Frequency-domain MLPs are More Effective Learners in Time Series Forecasting

Abstract: Time series forecasting has played the key role in different industrial, including finance, traffic, energy, and healthcare domains. While existing literatures have designed many sophisticated architectures based on RNNs, GNNs, or Transformers, another kind of approaches based on multi-layer perceptrons (MLPs) are proposed with simple structure, low complexity, and {superior performance}. However, most MLP-based forecasting methods suffer from the point-wise mappings and information bottleneck, which largely hinders the forecasting performance. To overcome this problem, we explore a novel direction of applying MLPs in the frequency domain for time series forecasting. We investigate the learned patterns of frequency-domain MLPs and discover their two inherent characteristic benefiting forecasting, (i) global view: frequency spectrum makes MLPs own a complete view for signals and learn global dependencies more easily, and (ii) energy compaction: frequency-domain MLPs concentrate on smaller key part of frequency components with compact signal energy. Then, we propose FreTS, a simple yet effective architecture built upon Frequency-domain MLPs for Time Series forecasting. FreTS mainly involves two stages, (i) Domain Conversion, that transforms time-domain signals into complex numbers of frequency domain; (ii) Frequency Learning, that performs our redesigned MLPs for the learning of real and imaginary part of frequency components. The above stages operated on both inter-series and intra-series scales further contribute to channel-wise and time-wise dependency learning. Extensive experiments on 13 real-world benchmarks (including 7 benchmarks for short-term forecasting and 6 benchmarks for long-term forecasting) demonstrate our consistent superiority over state-of-the-art methods.

• The paper introduces FreTS, a frequency-domain MLP that offers a global view of data to capture both spatial and temporal dependencies.
• The use of energy compaction in the frequency domain enhances noise filtering, allowing the model to focus on essential temporal features.
• Experiments on 13 real-world benchmarks demonstrate superior forecasting accuracy compared to state-of-the-art time series methods.

An Expert Review of "Frequency-domain MLPs are More Effective Learners in Time Series Forecasting"

This paper presents a novel approach to time series forecasting by introducing frequency-domain multi-layer perceptrons (MLPs), specifically designed to leverage the unique characteristics of the frequency domain. In contrast to conventional MLP methodologies that operate within the time domain and often encounter challenges like information bottlenecks and point-wise mapping limitations, the proposed frequency-domain MLPs are engineered to circumvent these issues.

Key Contributions

1. Global View Advantage: The use of frequency-domain MLPs enables a holistic view of the data, leveraging the frequency spectrum to better capture complex dependencies. This global perspective offers a substantial advantage for learning spatial and temporal dynamics within time series data.
2. Energy Compaction for Clarity: The frequency domain facilitates the concentration of signal energy into key components, making it easier to discern essential patterns while avoiding the distraction of noise. This capability is particularly beneficial in preserving core temporal features.
3. Architecture Innovation - FreTS: The study introduces FreTS, a straightforward yet potent framework built on the premises of frequency-domain MLPs. FreTS comprises two distinct learning phases: converting time-domain signals into frequency-domain spectra and employing restructured MLPs to process these spectrums. This dual-phase approach enhances the model’s capacity to learn channel-wise and time-wise dependencies.

Experimental Validation

The efficacy of FreTS is validated through extensive experiments across 13 real-world benchmarks. These benchmarks encompass various application domains—such as traffic, energy, and finance—and include both short-term and long-term forecasting scenarios. The results exhibit consistent superiority over state-of-the-art methods, affirming FreTS's potential to deliver enhanced forecasting accuracy with simpler structures.

Implications and Future Directions

The introduction of frequency-domain MLPs opens up new vistas for time series modeling, suggesting that such domain transformations can significantly enhance model performance. Practically, this approach could lead to more efficient implementation strategies for industries that rely heavily on time series data. Theoretically, it paves the way for further exploration into how frequency-domain representations can be integrated with other deep learning frameworks, like RNNs or Transformers.

Future research may explore several directions:

• Hybrid Models: Combining frequency-domain MLPs with other architectures could unlock additional advantages in feature extraction and pattern recognition.
• Adaptive Learning: Further studies could enhance the robustness of frequency-domain techniques in situations with limited training data or volatile environments.
• Automated Domain Transformation: Developing automated techniques to decide when and how to apply domain transformations could broaden the applicability of these models across different contexts and datasets.

In conclusion, the paper’s insights establish a solid foundation for leveraging frequency-domain characteristics in time series forecasting through MLPs, marking a promising step forward in both performance and simplicity of forecasting models. Such advancements underline the potential of domain-specific transformations in addressing inherent challenges in signal processing and prediction accuracy.