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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. Others

Transformer Dissection: A Unified Understanding of Transformer's Attention via the Lens of Kern

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Last updated 2 years ago

论文地址：

整体思路以及计算方式

整体思路是从Kernel的角度理解Attention，然后调整内积的计算方式：

  • 输入X∈Rn×dX\in \mathbb R^{n\times d}X∈Rn×d，位置矩阵P∈Rn×dP\in \mathbb R^{n\times d}P∈Rn×d

  • Q=XWQ∈Rn×d,K=XWK∈Rn×dQ=XW_Q\in \mathbb R^{n\times d}, K = XW_K\in \mathbb R^{n\times d}Q=XWQ​∈Rn×d,K=XWK​∈Rn×d

  • QP=PW1∈Rn×d,KP=PW2∈Rn×dQ_P=PW_{1}\in \mathbb R^{n\times d}, K_P = P W_2\in \mathbb R^{n\times d}QP​=PW1​∈Rn×d,KP​=PW2​∈Rn×d

  • 内积计算QK⊤+QPQK⊤∈Rn×nQK^\top + Q_P Q_K^{\top} \in \mathbb R^{n\times n}QK⊤+QP​QK⊤​∈Rn×n

  • 剩余部分相同

作者还测试了一些Kernel的性能：

  • f(x,y)=x⊤yf(x, y)= x^{\top} yf(x,y)=x⊤y（非常差）

  • f(x,y)=(x⊤y)2f(x, y)= (x^{\top} y)^2f(x,y)=(x⊤y)2（很差）

  • f(x,y)=exp⁡(x⊤y)f(x, y)= \exp (x^{\top} y)f(x,y)=exp(x⊤y)（默认设置，效果不错）

  • f(x,y)=exp⁡(−∥x−y∥2)f(x, y)= \exp (-\|x -y \|^2)f(x,y)=exp(−∥x−y∥2)（效果不错，和前者接近）

时间复杂度

不变。

训练以及loss

不变。

代码

实验以及适用场景

适用于所有场景，该论文是分析性的文章，性能不是卖点。

细节

作者给出了permutation equivariant的严格定义，还讨论了Value中是否应该包含位置信息，结论是不一定需要。

简评

提供了一个新的角度，之前也看过这篇论文，但没细看，这次重读得到了一些新的信息。

https://arxiv.org/abs/1908.11775