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$\_6)$

sc$1.$py script:

import torch

import torch.nn as nn

# $====$ Put your solutions here $====$

# Each function receives an nn$.$Linear.

# Hint #$1$: Make sure you print out the shape of the weights

# Hint #$2$: You can fill multiple weights at once by assigning

# the weights to a tensor. e$.$g$.$

# lin.weight.data$[$:$]=$ torch.tensor$([$

# $[1,0],$

# $[0,1],$

# $],$ dtype$=$lin.weight.dtype, device$=$lin.weight.device$)$

# $====$ Testing code: Tests your solutions $====$

def test$\_1($fnc$)$:

inp $=$ torch.tensor$([1.,5,11,20,21]).$reshape$([-1,1])$

tar $=$ torch.tensor$([2.,6,12,21,22]).$reshape$([-1,1])$

layer $=$ nn$.$Linear$(1,1)$

fnc$($layer$)$

out $=$ layer$($inp$)$

torch.allclose$($out$,$ tar$)$

def test$\_2($fnc$)$:

inp $=$ torch.tensor$([1.,5,11,20,21]).$reshape$([-1,1])$

tar $=$ torch.tensor$([5.,17,35,62,65]).$reshape$([-1,1])$

layer $=$ nn$.$Linear$(1,1)$

fnc$($layer$)$

out $=$ layer$($inp$)$

torch.allclose$($out$,$ tar$)$

def test$\_3($fnc$)$:

inp $=$ torch.tensor$([$

$[1.,1,1,1],$

$[5,10,15,20],$

$[11,20,21,25]$

$])$

tar $=$ inp.mean$($dim$=1,$ keepdim$=$True$)$

layer $=$ nn$.$Linear$(4,1)$

fnc$($layer$)$

out $=$ layer$($inp$)$

torch.allclose$($out$,$ tar$)$

def test$\_4($fnc$)$:

inp $=$ torch.tensor$([$

$[1.,1,1,1],$

$[5,10,15,20],$

$[11,20,21,25]$

$])$

tar $=$ torch.stack$([$

inp.mean$($dim$=1),$

inp.sum$($dim$=1)$

$],$ dim$=1)$

layer $=$ nn$.$Linear$(4,2)$

fnc$($layer$)$

out $=$ layer$($inp$)$

torch.allclose$($out$,$ tar$)$

def test$\_5($fnc$)$:

inp $=$ torch.tensor$([$

$[1.,1,1],$

$[5,10,15],$

$[11,20,21],$

$[4,12,2],$

$[6,5,4],$

$])$

tar $=$ torch.tensor$([$

$[1.,1,1],$

$[15,10,5],$

$[21,20,11],$

$[2,12,4],$

$[4,5,6],$

$])$

layer $=$ nn$.$Linear$(3,3)$

fnc$($layer$)$

out $=$ layer$($inp$)$

torch.allclose$($out$,$ tar$)$

def test$\_6($fnc$)$:

inp $=$ torch.tensor$([$

$[1.,2,3,4,5],$

$[1$e$5,2$e$10,3$e$15,4$e$20,5$e$25],$

$[-150,150,15,-15,0\mathrm{.}1]$

$])$

tar $=$ torch.tensor$([$

$[4.,2],$

$[4,2],$

$[4,2],$

$])$

layer $=$ nn$.$Linear$(5,2)$

fnc$($layer$)$

out $=$ layer$($inp$)$

torch.allclose$($out$,$ tar$)$