vLinear: A Powerful Linear Model for Multivariate Time Series Forecasting

2026-01-20

AI Summary

This work addresses the challenge of efficiently modeling inter-variable dependencies in multivariate time series forecasting, where existing self-attention-based methods suffer from O(N²) computational complexity. To overcome this limitation, the authors propose vLinear, a lightweight architecture featuring a novel vecTrans module that explicitly captures multivariate dependencies with linear O(N) complexity. Additionally, they introduce a Weighted Flow Matching Loss (WFMLoss), which enhances long-term forecasting performance by weighting trajectories according to prediction horizons. The resulting model is both architecturally simple and modular in its objective design. Empirical evaluation across 22 benchmarks and 124 experimental settings demonstrates that vLinear achieves state-of-the-art performance. Moreover, integrating vecTrans into Transformer-based models yields up to a 5× speedup, while WFMLoss consistently improves the accuracy of existing forecasters.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Computer Vision: Large Vision Models
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• multivariate time series forecasting
• computational complexity
• self-attention
• scalability
• efficiency

Innovation

• vLinear
• vecTrans
• WFMLoss
• linear time series forecasting
• multivariate correlation modeling