Parameter Decorrelation via Transition-Variance Alignment for Multivariate Time-series Forecasting

Multivariate time-series forecasting (MTSF) learns from high-dimensional covariates with strong temporal dependence, periodic structure, and cross-variable correlations. While modern pipelines often mitigate non-stationarity through instance-wise normalization and decomposition, these interventions operate at the data level and do not directly control dependence that can emerge among the parameters during training. We study MTSF optimization from a parameter-decorrelation viewpoint. Modeling stochastic optimization as a Markov chain in parameter space and leveraging its stochastic differential equation interpretation, we use the per-step transition-variance induced by gradient noise as a tractable signal for optimization-induced dependence and update uncertainty. This signal can empirically inflate during training; we theoretically show that such inflation can degrade generalization diagnostics. Motivated by this mechanism, we propose transition-variance alignment (TVA), an architecture-agnostic procedure that regulates transition-variance by smoothly gating the step size based on the mismatch between an estimated noise scale and a chosen target. TVA maintains effective transition-variance near a prescribed scale without architectural changes, incurs negligible overhead, and integrates seamlessly with diverse methods. Across real-world multivariate benchmarks, TVA consistently improves forecasting accuracy.