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experiment with a simple two variable function and see for what combinations of layers number of latent variables in each layer

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

1.    preferred way: Upload a single Python notebook .ipynb type. In the notebook, theoretical or written answers should be in the from of mark- down cell. And Python code in the code format. The grader should be able to run your code from the web browser and Jupyterlab without problem.

2.    Submit two files. A pdf file answering theoretical and written questions. This file can wither be either typeset or can be handwritten, and then scanned using apps such as CamScan. If  you  are  scanning  make  sure your file is in pdf format and legible. The second file should contain your Python scripts and be in the .py form. The grader should be able to copy and paste your file and run it without any problem.

1.    keras/Python Project:  In  this  project,  you  are  going  to  experiment with a simple, two-variable function, and see for what combinations of layers, number of latent variables in each layer, and size of data can get reasonably close to learning them.

R. We define the follow-

Suppose f(x, y) is a function from [0, 1] × [0, 1] →

ing classification problem: A point (x1, x2) is  “orange” if f(x1, x2) ≤ 0,

and “blue” if f(x1, x2) > 0. For instance, if

f(x1, x2) = (0.5 x2 y2)(1 x2 y2)(2 x2 y2)(4 x2 y2)(9 x2 y2)

then the true color classes look like the left diagram below. If we select a number of randomly chosen points in the range (x1, x2) ∈ [0, 1] ×[0, 1] and then plug their x1, x2 values in f( , ), we can color these points orange or blue, according to whether the value of f( , ) is positive or negative. A sample is shown in the graph on the right below.

 

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