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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

Luna: Linear Unified Nested Attention

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Last updated 2 years ago

论文地址：

整体思路以及计算方式

思路非常简单，利用MHA降维得到中间状态，然后再利用一个MHA计算最终结果，整体思路如下：

双向版本：

  • 外部输入P∈Rl×dP\in \mathbb R^{l\times d}P∈Rl×d，输入X∈Rn×dX\in \mathbb R^{n\times d}X∈Rn×d

  • YP=MHA(P,X)∈Rl×dY_P= \mathrm{MHA}(P, X)\in \mathbb R^{l\times d}YP​=MHA(P,X)∈Rl×d

  • YX=MHA(X,YP)∈Rn×dY_X=\mathrm{MHA}(X,Y_P)\in \mathbb R^{n\times d}YX​=MHA(X,YP​)∈Rn×d

单向版本：

  • 定义

    X∈Rn×d1Y∈Rn×d1Z∈Rn×d2F≜f(X,Y,Z)∈Rn×d2ft=1txt∑j=1⊤yj⊤zj∈Rd2\begin{aligned} X&\in \mathbb R^{n\times d_1}\\ Y&\in \mathbb R^{n\times d_1} \\ Z&\in \mathbb R^{n\times d_2}\\ F &\triangleq f(X, Y, Z) \in \mathbb R^{n\times d_2}\\ f_{t}&=\frac{1}{t} x_{t} \sum_{j=1}^{\top} y_{j}^{\top} z_{j}\in \mathbb R^{d_2} \end{aligned}XYZFft​​∈Rn×d1​∈Rn×d1​∈Rn×d2​≜f(X,Y,Z)∈Rn×d2​=t1​xt​j=1∑⊤​yj⊤​zj​∈Rd2​​

  • Apack=w(PX⊤)∈Rl×nA_{pack}=w(P X^{\top} )\in \mathbb R^{l\times n}Apack​=w(PX⊤)∈Rl×n

    • www可选1 + elu / softplus（不能按行使用Softmax，因为会有信息泄露）

  • Auppack=w(f(X,X,Apack⊤))∈Rn×lA_{uppack}=w(f(X, X,A_{pack}^{\top}))\in \mathbb R^{n\times l}Auppack​=w(f(X,X,Apack⊤​))∈Rn×l

    • www可选Softmax（按行归一化）

  • 输出Y=f(Auppack,Apack⊤,X)∈Rn×dY=f(A_{uppack},A_{pack}^{\top}, X)\in \mathbb R^{n\times d}Y=f(Auppack​,Apack⊤​,X)∈Rn×d

时间复杂度

单向双向的时间复杂度都为O(nd2)O(nd^2)O(nd2)，但是单向版本本质上是RNN，速度会比较慢。

训练以及loss

不变。

代码

实验以及适用场景

适用于所有场景，效果总的来说不错。

细节

暂无。

简评

这篇论文思路还是挺不错的，利用Attention来降维的思路也见到过很多次，然后单向版本的算法可以再仔细思考下。

https://arxiv.org/abs/2106.01540
https://github.com/XuezheMax/fairseq-apollo