Title: SKTformer: A Skeleton Transformer for Long Sequence Data. Abstract: Transformers have become a preferred tool for modeling sequential data. Many studies of using Transformers for long sequence modeling focus on reducing computational complexity. They usually exploit the low-rank structure of data and approximate a long sequence by a sub-sequence. One challenge with such approaches is how to make an appropriate tradeoff between information preserving and noise reduction: the longer the sub-sequence used to approximate the long sequence, the better the information is preserved but at a price of introducing more noise into the model and of course more computational costs. We propose skeleton transformer, SKTformer for short, an efficient transformer architecture that effectively addresses the tradeoff. It introduces two mechanisms to effectively reduce the impact of noise while still keeping the computation linear to the sequence length: a smoothing block to mix information over long sequences and a matrix sketch method that simultaneously selects columns and rows from the input matrix. We verify the effectiveness of SKTformer both theoretically and empirically. Extensive studies over both Long Range Arena (LRA) datasets and six time-series forecasting show that SKTformer significantly outperforms both villain Transformer and other state-of-the-art variants of Transformer.  Code is available at
https://anonymous.4open.science/r/SKTFormer-B33B/