Diagonal Adaptive Graph: Revisiting Channel Dependency in Multivariate Time Series Forecasting

Adaptive graph learning has become a widely adopted paradigm for multivariate time series forecasting when explicit physical topology is unavailable. In these approaches, node embeddings are typically used to construct dense adjacency matrices based on pairwise similarity, implicitly coupling representation learning with relational modeling. However, we observe that under identical training settings but different random initializations, the learned adjacency matrices can vary substantially while predictive performance remains nearly unchanged, indicating that the relational structure is often underdetermined by the forecasting objective. This observation suggests a mismatch between similarity-based structural learning and the forecasting objective. In this work, we revisit node embeddings from a sequence approximation perspective and propose a Diagonal Adaptive Graph (DiAG) module that restricts adaptive learning to diagonal elements. The diagonal coefficients are derived from channel-independent predictions, while off-diagonal interactions are constructed from the similarity of input sequences. This design decouples representation learning from relational modeling, allowing variables to adaptively switch between channel-independent and channel-dependent regimes. Experiments on multiple datasets show that DiAG improves forecasting performance without modifying the channel-independent backbones. These results indicate that channel-dependent forecasting can be achieved as a prediction-driven refinement over channel-independent backbones, without requiring fully learned dense relational structures.