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：基函数因其作为特征提取器或未来参考的能力，已成为现代基于深度学习的时间序列模型中不可或缺的组成部分。要发挥有效作用，基函数必须针对特定时间序列数据集定制，并与该集合中每个时间序列呈现独特的相关性。然而，当前最先进的方法在同时满足这两个要求方面存在局限性。为解决这一挑战，我们提出BasisFormer——一种利用可学习且可解释基函数的端到端时间序列预测架构。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，该方法将时间序列的历史与未来部分视为两个不同视图，并采用对比学习；其次，设计Coef模块，通过双向交叉注意力计算历史视图中时间序列与基函数之间的相似系数；最后，提出Forecast模块，基于相似系数选择并整合未来视图中的基函数，从而生成准确的未来预测。通过在六个数据集上的广泛实验，我们证明BasisFormer在单变量和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%。代码地址：\url{https://github.com/nzl5116190/Basisformer}