FITS: Modeling Time Series with $10k$ Parameters

TL;DR

FITS introduces a compact time series analysis framework that reframes forecasting and anomaly detection as interpolation in the complex frequency domain using a real-time FFT-based pipeline.A single complex-valued linear layer learns amplitude scaling and phase shifts for frequency interpolation, complemented by a low-pass filter and reversible normalization to produce efficient, edge-friendly models.Across forecasting benchmarks like Electricity, Weather, and ETTh/ETTm datasets and anomaly benchmarks like SMD and SWaT, FITS matches or approaches state-of-the-art performance with only $5k$–$10k$ parameters, vastly smaller than typical baselines.The work demonstrates the practical value of frequency-domain representations and complex-valued learning for scalable, resource-efficient time series modeling on edge devices.

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}

Figures (10)

• Figure 1: Illustration of Complex Number Visualization and Multiplication
• Figure 2: Pipeline of FITS, with a focus on the forecasting task. Initially, the time series is normalized to zero-mean, followed by rFFT for frequency domain projection. After LPF, a single complex-valued linear layer interpolates the frequency. Zero padding and irFFT then revert this back to the time domain, with iRIN finally reversing the normalization. The reconstruction task follows the same pipeline, except for the reconstruction supervision loss. Please check appendix for detail.
• Figure 3: Waveform (1st row) and amplitude spectrum (2nd row) of a time series segment selected from the 'OT' channel of the ETTh1 dataset, spanning from the 1500th to the 1980th data point. The segment has a length of 480, and its dominant periodicity is 24, corresponding to a base frequency of 20. The blue lines represent the waveform/spectrum with no applied filter, while the orange lines represent the waveform/spectrum with the filter applied. The filter cutoff frequency is chosen based on a harmonic of the original time series.
• Figure 4: Pipeline of FITS, with a focus on the Reconstruction task.
• Figure 5: Waveform of PSM dataset.