vLinear: A Powerful Linear Model for Multivariate Time Series Forecasting

In this paper, we present vLinear, an effective yet efficient linear-based multivariate time series forecaster featuring two components: the vecTrans module and the WFMLoss objective. Many state-of-the-art forecasters rely on self-attention or its variants to capture multivariate correlations, typically incurring O(N2) computational complexity with respect to the number of variates N. To address this, we propose vecTrans, a lightweight module that utilizes a learnable vector to model multivariate correlations, reducing the complexity to O(N). Notably, vecTrans can be seamlessly integrated into Transformer-based forecasters, delivering up to 5× inference speedups and consistent performance gains. Furthermore, we introduce WFMLoss (Weighted Flow Matching Loss) as the objective. In contrast to typical velocity-oriented flow matching objectives, we demonstrate that a final-series-oriented formulation yields significantly superior forecasting accuracy. WFMLoss also incorporates path- and horizon-weighted strategies to focus learning on more reliable paths and horizons. Empirically, vLinear achieves state-of-the-art performance across 22 benchmarks and 124 forecasting settings. Moreover, WFMLoss serves as an effective plug-and-play objective, consistently improving existing forecasters. The code is available at https://anonymous.4open.science/r/vLinear.