State-Conditioned Invertible Channel Dependencies for Multivariate Time Series Forecasting

Multivariate time series (MTS) forecasting requires jointly capturing inter-series dependencies and intra-series temporal evolutions. Although inverted Transformers (e.g., iTransformer) and Graph Neural Networks can capture arbitrary pairwise inter-channel dependencies, they typically suffer from unconstrained $\mathcal{O}(N^2)$ pairwise attention maps that are prone to overfitting spurious cross-channel correlations. Furthermore, aggregating multiple channels into a weighted sum risks destructive signal cancellation and over-smoothing across distinct channels. To address these limitations, we propose a State-conditioned Invertible Channel Dependencies Network (SICDNet) that comprises two dedicated components: Structured Invertible Channel Mixer (SICM) for inter-series correlation modeling and the Spectral-Gated Modulator (SGM) for intra-series feature extraction. SICM establishes pairwise channel interactions on latent features using a dyadic pairing schedule, which adopts a multi-stage, multi-round cascade with cyclic node-index shifts to cover more cross-channel pairs. Specifically, SICM groups the latent representations and executes Givens rotations within each paired channels of each group, and the rotation angles are conditioned dynamically based on pairwise energy. SICM is energy-preserving and mathematically invertible, enabling the extraction of robust inter-channel correlations. Complementarily, SGM combines static harmonic priors with data-dependent dynamic spectral gating and dual-domain gated fusion, adaptively capturing global periodic patterns. Theoretical analysis demonstrates that SICDNet reduces the inter-series mixing complexity from $\mathcal{O}(N^2)$ to $\mathcal{O}(N\log N)$ while maintaining channel-independent linear scaling in intra-series spectral processing, outperforming dense attention and graph estimation architectures.