FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting

TL;DR

FiLM enhances long-term time series forecasting by combining Legendre and Fourier projections to better preserve historical data while reducing noise, leading to significant accuracy improvements.

Contribution

Introduces FiLM, a novel frequency-based memory model that improves long-term forecasting accuracy by noise reduction and efficient historical data approximation.

Findings

FiLM improves forecasting accuracy by over 20%.

The model effectively reduces noise in historical data.

The representation module can enhance other deep learning models.

Abstract

Recent studies have shown that deep learning models such as RNNs and Transformers have brought significant performance gains for long-term forecasting of time series because they effectively utilize historical information. We found, however, that there is still great room for improvement in how to preserve historical information in neural networks while avoiding overfitting to noise presented in the history. Addressing this allows better utilization of the capabilities of deep learning models. To this end, we design a \textbf{F}requency \textbf{i}mproved \textbf{L}egendre \textbf{M}emory model, or {\bf FiLM}: it applies Legendre Polynomials projections to approximate historical information, uses Fourier projection to remove noise, and adds a low-rank approximation to speed up computation. Our empirical studies show that the proposed FiLM significantly improves the accuracy of state-of-the-art models in multivariate and univariate long-term forecasting by (\textbf{20.3\%}, \textbf{22.6\%}), respectively. We also demonstrate that the representation module developed in this work can be used as a general plug-in to improve the long-term prediction performance of other deep learning modules. Code is available at https://github.com/tianzhou2011/FiLM/