Global Shortcut Contamination in End-to-End Graph Learning for Multivariate Forecasting

Graph neural networks for multivariate time-series forecasting increasingly learn graph structures end-to-end, jointly optimizing latent relational structures and forecasting models from data. Although such learned graphs are often treated as variable dependency structures, the end-to-end forecasting objective does not inherently support their structural correctness. As a result, the learned graph should be viewed as a prediction-optimized structure, which it may fail to capture invariant local dependencies. Here we analyze why and when this mismatch arises. We show that, in the presence of persistent global predictive modes, end-to-end graph learning favors train-specific shortcut structures aligned with global components, and we theoretically characterize when such shortcut-contaminated graphs are preferred. Based on this analysis, we propose a simple projection-based decoupling strategy that removes dominant global components before graph learning in an architecture-agnostic manner. Experiments on controlled synthetic benchmarks and real traffic benchmarks under time-of-day shifts show that our proposed projection method substantially improves robustness for unstable graph learners and often reduces out-of-distribution (OOD) forecasting error, while its benefits for already stable architectures are shift-dependent. Beyond OOD robustness, our results highlight the importance of separating predictive usefulness from structural correctness when interpreting learned graphs in end-to-end forecasting models.