational modeling with frequency-domain residual learning. Speciffcally, Semantic-Conditioned Adaptive Modulation (SCAM) uses the embeddings for feature-level modulation of local temporal representations, while the Dynamic Semantic Graph (DSG) uses them to construct interaction topologies for dynamic cross-variable dependencies. A frequency-domain residual branch further complements local encoding by capturing long-range periodic and low-frequency patterns. Experiments on multiple real-world benchmarks show that TimeHSG achieves competitive or superior forecasting performance. By keeping the LLM frozen and reusing cached embeddings, TimeHSG also provides a favorable balance between forecasting accuracy and computational efffciency.