Sonnet: Spectral Operator Neural Network for Multivariable Time Series Forecasting
Yuxuan Shu, Vasileios Lampos
TL;DR
Sonnet introduces a spectral-operator approach to multivariable time series forecasting by combining learnable wavelet transforms with a frequency-domain Multivariable Coherence Attention (MVCA) to capture inter- and intra-variable dependencies. It further stabilizes temporal evolution through a Koopman operator and reconstructs forecasts via a wavelet-based decoder. Across 12 real-world datasets, Sonnet achieves the best performance on 34 of 47 tasks and yields notable MAE reductions, with MVCA alone delivering substantial improvements on challenging tasks like ILI forecasting. The work demonstrates that replacing naïve attention with MVCA, particularly in a spectral context, provides robust gains across diverse domains, though it remains empirically validated rather than theoretically proven.
Abstract
Multivariable time series forecasting methods can integrate information from exogenous variables, leading to significant prediction accuracy gains. The transformer architecture has been widely applied in various time series forecasting models due to its ability to capture long-range sequential dependencies. However, a naïve application of transformers often struggles to effectively model complex relationships among variables over time. To mitigate against this, we propose a novel architecture, termed Spectral Operator Neural Network (Sonnet). Sonnet applies learnable wavelet transformations to the input and incorporates spectral analysis using the Koopman operator. Its predictive skill relies on the Multivariable Coherence Attention (MVCA), an operation that leverages spectral coherence to model variable dependencies. Our empirical analysis shows that Sonnet yields the best performance on $34$ out of $47$ forecasting tasks with an average mean absolute error (MAE) reduction of $2.2\%$ against the most competitive baseline. We further show that MVCA can remedy the deficiencies of naïve attention in various deep learning models, reducing MAE by $10.7\%$ on average in the most challenging forecasting tasks.