Generalizing Multi-Scale Time-Series Modeling with a Single Operator

2026-05-29

AI Summary

This work addresses the limitations of existing time series multiscale modeling approaches, which typically rely on fixed, discrete scales and lack a unified theoretical foundation. The authors propose SiGMA, a novel architecture that unifies multiscale modeling as a family of operators grounded in scale-space theory and introduces a learnable continuous-scale mechanism. By employing learnable discrete Gaussian (LDG) kernels, SiGMA enables distance-aware continuous multiscale representations, overcoming the constraints of conventional fixed discrete scales. Empirical evaluations demonstrate that SiGMA achieves state-of-the-art performance on 13 out of 16 long-term forecasting benchmarks, with training speedups of up to 5.3× and memory consumption reductions of up to 3.8× compared to prior methods.

Abstract

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.

Problem

• multi-scale modeling
• time-series forecasting
• scale-space theory
• discrete scaling
• temporal dynamics

Innovation

• multi-scale modeling
• learnable discrete Gaussian kernel
• scale-space theory
• time-series forecasting
• SiGMA