vLinear: A Powerful Linear Model for Multivariate Time Series Forecasting

• URL: http://arxiv.org/abs/2601.13768v1
• Date: Tue, 20 Jan 2026 09:23:10 GMT
• Title: vLinear: A Powerful Linear Model for Multivariate Time Series Forecasting
• Authors: Wenzhen Yue, Ruohao Guo, Ji Shi, Zihan Hao, Shiyu Hu, Xianghua Ying,
• Abstract summary: vecTrans is a lightweight module that utilizes a learnable vector to model multivariate correlations.<n>WFMLoss is an effective plug-and-play objective, consistently improving existing forecasters.
• Score: 28.587343014443576
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we present \textbf{vLinear}, an effective yet efficient \textbf{linear}-based multivariate time series forecaster featuring two components: the \textbf{v}ecTrans module and the WFMLoss objective. Many state-of-the-art forecasters rely on self-attention or its variants to capture multivariate correlations, typically incurring $\mathcal{O}(N^2)$ 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 $\mathcal{O}(N)$. Notably, vecTrans can be seamlessly integrated into Transformer-based forecasters, delivering up to 5$\times$ inference speedups and consistent performance gains. Furthermore, we introduce WFMLoss (Weighted Flow Matching Loss) as the objective. In contrast to typical \textbf{velocity-oriented} flow matching objectives, we demonstrate that a \textbf{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.

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