Consider a multilayer perceptron $($MLP$)$ with two inputs and one output, f : R$2->$ R$,$ that seeks to approximate multiplication of two real numbers, i$.$e$.$ f $($x$,$ y$)$ x $$ y$.$

$($a$)$ Using only linear $($fully connected$)$ and ReLU layers, implement an MLP for

this task in PyTorch.

$($b$)$ Create an appropriate training loop to train the network on random data using a loss function of your choice. You should explicitly comment on what assumptions you are making about the range of the training data.

$($c$)$ Evaluate the network in terms of the absolute error in its prediction,

i$.$e$.|$ f $($x$,$ y$)($x $$ y$)|.$ You should report a mean error over random samples within the range of the training data but also a generalisation error when tested on inputs outside the range of the training data.