Generalizing Multi-Scale Time-Series Modeling with a Single Operator
This work provides a more flexible and efficient multi-scale modeling approach for researchers and practitioners working on time-series forecasting, offering substantial improvements in accuracy, speed, and memory.
This paper addresses the limitation of fixed and discrete scaling in multi-scale time-series forecasting by introducing SiGMA, which uses a learnable discrete Gaussian kernel for distance-aware scaling. SiGMA significantly outperforms state-of-the-art multi-scale baselines, achieving the best performance in 13 out of 16 long-term evaluation settings, while also improving training speed by up to 5.3 times and reducing memory consumption by up to 3.8 times.
Multi-scale modeling has emerged as an effective design principle for time-series forecasting by capturing temporal dynamics at multiple resolutions. As no principled foundation has been established in the literature, we unify existing scaling methods into a scaling operator family, revealing a fundamental limitation of existing approaches: reliance on fixed and discrete scaling. To address this limitation, we propose SiGMA (Single Generalized Multi-scale Architecture), which enables distance-aware scaling via the learnable discrete Gaussian (LDG) kernel grounded in scale-space theory. 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, especially achieving the best performance in 13 out of 16 long-term evaluation settings. Beyond accuracy, SiGMA significantly improves training speed by up to 5.3 times and reduces memory consumption by up to 3.8 times over the strongest competitors. Code is available at https://github.com/cheonwoolee/SiGMA.