# A Dot Product Attention Free Transformer

### A Dot Product Attention Free Transformer

论文地址：

* <https://openreview.net/forum?id=JVR4JswsEM>

### 整体思路以及计算方式

利用点乘的方式计算Attention：

* 输入：$$\mathbf Q, \mathbf K, \mathbf V\in \mathbb R^{n\times d}, \mathbf p\_1,\mathbf p\_2\in \mathbb R^{n\times d\_1}$$
* 计算$$\mathbf W= \mathbf p\_1\mathbf p\_2 ^\top \in \mathbb R^{n\times n}$$
* 输出：

  $$
  \mathbf o\_{i}=\sigma\_{q}\left(\mathbf q\_{i}\right) \odot \frac {\sum\_{j=1}^{n} \exp \left(\mathbf k\_{j}+w\_{i,j}\right) \odot \mathbf v\_{j}} {\sum\_{j=1}^{n} \exp \left(\mathbf k\_{j}+w\_{i,j}\right)}
  $$

### 时间复杂度

$$O(d^2n + n^2d\_1)$$

### 训练以及loss

不变。

### 代码

暂无，但是论文里有伪代码。

### 实验以及适用场景

Encoder和Decoder情形都进行了实验，总体来说效果还不错。

### 细节

因为没有计算Attention matrix，所以token之间的交互是通过$$\mathbf W$$矩阵。

### 简评

挺好的一个思路，可以考虑复现。


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