arXiv：cs.LG· Hao Wang, Licheng Pan, Yuan Lu, Zhichao Chen, Tianqiao Liu, Shuting He, Zhixuan Chu, Qingsong Wen, Haoxuan Li, Zhouchen Lin·· 7 小时前AI 评分37
QDF：面向多步时间序列预测模型的二次型直接预测学习目标
Quadratic Direct Forecast for Training Multi-Step Time-Series Forecast Models
AI 导读
针对 MSE 等现有学习目标忽略未来各步标签自相关、且对不同步长任务等权处理的问题，研究者提出二次型加权学习目标及 Quadratic Direct Forecast（QDF）算法，用自适应更新的加权矩阵训练预测模型。实验显示 QDF 可提升多种预测模型性能并取得 SOTA 结果，论文已被 ICLR 2026 接收，代码已开源。
正文
Abstract:The design of learning objectives is central to training time-series forecasting models. Existing learning objectives such as mean squared error mostly treat each future step as an independent, equally weighted task, which leads to the following two challenges: (1) they overlook the label autocorrelation effect among future steps, leading to biased learning objectives; (2) they fail to set heterogeneous task weights for different forecasting tasks corresponding to varying future steps, limiting the forecasting performance. To fill this gap, we propose a novel quadratic-form weighted learning objective, addressing both issues simultaneously. Specifically, the off-diagonal elements of the weighting matrix account for the label autocorrelation effect, whereas the non-uniform diagonals are expected to match the preferred weights of the forecasting tasks with varying future steps. On this basis, we propose a Quadratic Direct Forecast (QDF) learning algorithm, which trains the forecast model using the adaptively updated quadratic-form weighting matrix. Experiments show that our QDF effectively improves the performance of various forecast models, achieving state-of-the-art results. Code is available at this https URL.
| Comments: | Accepted by ICLR 2026 |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML) |
| Cite as: | arXiv:2511.00053 [cs.LG] |
| (or arXiv:2511.00053v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2511.00053 arXiv-issued DOI via DataCite |
|
| Journal reference: | ICLR 2026 |
Submission history
From: Hao Wang [view email]
[v1]
Tue, 28 Oct 2025 14:48:25 UTC (1,697 KB)
[v2]
Tue, 6 Oct 2026 12:23:11 UTC (2,083 KB)
来源：arXiv：cs.LG · arxiv.org