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.

翻译：本文提出了一种高效且有效的基于线性模型的多元时间序列预测器——\textbf{vLinear}，其包含两个核心组件：\textbf{v}ecTrans模块与WFMLoss目标函数。许多先进的预测器依赖自注意力机制或其变体来捕捉多元相关性，这通常会导致计算复杂度随变量数$N$呈$\mathcal{O}(N^2)$增长。为解决此问题，我们提出了vecTrans，这是一个轻量级模块，利用一个可学习向量来建模多元相关性，将复杂度降低至$\mathcal{O}(N)$。值得注意的是，vecTrans可以无缝集成到基于Transformer的预测器中，实现高达5倍的推理加速并带来持续的性能提升。此外，我们引入了WFMLoss（加权流匹配损失）作为目标函数。与典型的\textbf{面向速度}的流匹配目标不同，我们证明\textbf{面向最终序列}的公式化方法能显著提升预测精度。WFMLoss还结合了路径加权和时域加权策略，以将学习重点集中在更可靠的路径和预测时域上。实验表明，vLinear在22个基准测试和124种预测设定中均达到了最先进的性能。此外，WFMLoss可作为一种有效的即插即用目标函数，持续改进现有预测器。代码发布于 https://anonymous.4open.science/r/vLinear。