Consider the following neural network: do w w? a1 az w w2 a3 W w3 W...

 

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Consider the following neural network: do w w? a1 az w w2 a3 W w3 W a4 This is not a standard neural network as its neurons are not fully connected. The connection situation is shown in the figure above. The neural network does not contain bias in the forward propagation so that a = ;w}zj, z = fi(a) for i = 1,2,3,4. In the network, zo = ao (an input neuron), f3(x) = relu(x), and f(x)=f (x) = f4(x) = sigmoid(x). relu(x) corresponds to a rectified linear unit transfer function defined as: relu(x) = max {0, x}. The cost function is defined as J(w) = (Z y). We consider a single data sample x = 1.0 and the corresponding label y = 0.1. Use the training data to develop the neural network model and solve it by using gradient descent algorithm with an initial setting: w[0] = [w, w, w, w2, w, w, w3] = [0.3, 0, 0.5, 0.4, 1.0, 0.8, 0], and n = 0.01. a) Write a function F to simulate the neural network. [5 marks] b) Compute the values of w3[1], wi[1], w [1] after the first iteration. [15 marks] Consider the following neural network: do w w? a1 az w w2 a3 W w3 W a4 This is not a standard neural network as its neurons are not fully connected. The connection situation is shown in the figure above. The neural network does not contain bias in the forward propagation so that a = ;w}zj, z = fi(a) for i = 1,2,3,4. In the network, zo = ao (an input neuron), f3(x) = relu(x), and f(x)=f (x) = f4(x) = sigmoid(x). relu(x) corresponds to a rectified linear unit transfer function defined as: relu(x) = max {0, x}. The cost function is defined as J(w) = (Z y). We consider a single data sample x = 1.0 and the corresponding label y = 0.1. Use the training data to develop the neural network model and solve it by using gradient descent algorithm with an initial setting: w[0] = [w, w, w, w2, w, w, w3] = [0.3, 0, 0.5, 0.4, 1.0, 0.8, 0], and n = 0.01. a) Write a function F to simulate the neural network. [5 marks] b) Compute the values of w3[1], wi[1], w [1] after the first iteration. [15 marks]