FreqNet: A Lightweight and Interpretable Frequency-Domain Network With Adaptive Cross-Channel Gating for Time Series Forecasting

Abstract

Much of the recent improvement in multivariate time series forecasting has come from ever larger Transformer models, yet their parameter and compute budgets make them difficult to deploy where resources are limited. This paper presents FreqNet, a compact and interpretable forecaster that operates in the frequency domain. After instance normalization, FreqNet takes a real fast Fourier transform of each series and keeps only its lowest frequency coefficients, a compact and denoised representation sufficient for accurate future prediction. A parallel linear branch handles structure that is easier to express in the time domain, and a gate conditioned on the input decides how to weight the two branches for each series. We then extend the model to FreqNetCD by adding a cross-channel branch whose size does not grow with the number of variates, attached through a ReZero gate that starts at zero. The model therefore behaves as a channel-independent predictor at initialization and turns on cross-channel mixing only where the data call for it. Across eleven public benchmarks—including newly added air-quality (Beijing PM2.5) and financial (NASDAQ 100) datasets—and ten competitive baselines, FreqNetCD achieves the best average error on ETTh2, Exchange, and NASDAQ 100, is competitive across the remaining ETT datasets and the high-dimensional sets, and improves on the closely related frequency-domain baseline FITS in eight of the nine original benchmarks; Diebold–Mariano tests confirm that the improvements over FITS are statistically significant in 37 of 44 dataset–horizon settings. All of this is achieved with one to two orders of magnitude fewer parameters than the Transformer baselines. Multi-seed ablations, gate visualizations, and sensitivity studies validate each design choice and confirm that cross-channel mixing is activated selectively on high-dimensional datasets while remaining mostly dormant elsewhere.