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 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 column sampling, adaptive row normalization and pilot sampling reutilization. Experiments on the Long Range Arena benchmark demonstrate that our methods outperform alternatives with a consistently smaller time/space footprint.

The massive amount of trainable parameters in the pre-trained language models (PLMs) makes them hard to be deployed to multiple downstream tasks. To address this issue, parameter-efficient transfer learning methods have been proposed to tune only a few parameters during fine-tuning while freezing the rest. This paper looks at existing methods along this line through the kernel lens. Motivated by the connection between self-attention in transformer-based PLMs and kernel learning, we propose kernel-wise adapters, namely Kernel-mix, that utilize the kernel structure in self-attention to guide the assignment of the tunable parameters. These adapters use guidelines found in classical kernel learning and enable separate parameter tuning for each attention head. Our empirical results, over a diverse set of natural language generation and understanding tasks, show that our proposed adapters can attain or improve the strong performance of existing baselines.