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On this page
  • 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. Memory

LaMemo Language Modeling with Look-Ahead Memory

PreviousDo Transformers Need Deep Long-Range MemoryNextGMAT Global Memory Augmentation for Transformers

Last updated 2 years ago

论文地址：

整体思路以及计算方式

之前Transformer中使用memory的方式都是当前token和memory中token交互，但是memory中token无法和当前token交互，本文就是对这点进行改进。

符号：

  • 当前token：Xτ=[xτ+1,⋯ ,xτ+N]∈RN×d\mathbf {X}_{\tau}=\left[\mathbf {x}_{\tau+1}, \cdots, \mathbf {x}_{\tau+N}\right] \in \mathbb{R}^{N \times d}Xτ​=[xτ+1​,⋯,xτ+N​]∈RN×d

  • memory：Xτ−1=[xτ−M+1,⋯ ,xτ]∈RM×d\mathbf {X}_{\tau-1}=\left[\mathbf {x}_{\tau-M+1}, \cdots, \mathbf {x}_{\tau}\right] \in \mathbb{R}^{M \times d}Xτ−1​=[xτ−M+1​,⋯,xτ​]∈RM×d

  • X~τ−1=[xτ−N+2,⋯ ,xτ+1]∈RN×d\tilde{\mathbf {X}}_{\tau-1}=\left[\mathbf {x}_{\tau-N+2}, \cdots, \mathbf {x}_{\tau+1}\right] \in \mathbb{R}^{N \times d}X~τ−1​=[xτ−N+2​,⋯,xτ+1​]∈RN×d

计算：

  • Qτ=XτWq,Kτ=XτWk,Vτ=XτWv\mathbf{Q}_{\tau}=\mathbf{X}_{\tau} \mathbf{W}_{q}, \mathbf{K}_{\tau}=\mathbf{X}_{\tau} \mathbf{W}_{k}, \mathbf{V}_{\tau}=\mathbf{X}_{\tau} \mathbf{W}_{v}Qτ​=Xτ​Wq​,Kτ​=Xτ​Wk​,Vτ​=Xτ​Wv​

  • K~τ−1=X~τ−1Wk,V~τ−1=X~τ−1Wv\tilde{\mathbf{K}}_{\tau-1}=\tilde{\mathbf{X}}_{\tau-1} \mathbf{W}_{k}, \tilde{\mathbf{V}}_{\tau-1}=\tilde{\mathbf{X}}_{\tau-1} \mathbf{W}_{v}K~τ−1​=X~τ−1​Wk​,V~τ−1​=X~τ−1​Wv​

  • Cτ←=Softmax⁡lower-triangle(QτK~τ⊤d)V~τ\mathbf{C}_{\tau}^{\leftarrow}=\operatorname{Softmax}_{\text{lower-triangle}} \left(\frac{\mathbf{Q}_{\tau} \tilde{\mathbf{K}}_{\tau}^{\top}}{\sqrt{d}}\right) \tilde{\mathbf{V}}_{\tau}Cτ←​=Softmaxlower-triangle​(d​Qτ​K~τ⊤​​)V~τ​

  • Cτ→=Softmax⁡upper-triangle(QτK~τ⊤d)V~τ\mathbf{C}_{\tau}^{\rightarrow}=\operatorname{Softmax}_{\text{upper-triangle}} \left(\frac{\mathbf{Q}_{\tau} \tilde{\mathbf{K}}_{\tau}^{\top}}{\sqrt{d}}\right) \tilde{\mathbf{V}}_{\tau}Cτ→​=Softmaxupper-triangle​(d​Qτ​K~τ⊤​​)V~τ​

  • Cτ−1↔=ατsg⁡(Cτ→)+(1−ατ)Cτ←\mathbf{C}_{\tau-1}^{\leftrightarrow}=\mathbf{\alpha}_{\tau} \operatorname{sg}\left(\mathbf{C}_{\tau}^{\rightarrow}\right)+\left(1-\mathbf{\alpha}_{\tau}\right) \mathbf{C}_{\tau}^{\leftarrow}Cτ−1↔​=ατ​sg(Cτ→​)+(1−ατ​)Cτ←​

    • sg\mathrm{sg}sg表示不计算梯度；

    • ατ=sg⁡(sτ→)sg⁡(sτ→)+sτ←+ε\mathbf{\alpha}_{\tau}=\frac{\operatorname{sg}\left(\mathbf{s}_{\tau}^{\rightarrow}\right)}{\operatorname{sg}\left(\mathbf{s}_{\tau}^{\rightarrow}\right)+\mathbf{s}_{\tau}^{{\leftarrow}}+\varepsilon}ατ​=sg(sτ→​)+sτ←​+εsg(sτ→​)​；

    • 其中sτ→\mathbf{s}_{\tau}^{\rightarrow}sτ→​表示Cτ→\mathbf{C}_{\tau}^{\rightarrow}Cτ→​中Softmax矩阵归一化之前的元素和；

时间复杂度

时间复杂度为O(N(N+M)d)O(N(N+M)d)O(N(N+M)d)。

训练以及loss

不变。

代码

实验以及适用场景

适用于encoder和decoder；论文只测试了lm(decoder)场景，获得了一定的提升。

细节

暂无。

简评

提供了一种新的memory交互方式。

https://arxiv.org/abs/2204.07341
https://github.com/thu-coai/LaMemo