Title: Unifying Multi-Scale Design in Time-Series Forecasting
Primary area: learning on time series and dynamical systems
Keywords: Time-series forecasting, Multi-scale Analysis, Deep learning

Abstract: Multi-scale modeling in time-series forecasting, which seeks to capture cross-scale relationships for modeling complex dependencies, is increasingly popular. While previous work lacks principled foundations, we unify existing scaling methods into a scaling operator family, providing a general theoretical basis for multi-scaling methods and revealing two key limitations of current models: non-adaptive scaling and inflexible cross-scale modeling.
To address these limitations, we propose SiGMA (Single Gaussian Multi-scale Architecture), a simple yet principled multi-scale framework. It enables adaptive scaling via the learnable discrete Gaussian (LDG) kernel grounded in scale-space theory, coupled with a lightweight MLP processor for efficient cross-scale interaction. We evaluate SiGMA comprehensively on long- and short-term forecasting benchmarks against state-of-the-art multi-scale baselines. SiGMA outperforms all competitors on both tasks, achieving the best performance in 55 out of 80 long-term evaluation settings. Beyond accuracy, SiGMA improves training speed by up to 3.8 times and reduces memory consumption by up to 5.3 times compared to the strongest competitors.

TL;DR: We unify existing multi-scale forecasting methods and propose SiGMA, a simplified yet adaptive architecture for multi-scale time-series modeling.