FIST: Frequency-Conditioned Interaction with Sparse Topology for Multivariate Forecasting

Multivariate forecasting faces a fundamental trade-off: ignoring other variables may miss useful information, while indiscriminate interaction can introduce irrelevant dependencies. More importantly, a dependency useful for one temporal pattern may be unhelpful for another, yet cross-variable interaction is often shared across temporal components. We introduce FIST, a frequency-conditioned forecasting framework that follows a simple principle: preserve each variable's temporal dynamics before selectively introducing information from others. FIST first encodes variables independently, then partitions the learned representation into latent frequency bands and constructs a sparse interaction graph for each band. This design naturally supports independent, shared-graph, and band-conditioned variants under the same temporal backbone. A restricted linear analysis shows that sharing one interaction operator incurs an approximation cost when dependency patterns differ across bands, which controlled experiments verify. Across 165 forecasting runs on four datasets, however, band-specific interaction yields modest and setting-dependent gains after representation learning. These results distinguish the existence of component-specific dependencies from their actual predictive value, and clarify when frequency-conditioned interaction is useful for multivariate forecasting. Code is available at: https://anonymous.4open.science/r/FigNet-D2BC.