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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. Pe

PermuteFormer Efficient Relative Position Encoding for Long Sequences

PreviousKERPLE Kernelized Relative Positional Embedding for Length ExtrapolationNextRethinking Positional Encoding in Language Pre-training

Last updated 2 years ago

论文地址：

整体思路以及计算方式

整体思路是介绍一种适用于Linear Attention的相对位置编码方式。在Vanilla Attention中，因为会计算S=QK⊤\mathbf S=\mathbf Q \mathbf K^{\top}S=QK⊤，所以可以使用各种各样的相对位置编码。但是在Linear Attention中，因为不计算S\mathbf SS，所以可以使用的相对位置编码较少，本文就是解决这点，最后提供的方案为：

sim⁡(qi,kj)=(riPπiϕ(qi))⊤(r−jPπjϕ(kj))\operatorname{sim} \left(\mathbf{q}_{i}, \mathbf{k}_{j}\right)=\left(r^{i} \mathbf{P}_{\pi}^{i} \mathbf {\phi}\left(\mathbf{q}_{i}\right)\right)^{\top}\left(r^{-j} \mathbf{P}_{\pi}^{j} \mathbf {\phi}\left(\mathbf{k}_{j}\right)\right)sim(qi​,kj​)=(riPπi​ϕ(qi​))⊤(r−jPπj​ϕ(kj​))

这里Pπ\mathbf P_{\pi}Pπ​为置换矩阵，0<r<10<r<10<r<1，rrr的本意是想提供远程衰减性，但是个人认为这里的实现不太合理，因为ri−j≠rj−ir^{i-j}\neq r^{j-i}ri−j=rj−i，不过论文似乎效果还不错。

时间复杂度

不考虑。

训练以及loss

不变。

代码

实验以及适用场景

总体来说，都提升了Performer的效果。

细节

暂无。

简评

思路很巧妙，性能也不错，值得复现的工作。

https://arxiv.org/abs/2109.02377
https://github.com/cpcp1998/PermuteFormer