Neural Fourier Modelling: A Highly Compact Approach to Time-Series Analysis

TL;DR

Neural Fourier Modelling (NFM) introduces a Fourier domain-based approach for time-series analysis, enabling compact, flexible, and state-of-the-art performance across various tasks by directly modeling and manipulating frequency representations.

Contribution

This work pioneers direct Fourier domain modeling for time-series, introducing NFM with novel modules for frequency extrapolation and interpolation, achieving high performance with minimal parameters.

Findings

NFM outperforms existing methods on forecasting, anomaly detection, and classification.

NFM operates effectively with unseen sampling rates at test time.

NFM is highly compact, using fewer than 40K parameters across tasks.

Abstract

Neural time-series analysis has traditionally focused on modeling data in the time domain, often with some approaches incorporating equivalent Fourier domain representations as auxiliary spectral features. In this work, we shift the main focus to frequency representations, modeling time-series data fully and directly in the Fourier domain. We introduce Neural Fourier Modelling (NFM), a compact yet powerful solution for time-series analysis. NFM is grounded in two key properties of the Fourier transform (FT): (i) the ability to model finite-length time series as functions in the Fourier domain, treating them as continuous-time elements in function space, and (ii) the capacity for data manipulation (such as resampling and timespan extension) within the Fourier domain. We reinterpret Fourier-domain data manipulation as frequency extrapolation and interpolation, incorporating this as a core learning mechanism in NFM, applicable across various tasks. To support flexible frequency extension with spectral priors and effective modulation of frequency representations, we propose two learning modules: Learnable Frequency Tokens (LFT) and Implicit Neural Fourier Filters (INFF). These modules enable compact and expressive modeling in the Fourier domain. Extensive experiments demonstrate that NFM achieves state-of-the-art performance on a wide range of tasks (forecasting, anomaly detection, and classification), including challenging time-series scenarios with previously unseen sampling rates at test time. Moreover, NFM is highly compact, requiring fewer than 40K parameters in each task, with time-series lengths ranging from 100 to 16K.