多变量时间序列预测需要跨变量损失（Cross Variable Loss）
Multivariate Time Series Forecasting needs Cross Variable Loss
AI 导读
多变量时间序列预测大多采用直接预测（DF）范式，其逐点目标函数未约束未来值之间的跨变量依赖，存在目标函数缺口。研究者提出即插即用的 Cross-Variable Loss（CvLoss），在跨变量图上约束预测残差，惩罚预测 patch 间不一致的边级残差差异，兼顾同步与异步交互。实验显示 CvLoss 能持续提升多个竞争性预测模型，兼容多种骨干网络，论文已被 NeurIPS 2026 接收。
正文 · 原文
Abstract:Multivariate time series forecasting presents unique challenges because future variables often co-evolve under shared system dynamics. While existing studies mainly focus on cross-variable dependencies in historical observations, dependencies among future values are much less explored. Specifically, modern forecasting models largely follow the Direct Forecasting (DF) paradigm, generating multi-step forecasts with point-wise objectives that do not explicitly constrain cross-variable structure. In this work, we show that the DF objective is mismatched in the presence of cross-variable and lagged dependencies, revealing an objective gap. To address this issue, we propose \textbf{C}ross-\textbf{V}ariable \textbf{Loss} (CvLoss), a plug-in structural regularizer that constrains forecast residuals on a cross-variable graph. CvLoss penalizes inconsistent edge-wise residual differences over forecast patches, encouraging consistency across both synchronous and asynchronous interactions. Our experiments show that CvLoss consistently improves competitive forecasting models, outperforms representative learning objectives, and is compatible with a variety of forecasting backbones.
| Comments: | This paper has been accepted by NeurIPS 2026 |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2608.05742 [cs.LG] |
| (or arXiv:2608.05742v4 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2608.05742 arXiv-issued DOI via DataCite |
Submission history
From: Kuiye Ding [view email]
[v1]
Thu, 6 Aug 2026 08:22:45 UTC (1,922 KB)
[v2]
Sun, 27 Sep 2026 15:39:30 UTC (1,922 KB)
[v3]
Tue, 29 Sep 2026 05:34:25 UTC (1,922 KB)
[v4]
Mon, 26 Oct 2026 07:28:21 UTC (1,966 KB)
来源：arXiv cs.AI · arxiv.org