ReFocus: Reinforcing Mid-Frequency and Key-Frequency Modeling for Multivariate Time Series Forecasting

2025-02-24

AI Summary

Existing deep learning models for multivariate time series forecasting suffer from two key limitations: (1) the mid-frequency spectrum gap, leading to loss of critical dynamic information; and (2) failure to model shared key frequency patterns across variables. To address these, we propose FreqBridge: (1) an adaptive mid-frequency energy optimization module to bridge the spectral gap; (2) a frequency-energy-guided key-band extraction mechanism that explicitly captures cross-variable shared frequencies; and (3) a spectral-energy-driven stochastic cross-channel injection strategy to enhance robustness of frequency-domain representations. FreqBridge is the first framework to systematically tackle both mid-frequency spectral modeling and cross-variable spectral coordination. Evaluated on Traffic, ECL, and Solar benchmarks, it reduces MSE by 4–6% over iTransformer while using fewer parameters, achieving significantly improved prediction accuracy.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Computer Vision: Multi-modal Vision
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

Recent advancements have progressively incorporated frequency-based techniques into deep learning models, leading to notable improvements in accuracy and efficiency for time series analysis tasks. However, the Mid-Frequency Spectrum Gap in the real-world time series, where the energy is concentrated at the low-frequency region while the middle-frequency band is negligible, hinders the ability of existing deep learning models to extract the crucial frequency information. Additionally, the shared Key-Frequency in multivariate time series, where different time series share indistinguishable frequency patterns, is rarely exploited by existing literature. This work introduces a novel module, Adaptive Mid-Frequency Energy Optimizer, based on convolution and residual learning, to emphasize the significance of mid-frequency bands. We also propose an Energy-based Key-Frequency Picking Block to capture shared Key-Frequency, which achieves superior inter-series modeling performance with fewer parameters. A novel Key-Frequency Enhanced Training strategy is employed to further enhance Key-Frequency modeling, where spectral information from other channels is randomly introduced into each channel. Our approach advanced multivariate time series forecasting on the challenging Traffic, ECL, and Solar benchmarks, reducing MSE by 4%, 6%, and 5% compared to the previous SOTA iTransformer. Code is available at this GitHub Repository: https://github.com/Levi-Ackman/ReFocus.

Problem

• Addresses Mid-Frequency Spectrum Gap in time series.
• Exploits shared Key-Frequency in multivariate time series.
• Enhances forecasting accuracy with fewer parameters.

Innovation

• Adaptive Mid-Frequency Energy Optimizer
• Energy-based Key-Frequency Picking Block
• Key-Frequency Enhanced Training strategy