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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. Memory

Compressive Transformers for Long-Range Sequence Modelling

PreviousMemoryNextMemformer The Memory-Augmented Transformer

Last updated 2 years ago

论文地址：

整体思路以及计算方式

计算方式：

  • 构造记忆m∈Rnm×d\mathbf m\in \mathbb R^{n_m\times d}m∈Rnm​×d和压缩记忆cm∈Rncm×d\mathbf {cm}\in \mathbb R^{n_{cm}\times d}cm∈Rncm​×d；

  • 对于输入x∈Rn×d\mathbf x\in \mathbb R^{n\times d}x∈Rn×d，将记忆和压缩记忆拼接为整体记忆mem=concat(cm,m,x)∈R(nm+ncm+n)×d\mathbf{mem}=\mathrm{concat}(\mathbf {cm},\mathbf m,\mathbf x) \in \mathbb R^{(n_m+ n_{cm}+n)\times d}mem=concat(cm,m,x)∈R(nm​+ncm​+n)×d，得到输出MHA(x,mem)∈Rn×d\mathrm{MHA}(\mathbf x, \mathbf{mem}) \in \mathbb R^{n\times d}MHA(x,mem)∈Rn×d。

记忆的更新方式为：

  • 记忆：

    • 拼接，选择最近的nmn_mnm​个记忆：m=concat(m,x)[−nm:]∈Rnm×d\mathbf m =\mathrm{concat}(\mathbf m,\mathbf x)[-n_m:] \in \mathbb R^{n_m \times d}m=concat(m,x)[−nm​:]∈Rnm​×d

  • 压缩记忆：

    • 对m[:n]\mathbf m[:n]m[:n]的序列维度降维ccc倍得到cmtmp∈R⌊nc⌋×d\mathbf {cm}_{tmp}\in \mathbb R^{\left\lfloor\frac{n}{c}\right\rfloor \times d}cmtmp​∈R⌊cn​⌋×d

    • 拼接，选择最近的ncmn_{cm}ncm​个记忆：cm=concat(cm,cmtmp)[−ncm:]∈Rncm×d\mathbf {cm}=\mathrm{concat}(\mathbf {cm}, \mathbf {cm}_{tmp})[-n_{cm}:]\in \mathbb R^{n_{cm}\times d}cm=concat(cm,cmtmp​)[−ncm​:]∈Rncm​×d

时间复杂度

依然是标准Attention的计算方式，所以时间复杂度为O(ns(nm+ncm+n)d)O(n_s(n_m+ n_{cm} +n) d)O(ns​(nm​+ncm​+n)d)。

训练以及loss

训练方式一致，loss部分增加了如下部分：

∥MHA(x,old_mem)−MHA(x,mem)∥2\left\| \mathrm{MHA}(\mathbf x, \mathbf{old\_{mem}}) - \mathrm{MHA}(\mathbf x, \mathbf {mem}) \right\|_2​MHA(x,old_mem)−MHA(x,mem)​2​

其中old_mem/mem\mathbf {old\_mem/mem}old_mem/mem表示m,cm\mathbf {m},\mathbf c_mm,cm​更新前/后拼接得到的整体记忆，应该是确保训练稳定。

代码

实验以及适用场景

单向双向模型均适用；论文里只测试了lm（单向模型），效果有所提升。

细节

记忆和压缩记忆都不在计算图内，即不使用梯度方式更新。

简评

优点：

  • 适用于单向和双向模型；

  • 引入了记忆机制，提升了性能；

不足：

  • 引入的记忆机制增增加了不少显存，时间复杂度也增加了；

  • 压缩记忆的动机不够清晰；

总结：

  • 是一种时间和空间换性能的方法，不会进行复现；

https://arxiv.org/abs/1911.05507
https://github.com/lucidrains/compressive-transformer-pytorch