Snow: A Stable Signed Channel Interaction Module for High-Dimensional Time Series Forecasting

Time series forecasting is crucial across fields such as economics, energy, and traffic. Modeling cross-channel dependencies in high-dimensional time series remains challenging. Current methods are commonly divided into channel-independent (CI) and channel-dependent (CD) models. CI models process each channel independently, which contributes to their robustness. However, they ignore cross-channel dependencies and become less effective as the number of channels increases. CD models explicitly model interactions among channels, yet they may struggle to represent negative cross-channel relationships, produce inconsistent predictions when the channel order is permuted, and amplify perturbations during cross-channel propagation. These limitations motivate us to explore an alternative path: instead of designing complex CD models, we equip CI models with cross-channel capabilities. Based on this motivation, we propose Snow, a plug-and-play channel interaction module. Snow adds cross-channel communication through Sample-adaptive Cluster Representations. It enables signed and low-rank channel mixing to stabilize cross-channel propagation. Snow satisfies three properties: signed-interaction compatibility, channel-permutation equivariance, and interference stability. We provide theoretical analysis of these properties and validate them empirically. Extensive experiments show that inserting Snow into CI models consistently improves forecasting performance on high-dimensional datasets, while replacing interaction modules in CD models also yields consistent gains. Code is available at: https://anonymous.4open.science/r/snow-iclr/README.md