Bases have become an integral part of modern deep learning-based models for time series forecasting due to their ability to act as feature extractors or future references. To be effective, a basis must be tailored to the specific set of time series data and exhibit distinct correlation with each time series within the set. However, current state-of-the-art methods are limited in their ability to satisfy both of these requirements simultaneously. To address this challenge, we propose BasisFormer, an end-to-end time series forecasting architecture that leverages learnable and interpretable bases. This architecture comprises three components: First, we acquire bases through adaptive self-supervised learning, which treats the historical and future sections of the time series as two distinct views and employs contrastive learning. Next, we design a Coef module that calculates the similarity coefficients between the time series and bases in the historical view via bidirectional cross-attention. Finally, we present a Forecast module that selects and consolidates the bases in the future view based on the similarity coefficients, resulting in accurate future predictions. Through extensive experiments on six datasets, we demonstrate that BasisFormer outperforms previous state-of-the-art methods by 11.04\% and 15.78\% respectively for univariate and multivariate forecasting tasks. Code is available at: \url{https://github.com/nzl5116190/Basisformer}

翻译：基函数已成为现代基于深度学习的时间序列预测模型的核心组成部分，其作用体现在特征提取或未来参考等方面。为实现有效预测，基函数必须针对特定时间序列数据集进行定制，并与该数据集中的每条时间序列呈现差异化相关性。然而，现有最先进的方法在同时满足这两项要求方面存在局限性。为解决这一挑战，我们提出BasisFormer——一种端到端的时间序列预测架构，该架构利用可学习且可解释的基函数。该架构包含三个组成部分：首先，通过自适应自监督学习获取基函数，将时间序列的历史片段与未来片段视为两种不同视角，并采用对比学习进行训练；其次，设计系数计算模块，通过双向交叉注意力机制计算历史视角下时间序列与基函数之间的相似系数；最后，提出预测模块，基于相似系数对未来视角下的基函数进行筛选与整合，从而实现精准的未来预测。在六个数据集上的广泛实验表明，BasisFormer在单变量与多变量预测任务中分别比先前最先进方法提升11.04%和15.78%的性能。代码开源地址：\url{https://github.com/nzl5116190/Basisformer}