Goals. The goal of this exercise is to
• familiarize yourself with the theory related to SVD.
• have time to discuss Project 2 with the assistants and teammates.
1 Theory Questions
Problem 1 (How to compute U and S efficiently):
In class, we saw that solving the eigenvector/value problem for the matrix XX⊤ gives us a way to compute U and S. But in some instances D≫N. In those cases, is there a way to accomplish this computation more efficiently?
Problem 2 (Positive semi-definite):
Show that if X is a N×N symmetric matrix then the SVD has the form USU⊤, where U is a N×N unitary matrix and S is a N×N diagonal matrix with non-necessarily positive entries. Show that if X is positive semi-definite, then all entries of S are non-negative.
2 Generative Adversarial Networks
Recommended reading: explore how to implement a simple GAN in PyTorch using the Jupyter notebook gans.ipynb:
• Open in Colab: colab.research.google.com/github/epfml/ML course/blob/master/labs/ex12/template/gans.ipynb.
This gives you access to a free GPU.
• Change the ‘runtime type’ to GPU under ‘Runtime → Change runtime type’.
