# Block-Recurrent Transformers

论文地址：

* <https://arxiv.org/abs/2203.07852>

## 整体思路以及计算方式

利用Memory的方式增加Transformer的性能，利用窗口的方式降低计算复杂度，对Memory部分使用递归的方式更新。

计算方式：

* 输入：$$\mathbf X\in \mathbb R^{n\times d}, \mathbf M \in \mathbb R^{m\times d}$$；
  * $$\mathbf M$$表示Memory；
* 输出部分更新方式：
  * $$\mathbf X\_1=\mathrm{MHA}\_{w}(\mathbf X, \mathbf X)\in \mathbb R^{n\times d}$$
  * $$\mathbf Y\_1=\mathrm{MHA}\_{w}(\mathbf X, \mathbf M)\in \mathbb R^{n\times d}$$
  * $$\mathbf O =\[\mathbf X\_1, \mathbf Y\_1] \mathbf W \in \mathbb R^{n\times d}$$
* Memory部分更新方式：
  * $$\mathbf M\_1=\mathrm{MHA}\_{w}(\mathbf M, \mathbf M)\in \mathbb R^{m\times d}$$
  * $$\mathbf Y\_1=\mathrm{MHA}\_{w}(\mathbf M, \mathbf X)\in \mathbb R^{m\times d}$$
  * $$\mathbf O =\[\mathbf M\_1, \mathbf Y\_1] \mathbf W \in \mathbb R^{m\times d}$$

备注，这里省略了ffn部分，其中$$\mathbf M$$的ffn为rnn。

整体结构：

![](https://2520240655-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Fb2lKDIgZ0I1cirExLedu%2Fuploads%2Fgit-blob-2d2fdd6915ff703e4f9390da8de7e2d5714a5863%2F1.jpg?alt=media)

## 时间复杂度

$$O((n+m)wd)$$。

## 训练以及loss

不变。

## 代码

* <https://github.com/dashstander/block-recurrent-transformer>

## 实验以及适用场景

论文测试了lm，效果还不错。

## 细节

暂无。

## 简评

依然是一个空间换性能的方法。


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