Pytorch Learning

This repo contains my learnings for pytorch.

Examples

The bare minimum hello world for pytorch.

poetry run src/pytorch-hello.py

Train a simple feed forward neural network for fashionMNIST.

poetry run src/fashion-mnist.py

Formula	Description
$Q$	The Query
$K$	The Key
$V$	The Value
$\text{Attention}(Q, K, V) = \text{softmax}({\Large QK^T \over \sqrt{d_k}})V$	The self attention function, known as scaled dot-product attention
$x^{(i)}$	An embedded input
$W_q, W_k, W_v$	Weight queries, used to train the attention.
$T$	The number of embedded input vectors
$d$	The length of a single word embedding vector
$q_i = W_qx \text{ for } i \in [1, T]$
$k_i = W_kx \text{ for } i \in [1, T]$
$v_i = W_vx \text{ for } i \in [1, T]$
$q^{(i)}$ and $k^{(i)}$	Vectors of dimension $d_k$

$$ \mathbf{QK}^T =

\begin{bmatrix}

e_{11} & e_{12} & \dots & e_{1n} \

e_{21} & e_{22} & \dots & e_{2n} \

\vdots & \vdots & \ddots & \vdots \

e_{m1} & e_{m2} & \dots & e_{mn} \

\end{bmatrix} $$

$$ \frac{\mathbf{QK}^T}{\sqrt{d_k}} =

\begin{bmatrix}

\tfrac{e_{11}}{\sqrt{d_k}} & \tfrac{e_{12}}{\sqrt{d_k}} & \dots & \tfrac{e_{1n}}{\sqrt{d_k}} \

\tfrac{e_{21}}{\sqrt{d_k}} & \tfrac{e_{22}}{\sqrt{d_k}} & \dots & \tfrac{e_{2n}}{\sqrt{d_k}} \

\vdots & \vdots & \ddots & \vdots \

\tfrac{e_{m1}}{\sqrt{d_k}} & \tfrac{e_{m2}}{\sqrt{d_k}} & \dots & \tfrac{e_{mn}}{\sqrt{d_k}} \

\end{bmatrix} $$

$$ \text{softmax} \left( \frac{\mathbf{QK}^T}{\sqrt{d_k}} \right) =

\begin{bmatrix}

\text{softmax} ( \tfrac{e_{11}}{\sqrt{d_k}} & \tfrac{e_{12}}{\sqrt{d_k}} & \dots & \tfrac{e_{1n}}{\sqrt{d_k}} ) \

\text{softmax} ( \tfrac{e_{21}}{\sqrt{d_k}} & \tfrac{e_{22}}{\sqrt{d_k}} & \dots & \tfrac{e_{2n}}{\sqrt{d_k}} ) \

\vdots & \vdots & \ddots & \vdots \

\text{softmax} ( \tfrac{e_{m1}}{\sqrt{d_k}} & \tfrac{e_{m2}}{\sqrt{d_k}} & \dots & \tfrac{e_{mn}}{\sqrt{d_k}} ) \

\end{bmatrix} $$