Implement the forward and backward passes for fully-connected deep neural networks as in the image below. Use all MNIST training data to learn a 10-class classifier using your own back-propagation implementation, investigate various network structures (such as different number of layers and nodes per layer), and report the best possible classification performance in the held-out MNIST test images. Note that you are only allowed to use libraries for linear algebra operations, such as matrix multiplication, matrix inversion, and etc. You are not allowed to use any existing machine learning or statistics toolkits or libraries or any open-source code for this question. Use the MNIST data set for this question.

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