### Task $2\mathrm{.}2-$ Backward propagation

In this task, you will start with random weights for $`$w$0`$ and $`$w$1`,$ and iteratively perform forward passes and backward propagation multiple times to converge on a solution.

Submit your values of $`$w$0`,`$w$1`,$ and $`$loss$`$ value onto Coursemology. Your $`$loss$`$ value should be less than $1.$

torch.manual$\_$seed$(1)$ # Set seed to some fixed value

w$0=$ torch.randn$(2,2,$ requires$\_$grad$=$True$)$

w$1=$ torch.randn$(3,1,$ requires$\_$grad$=$True$)$

learning$\_$rate $=1$e$-3$

print$(\text{'}$iter$\text{'},$ 'loss', $\text{'}$

$----\text{'},\text{'}----\text{'},$ sep$=\text{'}\backslash$t$\text{'})$

for t in range$(1,10001)$:

# Forward pass: compute predicted y

y$\_$pred $=$ forward$\_$pass$($x$,$ w$0,$ w$1,$ torch.relu$)$

loss $=$ torch.mean$($torch$.$square$($y $-$ y$\_$pred$))$

loss.backward$()$

if t $\%1000==0$:

print$($t$,$ loss.item$(),$ sep$=\text{'}\backslash$t$\text{'})$

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

# Update weights and then reset the gradients to zero

raise NotImplementedError

print$("---$ w$0---",$ w$0,$ sep$=\text{'}$

$\text{'})$

print$("---$ w$1---",$ w$1,$ sep$=\text{'}$

$\text{'})$

y$\_$pred $=$ forward$\_$pass$($x$,$ w$0,$ w$1,$ torch.relu$)$

plt$.$plot$($x$,$ y$,$ linestyle$=$'solid', label$=\text{'}|$x$-1|\text{'})$

plt$.$plot$($x$,$ y$\_$pred.detach$().$numpy$(),$ linestyle$=$'dashed', label$=$'perceptron'$)$

plt$.$axis$(\text{'}$equal$\text{'})$

plt$.$title$(\text{'}$Fit NN on abs function'$)$

plt$.$legend$()$

plt$.$show$()$

# Task $5$: Submit the values of $`$w$0`,`$w$1`,$ and $`$loss$`$ values after fitting

# Note: An acceptable loss value should be less than $1\mathrm{.}0$

# You should try adjusting the random seed, learning rate, or

# number of iterations to improve your model.

w$0=[[0\mathrm{.}0,0\mathrm{.}0],[0\mathrm{.}0,0\mathrm{.}0]]$ # to be computed

w$1=[[0\mathrm{.}0],[0\mathrm{.}0],[0\mathrm{.}0]]$ # to be computed

loss $=0\mathrm{.}0$ # to be computed

w$0=$ torch.tensor$($w$0)$

w$1=$ torch.tensor$($w$1)$

x $=$ torch.linspace$(-10,10,1000).$reshape$(-1,1)$

y $=$ torch.abs$($x$-1)$

#IMPORTANT: Your forward pass above have to be correctly implemented

y$\_$pred $=$ forward$\_$pass$($x$,$ w$0,$ w$1,$ torch.relu$)$

computed$\_$mse$\_$loss $=$ torch.mean$($torch$.$square$($y $-$ y$\_$pred$)).$item$()$

assert loss $<1$

assert isclose$($computed$\_$mse$\_$loss, loss, atol$=1$e$-5,$ rtol$=1$e$-2)$