  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}
