The train$(...)$ function will implement batch qradient descent to train the model.

Use PyTorch autograd to estimate gradients and update parameters during gradient descent.

def train$($model$,x,y,$ num$\_$epochs$=20,$ learning$\_$rate$=0\mathrm{.}1,$ seed$=1,$ log$=$False$)$:

$cost=[]$

torch.manual$\_$seed$($seed$)$

for ii in range$($num$\_$epochs$)$:

## Forward Propagation and loss ##

### BEGIN SOLUTION ###

$=$

### END SOLUTION ###

## Compute gradient and update parameters ##

## The grad$(.)$ function gets the gradients of the loss w$.$r$.$t parameters in a list

## The output gradients is a list of corresponding parameter gradients

gradients $=$ grad$(105$s$,$ list$($model$.$parameters.values$()))$

## Whenever a parameter changes during an operation,

## a graph is maintained to estimate the gradient

## PyTorch does not allow to modify such

## parameters in place $($for e$.$g$.$ assigning an arbitrary value to the parameter$)$

## Becasue such operations will not be able to estimate the gradient

## We therefore turn$-$off the gradient during parameter update

with torch.no$\_$grad$()$:

for ly in range$($model$.$num$\_$layers$)$:

## Access the gradients list to get $dw$ and $db$

## and update parameters using $-$learing$\_$ratedb

## For e$.$g$.$

## gradients $[0]$ is the gradient for W$1$

## gradients$[1]$ is the gradient for b$1$

## gradients$[2]$ is the gradient for W$2$

## gradients$[3]$ is the gradient for b$2$

## gradients$[2*1$y$]$ is the gradient for $w(1y+1)$

## gradients $2**1y+1$ is the gradient for $b(1y+1)$

### BEGIN SOLUTION ###

### END SOLUTION ###

## Print loss every epoch ##

## We do not need to track gradient during the evaluation

cost$.$append $($loss$.$detach$())$

if not ii$\%20$:

print$(\text{'}$Epoch: $\%02$d $|$ Loss: $\%\mathrm{.}5$f$\text{'}\%(($ii$+1),1055))$