FLAG: Factor-Lag Relational Context for Adaptive Group Communication in Multivariate Time Series Forecasting

Effectively modeling and using cross-variable dependencies is an important route to better multivariate time series forecasting. Prior work has explored several mechanisms for interaction among variables, but it remains challenging to represent lagged relations compactly while adjusting how those relations are used according to the current input. In particular, cross-variable dependencies can recur across observation windows, yet their contribution to a forecast depends on the current state. If this difference is not taken into account, information aggregation can mix cross-variable information that is useful for the current input with information that is not. To address this problem, we propose FLAG, a unified framework that jointly models lagged relations and performs input-adaptive information exchange within the same representation. FLAG first combines shared low-rank latent factors with lag-specific factor interactions, incorporating other variables' histories into each variable's representation and forming a relational context. This design retains lag-specific interaction detail without constructing dense variable-pair matrices. Group communication then produces input-dependent aggregation weights and messages from this context and updates the same representation, so that the shared relations take part in the forecast according to the current state. With the other model and temporal dimensions held fixed, both the number of parameters and the computation grow linearly with the number of variables. Experiments on eight benchmarks show that FLAG achieves competitive forecasting performance. Code is available at https://anonymous.4open.science/r/FLAG-DE06.