  Transformer-based models are not efficient in processing long sequences due
to the quadratic space and time complexity of the self-attention modules. To
address this limitation, Linformer and Informer are proposed to reduce the
quadratic complexity to linear (modulo logarithmic factors) via low-dimensional
projection and row selection respectively. These two models are intrinsically
connected, and to understand their connection, we introduce a theoretical
framework of matrix sketching. Based on the theoretical analysis, we propose
Skeinformer to accelerate self-attention and further improve the accuracy of
matrix approximation to self-attention with three carefully designed
components: column sampling, adaptive row normalization and pilot sampling
reutilization. Experiments on the Long Range Arena (LRA) benchmark demonstrate
that our methods outperform alternatives with a consistently smaller time/space
footprint.
