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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.13768 |
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| _version_ | 1866918296773722112 |
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| author | Yue, Wenzhen Guo, Ruohao Shi, Ji Hao, Zihan Hu, Shiyu Ying, Xianghua |
| author_facet | Yue, Wenzhen Guo, Ruohao Shi, Ji Hao, Zihan Hu, Shiyu Ying, Xianghua |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13768 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | vLinear: A Powerful Linear Model for Multivariate Time Series Forecasting Yue, Wenzhen Guo, Ruohao Shi, Ji Hao, Zihan Hu, Shiyu Ying, Xianghua Machine Learning Artificial Intelligence 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. |
| title | vLinear: A Powerful Linear Model for Multivariate Time Series Forecasting |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2601.13768 |