Description
Problem 1 (10 points)
We want to build an MLP that composes the decision boundary shown in the figure below. The
output of the MLP must 1 in the yellow regions and 0 elsewhere
The MLP we design is suboptimal and has the structure and weights shown in the figure
below, where each perceptron computes the function.
� = $
1 �� (����ℎ�.. �����. + ����.
.
≥ 0
0 ����
Problem 2 (10 points)
We are given the relationship
� = �(�, �(�, �))�(�, �(�, �))
Where x is a vector. �(.) and �(.) are both scalar functions which take a vector and a scalar as
inputs. What is ��
��?
Note that the relationship between x, f(.) and g(.) is presented as following figure and we use dx
for full derivate and ¶x for partial derivative
Problem 3 (40 points)
Manually design MLP network to perform the XOR Gate with the truth table and its plot on 2D
as follows:
The goal of the neural network is to classify the input patterns according to the above truth table.
As mentioned in the class, the network is designed in similar following architecture
Where:
inputs = ([[0,0],[0,1],[1,0],[1,1]])
expected_output ([[0],[1],[1],[0]])
Start with uniform random initialization for parameters wij . Perform forward and backward pass in
the following case:
1. Activation function is (a) Sigmod (b) ReLu, (c)Tanh
2. Divergence is defined as (a) L2_norm, (b) cross entropy
3. Train the network for 2 iterations (3 forward pass and 2 backward pass)
Please report the parameters and actual output from the MLP in each iteration
Problem 4 (40 points)
Building a MLP with one hidden layer to perform classification task with the following
description:
+ Training data (X, Y):
Training data contains N1 = 10,000 points in 2-dimentional space and are followed by the
uniform radius between 0 and 2 and its label is 1 is it is inside the yellow circle, otherwise it is 0
+ Validation data (X, Y):
Validation data contains N2 = 2,000 points in 2-dimentional space and are followed by
the uniform radius between 0 and 2 and its label is 1 is it is inside the yellow circle, otherwise it is
0
+ Testing data (X, Y):
Testing data contains N2 = 2,000 points in 2-dimentional space and are followed by the
uniform radius between 0 and 2 and its label is 1 is it is inside the yellow circle, otherwise it is 0
Assume that we use CrossEntropyLoss (nn. CrossEntropyLoss) and
GradientDescent(torch.optim.SGD) with lr = 0.01
Report the training loss, validation loss, testing accuracy (in number and visualized by figure) in
the following case
+ Train the MLP with 10 iterations
+ Train the MLP with 100 iterations
+ Train the MLP with 1000 iterations
Note: use import matplotlib.pyplot to plot figures
