Beyond Time: Cross-Dimensional Frequency Supervision for Time Series Forecasting

2025-05-16

AI Summary

Existing time-series forecasting methods often rely on complex architectures and suffer from poor generalization, while implicitly assuming independent and identically distributed (IID) data—contradicting the inherent non-IID nature of temporal sequences. To address this, we propose X-Freq, the first purely frequency-domain supervised paradigm, which eliminates dependence on time-domain labels. X-Freq jointly models frequency-domain determinism via Fourier transform along the time dimension and wavelet transform along the channel dimension, and computes supervision loss uniformly in the frequency domain. We theoretically prove that the frequency domain exhibits lower entropy, enabling more effective supervision. Crucially, X-Freq requires no architectural modifications or hyperparameter tuning—offering plug-and-play compatibility. Evaluated on 14 real-world datasets, X-Freq achieves average improvements of 3.3% for long-term forecasting and 27.7% for short-term forecasting, significantly enhancing both generalization and practical applicability.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

Time series forecasting plays a crucial role in various fields, and the methods based on frequency domain analysis have become an important branch. However, most existing studies focus on the design of elaborate model architectures and are often tailored for limited datasets, still lacking universality. Besides, the assumption of independent and identically distributed (IID) data also contradicts the strong correlation of the time domain labels. To address these issues, abandoning time domain supervision, we propose a purely frequency domain supervision approach named cross-dimensional frequency (X-Freq) loss. Specifically, based on a statistical phenomenon, we first prove that the information entropy of the time series is higher than its spectral entropy, which implies higher certainty in frequency domain and thus can provide better supervision. Secondly, the Fourier Transform and the Wavelet Transform are applied to the time dimension and the channel dimension of the time series respectively, to capture the long-term and short-term frequency variations as well as the spatial configuration features. Thirdly, the loss between predictions and targets is uniformly computed in the frequency domain. Moreover, we plug-and-play incorporate X-Freq into multiple advanced forecasting models and compare on 14 real-world datasets. The experimental results demonstrate that, without making any modification to the original architectures or hyperparameters, X-Freq can improve the forecasting performance by an average of 3.3% on long-term forecasting datasets and 27.7% on short-term ones, showcasing superior generality and practicality. The code will be released publicly.

Problem

• Existing time series forecasting methods lack universality across datasets
• IID assumption contradicts time domain label correlations in forecasting
• Proposes frequency domain supervision to improve forecasting accuracy and generality

Innovation

• Purely frequency domain supervision via X-Freq loss
• Fourier and Wavelet Transforms for multi-dimensional analysis
• Uniform frequency domain loss computation for predictions