FITS: Modeling Time Series with $10k$ Parameters

Abstract: In this paper, we introduce FITS, a lightweight yet powerful model for time series analysis. Unlike existing models that directly process raw time-domain data, FITS operates on the principle that time series can be manipulated through interpolation in the complex frequency domain. By discarding high-frequency components with negligible impact on time series data, FITS achieves performance comparable to state-of-the-art models for time series forecasting and anomaly detection tasks, while having a remarkably compact size of only approximately $10k$ parameters. Such a lightweight model can be easily trained and deployed in edge devices, creating opportunities for various applications. The code is available in: \url{https://github.com/VEWOXIC/FITS}

• The paper presents FITS, a model using complex frequency interpolation with under 10k parameters to achieve high forecasting accuracy.
• It leverages rFFT and irFFT operations with low-pass filtering to interpolate frequency components for efficient time series reconstruction.
• Benchmark comparisons reveal that FITS outperforms larger models on datasets like ETTh1 and Weather, making it ideal for edge computing.

A Review of "FITS: Modeling Time Series with 10k Parameters"

The paper "FITS: Modeling Time Series with 10k Parameters" introduces an innovative approach to time series analysis via a model named FITS, which relies on complex frequency domain interpolation. This model is notable for its exceptionally modest parameter count, underlining its suitability for deployment on resource-constrained edge devices. The researchers propose a methodology that transcends traditional time-domain processing, leveraging interpolation within the complex frequency domain to achieve state-of-the-art performance in forecasting and anomaly detection tasks.

Overview of FITS

FITS operates by interpreting time series forecasting and reconstruction as tasks of frequency interpolation. This perspective facilitates the extrapolation of an input segment's frequency representation to generate extended time series outputs. Notably, this process relies on a complex-valued linear layer designed to learn amplitude scaling and phase shifts, ensuring the interpolation effectively captures essential frequency domain patterns.

Despite functioning primarily in the frequency domain, FITS employs real Fast Fourier Transform (rFFT) operations to transition from the time domain. Upon interpolation, inverse rFFT (irFFT) is used to revert to the time domain, concluding in an extended segment that is ready for supervisory tasks. FITS integrates a low-pass filter to retain critical frequency components while discarding high-frequency noise. This fusion of frequency-domain operations and traditional time-domain supervision allows FITS to achieve its compact yet potent architecture.

Quantitative Results and Comparative Analysis

FITS demonstrates exemplary performance on several benchmark datasets such as ETT (ETTh1, ETTh2, ETTm1, ETTm2), Weather, Electricity, Traffic, and short-term forecasting datasets like M4. The model consistently yields competitive results, often outperforming larger models like TimesNet and transformer-based architectures such as FEDformer and Informer. For instance, FITS achieves superior MSE results on datasets such as ETTh1 and Weather, with significant improvements over the runner-up models.

Crucially, FITS accomplishes this with substantially fewer parameters—ranging from 4.5K to 16K—compared to other models that utilize hundreds of thousands to millions of parameters. This characteristic underscores FITS as an efficient solution for time series analysis, especially in scenarios with limited computational resources.

Implications and Future Directions

The development of FITS has significant implications for the deployment of time series models in edge computing environments. Its low computational footprint makes it a suitable candidate for tasks like anomaly detection and forecasting in domains ranging from industrial IoT to financial analytics. By effectively minimizing computational and memory requirements through its frequency-domain approach, FITS sets a new standard for model efficacy in low-resource and real-time applications.

Looking forward, the insights provided by this research could pave the way for further exploration into complex-valued neural networks and their broader applicability in AI. Future research may focus on extending this methodology to larger-scale networks, such as complex-valued transformers, to understand the scalability of frequency domain-based approaches in modeling complex temporal dynamics.

In conclusion, the introduction of FITS marks a significant step forward in the field of time series analysis, demonstrating that state-of-the-art performance can be achieved with a fraction of the parameters traditionally required. This work not only highlights the efficacy of frequency domain interpolation but also calls for a reevaluation of prevailing methodologies in lightweight model design.