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  • 整体思路以及计算方式
  • 时间复杂度
  • 训练以及loss
  • 代码
  • 实验以及适用场景
  • 细节
  • 简评
  1. MHA
  2. SparseOrLowRank

Fast Transformers with Clustered Attention

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Last updated 2 years ago

论文地址：

整体思路以及计算方式

对QQQ进行聚类，从而降低时间复杂度。

输入：

  • Q∈Rn×d,K∈Rn×d,V∈Rn×dQ\in \mathbb R^{n\times d}, K\in \mathbb R^{n\times d}, V\in \mathbb R^{n\times d}Q∈Rn×d,K∈Rn×d,V∈Rn×d

  • 聚类矩阵：S∈{0,1}n×cS\in \{0,1\}^{n\times c}S∈{0,1}n×c

  • qjc=∑i=1Nsijqi∑i=1Nsijq_{j}^{c}=\frac{\sum_{i=1}^{N} s_{i j} q_{i}}{\sum_{i=1}^{N} s_{i j}}qjc​=∑i=1N​sij​∑i=1N​sij​qi​​

  • Ac=softmax⁡(QcK⊤)∈Rc×nA^{c}=\operatorname{softmax}\left({Q^{c} K^{\top}}\right)\in \mathbb R^{c\times n}Ac=softmax(QcK⊤)∈Rc×n

  • Oˉ=AcV∈Rc×d\bar O=A^{c} V\in \mathbb R^{c\times d}Oˉ=AcV∈Rc×d

  • oi=∑j=1csijoˉjo_{i}=\sum_{j=1}^{c} s_{i j} \bar o_{j}oi​=∑j=1c​sij​oˉj​

聚类方式见论文。

时间复杂度

O(ncd)O(ncd)O(ncd)。

训练以及loss

不变。

代码

实验以及适用场景

作者跑了Encoder实验，Decoder部分需要适配。

细节

暂无。

简评

一个很简洁的思路，不过高效实现需要花一定的功夫，主要是聚类方式部分。

https://arxiv.org/abs/2007.04825
https://github.com/idiap/fast-transformers