Sketching as a Tool for Understanding and Accelerating Self-attention for Long Sequences

Abstract

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 lowdimensional 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. 1 * Equal contribution.