The purpose of this homework is to allow you to obtain deeper understanding of the underlying working mechanisms and theory behind neural networks. The homework consists of a series of tasks which allow you to understand, develop or re-implement some of the features of the neural networks.
__Task 1:__
Read and fully understand the article Nothing but NumPy: Understanding & Creating Neural Networks with Computational Graphs from Scratch [Link](https://www.kdnuggets.com/2019/08/numpy-neural-networks-computational-graphs.html). If you have not programmed in Python before, please type yourself all the code provided at the end of the article. This will help you get a feel of Python programming and help you understand what is going on. (Even if you programmed in Python before I strongly recommend you do not skip this step.)
__Task 2:__
Get the program from Task 1 to work on the MNIST database [Link](http://yann.lecun.com/exdb/mnist/). Evaluate the performance (classification error) of your program in comparison to others [Link](https://rodrigob.github.io/are_we_there_yet/build/classification_datasets_results.html). Use minimum 3 internal layers with minimum 20 activation nodes in each internal layer.
Save your program and the corresponding results as the version 1 (V1).
__Task 3:__
Change the following in your program:
Replace batch gradient descent with mini-batch gradient descent [Link](http://cs231n.github.io/optimization-1/#gd) to train the network. Re-run your program on the MNIST dataset and compare the performance (execution speed due to mini-batch change and the classification error). Save this program as version 2 (V2).
Change the activation function to another based on your choice [Link](https://en.wikipedia.org/wiki/Activation_function). Note that changing the activation function will require you to change backpropagation derivatives. Re-run your program on the MNIST dataset and compare the performance (execution speed due to the activation function change and the classification error). Save this program as version 3 (V3).
__Task 4:__
Summarize and explain the observed performance changes in all 3 versions of your program in a short presentation (not more than 10 slides).
