@inproceedings{
chou2024metala,
title={Meta{LA}: Unified Optimal Linear Approximation to Softmax Attention Map},
author={Yuhong Chou and Man Yao and Kexin Wang and Yuqi Pan and Rui-Jie Zhu and Jibin Wu and Yiran Zhong and Yu Qiao and Bo XU and Guoqi Li},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=Y8YVCOMEpz}
}
Various linear complexity models, such as Linear Transformer (LinFormer), State Space Model (SSM), and Linear RNN (LinRNN), have been proposed to replace the conventional softmax attention in Transformer structures. However, the optimal design of these linear models is still an open question. In this work, we attempt to answer this question by finding the best linear approximation to softmax attention from a theoretical perspective. We start by unifying existing linear complexity models as the linear attention form and then identify three conditions for the optimal linear attention design: (1) Dynamic memory ability; (2) Static approximation ability; (3) Least parameter approximation. We find that none of the current linear models meet all three conditions, resulting in suboptimal performance. Instead, we propose Meta Linear Attention (MetaLA) as a solution that satisfies these conditions. Our experiments on Multi-Query Associative Recall (MQAR) task, language modeling, image classification, and Long-Range Arena (LRA) benchmark demonstrate that MetaLA is more effective than the existing linear models.
MetaLA: Unified Optimal Linear Approximation to Softmax Attention Map
Yuhong Chou Man Yao Kexin Wang Yuqi Pan Rui-Jie Zhu Jibin Wu Yiran Zhong Yu Qiao Bo XU Guoqi Li