What If We Let Forecasting Forget? A Sparse Bottleneck for Cross-Variable Dependencies

Multivariate time series forecasting is critical in many real-world systems, and thus modeling cross-channel dependencies is essential. Although existing methods improve overall accuracy by enhancing representations and cross-channel interactions, it remains challenging to reliably capture inter-variable dependencies under specific conditions. We observe that dependencies in real data are often state-dependent and noisy; in such cases, dense interactions can amplify spurious correlations and lead to representation over-smoothing, which may yield unreliable predictions in certain scenarios. Motivated by this, we propose MS-FLOW, a sparse-bottleneck framework that explicitly models inter-variable interaction as capacity-limited information flow. Specifically, MS-FLOW replaces fully connected communication with selective sparse routing, retaining only a few critical dependency paths and injecting cross-variable signals under a strict communication budget, thereby suppressing redundant connections and spurious-correlation propagation. Extensive experiments demonstrate that MS-FLOW learns more reliable multivariate correlations, achieving state-of-the-art forecasting accuracy on 12 real-world benchmarks while producing fewer yet more reliable dependencies, shifting multivariate forecasting from “more interaction” to “more effective interaction”.

Modern forecasting systems often track many related signals at once, such as traffic, electricity, or weather. A common challenge is deciding which signals truly help each other. Using every possible connection can spread noise and hurt prediction quality. We propose MS-FLOW, a method that keeps only a small number of important connections between variables instead of using all of them. This helps the model focus on the most useful information and avoid misleading relationships. Experiments on 12 real-world datasets show that MS-FLOW makes more accurate predictions than previous methods while learning fewer but more reliable connections. Our results suggest that, for multivariate forecasting, better performance comes not from using more interactions, but from using more effective ones.