Appendix382 AAdditional Experiments3383 A.1 Experiments on the ETT datasets384 In the main body, we present a comparison of the benchmark methods on the ETTm2 dataset. In this385 section, we extend our analysis to the remaining three ETT datasets, namely ETTh1, ETTh2, and386 ETTm1, as summarized in Table 7. Our experimental results reveal that Basisformer outperforms all387 other methods in terms of MSE and MAE. In all experiments, lower MSE values indicate better model performance, and we present the best results in boldface. Experimental results with longer length input setting391 Throughout our research, we maintain consistency in our experimental settings by fixing the input392 length to be 96(with a reduced input length of 36for the illness dataset), instead of using a longer393 length.

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.

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.

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}