Bridging the Spectrum Gap: Mid‑Frequency Augmentation and Key‑Frequency Mining for Multivariate Time Series

ICLR 2026 Conference Submission17907 Authors

Keywords: Leaning in the frequency domain, Efficiency, Deep learning, Channel Interaction.

TL;DR: More accurate time series forecasting by enhancing the modeling of shared frequency and middle frequency among multivariate time series.

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 bridges these two gaps by: ***(i)*** introducing a novel module, 'Adaptive Mid-Frequency Energy Optimizer', based on convolution and residual learning, to emphasize the significance of mid-frequency bands; ***(ii)*** proposing an 'Energy-based Key-Frequency Picking Block' to capture shared Key-Frequency, which achieves superior inter-series modeling performance with fewer parameters; ***(iii)*** employing 'Key-Frequency Enhanced Training' strategy 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 [**Anonymous Repo**](https://anonymous.4open.science/r/ReFocus-2889).

Primary Area: learning on time series and dynamical systems

Submission Number: 17907