FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting (2205.08897v4)

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/

• The paper introduces the FiLM architecture that leverages a Legendre Projection Unit and a Frequency Enhanced Layer to retain historical data and filter noise effectively.
• It incorporates Fourier analysis to prioritize low-frequency components, achieving 19.2% and 26.1% reductions in mean squared error for multivariate and univariate forecasts respectively.
• The model employs a multiscale strategy to handle various temporal scales while reducing parameters and memory usage, making it applicable across diverse forecasting applications.

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

The paper presents a novel approach to long-term time series forecasting, addressing the critical challenge of effectively preserving historical data while mitigating noise. The proposed methodology, termed as Frequency improved Legendre Memory model (FiLM), advances the state-of-the-art in long-term forecasting by incorporating orthogonal bases such as Legendre polynomials and Fourier transforms to achieve robust data representation. The paper introduces a comprehensive model architecture that facilitates capturing long-term dependencies, while emphasizing computational efficiency and accuracy improvements in multivariate and univariate forecasting scenarios.

Core Contributions

1. FiLM Architecture: The FiLM architecture is designed with a Legendre Projection Unit (LPU) and a Frequency Enhanced Layer (FEL). The LPU leverages Legendre polynomials for historical data representation, serving as a mechanism to ensure critical information is retained over long sequences.
2. Noise Reduction via Fourier Analysis: By applying a Fourier transform within the FEL, FiLM implements a noise-filtering strategy that allows the model to focus on low-frequency components, which are typically more informative for forecasting tasks. The low-rank matrix approximation further enhances this process by reducing dimensional inaccuracies introduced by noise.
3. Multiscale Mechanism: The proposed model employs a multiscale strategy to handle various temporal scales efficiently. This effectively addresses data variability across different time horizons, which is pivotal for accurate long-term forecasts.
4. Performance and Efficiency: Through extensive empirical evaluations on multiple benchmark datasets, FiLM demonstrates notable improvements over existing methods, achieving a 19.2% and 26.1% reduction in mean squared error for multivariate and univariate forecasts, respectively. The architecture also provides computational benefits, with significant reductions in parameters and memory usage due to its streamlined design.

Theoretical Insights

FiLM's architecture hinges on theoretical foundations that exploit the properties of orthogonal functions, offering both robust function approximation and noise resilience. The paper presents theoretical analyses and proofs, such as showing the utility of the Legendre projection for function approximation and demonstrating the efficacy of Fourier-based components in filtering out noise while preserving key historical patterns.

Implications and Future Directions

FiLM represents a significant advancement in time series forecasting models, specifically in its adaptation of orthogonal projections for enhanced data representation and denoising. The implications are manifold:

• Practical Applications: The application of FiLM is well-suited to industries relying heavily on long-term forecasts, such as energy management, economic forecasting, and climate modeling.
• Scalability and Adaptability: The adaptability of FiLM's framework and its integration potential with various neural network architectures ensure its relevance across different domains and forecasting challenges.

Future developments could explore alternative orthogonal bases and delve further into the ensemble strategies within FiLM's framework to enhance performance in extremely noisy environments or complex multi-modal datasets. This work opens avenues for future research to develop even more robust, scalable, and efficient forecasting models capable of addressing the ever-increasing demand for precise long-term predictions in diverse real-world applications.