This challenge task is quite difficult and will really test your mastery of PyTorch and nn$.$Linear layers.

We can manually assign weights to an nn$.$Linear like this:

import torch

import torch.nn as nn

lin $=$ nn$.$Linear$(10,20)$

manual$\_$weights $=$ torch.arange$(20*10).$reshape$($lin$.$weight.shape$)$

lin.weight.data$[$:$]=$ manual$\_$weights

lin.bias.data$[$:$]=0$

But this does not calculate anything useful. A Linear layer simply performs a weighted sum $($plus bias$).$ We can choose weights$/$biases to perform known operations.

INSTRUCTIONS:

Given an nn$.$Linear$(1,1)$ layer, set the weights such that the layer adds $1$ to it's input.

Given an nn$.$Linear$(1,1)$ layer, set the weights such that the layer calculates y $=3$x $+2.$

Given an nn$.$Linear$(4,1)$ layer, set the weights such that the layer calculates the average of it's inputs.

Given an nn$.$Linear$(4,2)$ layer, set the weights such that the layer calculates both the average of it's inputs and the sum of the inputs.

Given an nn$.$Linear$(3,3)$ layer, set the weights such that the layer returns the inputs, but in reverse order.

Given an nn$.$Linear$(5,2)$ layer, set the weights such that the layer always returns $(4,2)$

Note: We would never use this in a deep learning model; this challenge is to prove that you understand the mathematics and coding mechanics of the nn$.$Linear layer.

import sc$1$

sc$1.$test$\_1($sc$1.$modify$\_$lin$\_1)$

sc$1.$test$\_2($sc$1.$modify$\_$lin$\_2)$

sc$1.$test$\_3($sc$1.$modify$\_$lin$\_3)$

sc$1.$test$\_4($sc$1.$modify$\_$lin$\_4)$

sc$1.$test$\_5($sc$1.$modify$\_$lin$\_5)$

sc$1.$test$\_6($sc$1.$modify$\_$lin$\_6)$

give me the correct output and explain what is this sc$1$ and where and why are we using