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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
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  1. MHA
  2. Others

IGLOO: Slicing the Features Space to Represent Sequences

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Last updated 2 years ago

论文地址:

整体思路以及计算方式

引入了一个全新的计算Attention的方式,主要分为两个部分IGLOO-base和IGLOO-seq,原论文写的非常不清楚,所以这里按照自己的理解进行梳理。

IGLOO-base(记为fff):

  • 输入:X∈Rn×dX \in \mathbb R^{n\times d}X∈Rn×d

  • X1=Conv1d(X)∈Rn×d1X_1 = \mathrm{Conv1d}(X)\in \mathbb R^{n\times d_1}X1​=Conv1d(X)∈Rn×d1​

  • 降采样:X2=DownSample(X1)∈Rm×d1X_2= \mathrm{DownSample}(X_1)\in \mathbb R^{m\times d_1}X2​=DownSample(X1​)∈Rm×d1​

  • 重复降采样lll次得到:X3=Concat([X2]1,…,[X2]l)∈Rl×m×d1X_3 =\mathrm{Concat}([X_2]_1,\ldots, [X_2]_l)\in \mathbb R^{l\times m \times d_1}X3​=Concat([X2​]1​,…,[X2​]l​)∈Rl×m×d1​

  • O1=Sum(X3,d=1,2)∈RlO_1=\mathrm{Sum}(X_3, d=1,2)\in \mathbb R^{l}O1​=Sum(X3​,d=1,2)∈Rl

  • 重复kkk次可得O∈Rk×lO\in \mathbb R^{k\times l}O∈Rk×l

IGLOO-seq:

  • 输入:X∈Rn×d,Y∈Rn×dX\in \mathbb R^{n\times d}, Y \in \mathbb R^{n\times d}X∈Rn×d,Y∈Rn×d

  • T1=reshape(f(Q))∈Rn×1×d1T_1=\mathrm{reshape}(f(Q))\in \mathbb R^{n\times 1 \times d_1}T1​=reshape(f(Q))∈Rn×1×d1​

    • k=n,l=d1k=n,l=d_1k=n,l=d1​

  • P=Softmax(T1)∈Rn×1×d1P=\mathrm{Softmax}(T_1)\in \mathbb R^{n\times 1 \times d_1}P=Softmax(T1​)∈Rn×1×d1​

  • T2=YW1∈Rn×dT_2=Y W_1\in \mathbb R^{n\times d}T2​=YW1​∈Rn×d

  • T3=repeat(T2)∈Rn×d1×dT_3=\mathrm{repeat}(T_2)\in \mathbb R^{n\times d_1 \times d}T3​=repeat(T2​)∈Rn×d1​×d

  • 可学习矩阵:B∈Rn×1×dB\in \mathbb R^{n\times 1 \times d}B∈Rn×1×d

  • T4=T3⊙B∈Rn×d1×dT_4 = T_3\odot B \in \mathbb R^{n\times d_1 \times d}T4​=T3​⊙B∈Rn×d1​×d

  • O1=PT4∈Rn×1×dO_1=PT_4 \in \mathbb R^{n\times 1\times d}O1​=PT4​∈Rn×1×d

  • O2=reshape(O1)∈Rn×dO_2=\mathrm{reshape}(O_1)\in \mathbb R^{n\times d}O2​=reshape(O1​)∈Rn×d

时间复杂度

有点复杂,但关于nnn应该是线性复杂度。

训练以及loss

不变。

代码

实验以及适用场景

作者做了一些实验,但是参数量无法对齐,所以有效性不太好说。

细节

暂无。

简评

论文写的非常不清楚,实验也不严格,是否有效需要验证。

https://arxiv.org/abs/1807.03402
https://github.com/redna11/lra-igloo