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 this https URL.
Abstract (translated)
在这篇论文中，我们提出了**vLinear**，这是一种基于线性且有效的多变量时间序列预测器，具有两个组成部分：**vecTrans**模块和WFMLoss目标。许多最先进的预测模型依赖于自注意力机制或其变体来捕捉多变量相关性，这通常会导致相对于变量数量$N$的$\mathcal{O}(N^2)$计算复杂度。为了解决这一问题，我们提出了一个轻量级模块**vecTrans**，该模块使用可学习向量来建模多变量的相关性，从而将复杂度降低到$\mathcal{O}(N)$。值得注意的是，**vecTrans**可以无缝地集成到基于Transformer的预测器中，提供高达5倍的推理加速，并且性能一致提高。 此外，我们引入了WFMLoss（加权流匹配损失）作为目标函数。不同于常见的以速度为导向的流匹配目标函数，我们证明了一种面向最终序列的目标函数形式可以显著提升预测准确性。此外，WFMLoss还集成了路径和时间范围上的加权策略，以便将学习集中在更可靠的路径和时间段上。 在实证研究中，vLinear模型在22个基准测试和124个预测设置中达到了最先进的性能水平。此外，WFMLoss可以作为一个有效的即插即用目标函数来改进现有的预测器，并且始终能够提高现有预测器的性能。代码可在该网址获得：[此处提供URL]。
URL
https://arxiv.org/abs/2601.13768
