CoVariance Neural Networks and their extensions have emerged as effective tools for processing multivariate data, deriving graph shift operators directly from second-order statistics. These architectures, however, are designed for independent and identically distributed observations and do not fully capture the joint structure of temporal and cross-variable dependencies in multivariate time series. In this work, we introduce Inverse Cross-Spectral Neural Networks (iCSNNs), a class of graph neural networks for stationary multivariate time series whose shift operators are the inverse cross-spectral density (iCSD) matrices. These operators encode frequency-specific conditional relationships among variables, exploiting the decomposition provided by the spectral representation theorem. Leveraging spectral smoothness, frequencies are grouped into bands sharing a single iCSD operator, yielding a compact parametrisation that retains the frequency-dependent structure of the process. We further propose a joint learning procedure to estimate both the Fourier-domain dependence structure and the iCSNN parameters, adapting the iCSD operators to the downstream task. When tested on synthetic data, iCSNN outperforms baselines from different methodological families.
Figures & tables
Figure 1 : The pipeline of the iCSNN.
Figure 2 : Macro-averaged F1 scores of the jointly trained iCSNN, its Disjoint ablation and baseline methods, averaged over 20 synthetic datasets. The red dashed line represents the chance-level score of 0.20 for five balanced classes.