[Solved] EE599 Homework 2-Caracter recognition using a trained MLPh

1 Caracter recognition using a trained MLPh

The purpose of this problem is to have you program, using numpy, the feedforward processing for a multilayerperceptron (MLP) deep neural network. This processing is dened on slide 33 of the introduction lectureslides. The grading of this homework will give you feedback on your FF program which is valuable since ina future homework, you will be building on this to program the back-propagation as well.The MNIST dataset of handwritten digits is widely used as a beginner dataset for benchmarking machinelearning classiers. It has 784 input features (pixel values in each image) and 10 output classes representingnumbers 0{9. We have trained a MLP on MNIST, with a 784-neuron input layer, 2 hidden layers of 200 and100 neurons, and a 10-neuron output layer. The activation functions used are ReLU for the hidden layersand softmax for the output layer.(a) Extract the weights and biases of the trained network from mnist_network_params.hdf5. The lehas 6 keys corresponding to numpy arrays W1, b1, W2, b2, W3, b3. You may want to check theirdimensions by using the `shape attribute of a numpy array.(b) The le mnist_testdata.hdf5 contains 10,000 images in the key `xdata and their corresponding labelsin the key `ydata. Extract these. Note that each image is 784-dimensional and each label is one-hot10-dimensional. So if the label for an image is [0; 0; 0; 1; 0; 0; 0; 0; 0; 0], it means the image depicts a 3.(c) Write functions for calculating ReLU and softmax. These are given as:ReLU(x) = max (0; x)Softmax(x) =

ex1Pni=1 exi;ex2Pni=1 exi; ;exnPni=1 exn

. Note that the softmax function oper-ates on a vector of size n and returns another vector of size n which is a probability distribution.For example, Softmax ([0; 1; 2]) = [0:09; 0:24; 0:67]. This indicates that the 3rd element is the mostlikely outcome. For the MNIST case, n = 10.(d) Using numpy, program a MLP that takes a 784-dimensional input image and calculates its 10-dimensionaloutput. Use ReLU activation for the 2 hidden layers and softmax for the output layer.(e) Compare the output with the true label from `ydata. The input is correctly classied if the positionof the maximum element in the MLP output matches with the position of the 1 in ydata. Find thetotal number of correctly classied images in the whole set of 10,000. You should get 9790 correct.(f) Sample some cases with correct classication and some with incorrect classication. Visually inspectthem. For those that are incorrect, is the correct class obvious to you? You can use matplotlib forvisualization:1c K.M. Chugg, B. Franzke February 8, 2020{ EE599 Deep Learning 2hn <latexit sha1_base64=(null)>(null)</latexit><latexit>xn <latexit sha1_base64=(null)>(null)</latexit><latexit> yn <latexit sha1_base64=(null)>(null)</latexit><latexit>qn <latexit sha1_base64=(null)>(null)</latexit><latexit>zn <latexit sha1_base64=(null)>(null)</latexit><latexit>xn <latexit sha1_base64=(null)>(null)</latexit><latexit>wn <latexit sha1_base64=(null)>(null)</latexit><latexit>yn <latexit sha1_base64=(null)>(null)</latexit><latexit>wn+1 = wn + (yn wtnxn)xnyn =LX