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# Attention without RNN

## Attention Layer: Attention without RNN

Compared with Simple RNN + Attention, it's not using hidden states from RNN to compute Key, Value, Query parameters.

* We study Seq2Seq model (encoder + decoder).
* Encoder’s inputs are vectors $$x\_1,x\_2,...,x\_m$$.
* Decoder’s inputs are vectors $$x'\_1,x'\_2,...,x'\_t$$.
* Keys and values are based on encoder’s inputs $$x\_1,x\_2,...,x\_m$$.
  * Key: $$k\_{:i}=W\_K x\_i$$
  * Value: $$v\_{:i}=W\_V x\_i$$
* Queries are based on decoder’s inputs $$x'\_1,x'\_2,...,x'\_t$$
* Query: $$q\_{:j}=W\_Q x'\_j$$

![](/files/15mhpUl4aT0DBMNsoW4t)

* Compute weights: $$\alpha\_{:j}=Softmax(K^T q\_{:j}) \in R^m$$

![](/files/sOFnavZcI1gSowoPdJLx)

* Context vector: $$c\_j=\alpha\_{ij} v\_{:1} + ... +\alpha\_{mj} v\_{:m}=V \alpha\_{:j}$$
  * Thus, $$c\_{:j}$$is a function of $$x'\_j$$and $$\[x\_1,...x\_m]$$

![](/files/rF6cbMjvJ0DcfD7pSQDE)

* Output of attention layer: $$C=\[c\_{:1}, c\_{:2},c\_{:3},...,c\_{:t}]$$

### Attention layer summary

* Attention layer: $$C=Attn(X,X')$$
  * Encoder's inputs: $$X=\[x\_1, x\_2,...,x\_m]$$
  * Decoder's inputs: $$X'=\[x'\_1,x'\_2,...,x'\_t]$$
  * Parameters: $$W\_Q,W\_K, W\_V$$

![](/files/dsEGA8UbMU0eYr1xHHIA)

### Self-Attention layer summary

* Self-Attention layer: $$C=Attn(X,X)$$
  * Inputs: $$X=\[x\_1, x\_2,...,x\_m]$$
  * Parameters: $$W\_Q,W\_K, W\_V$$

![](/files/ZZaGnxfYaKFgqqucV3Td)

## Summary

* Attention was originally developed for Seq2Seq RNN models \[1].
* Self-attention: attention for all the RNN models (not necessarily Seq2Seq models \[2].
* Attention can be used without RNN \[3].
* We learned how to build attention layer and self-attention layer.

## Reference

* Original paper: Vaswani et al. Attention Is All You Need. In NIPS, 2017.
* [youtube](https://www.youtube.com/watch?v=aButdUV0dxI\&t=1s)


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