Q1. Consider the neural network in Figure 25.13. Let bias values be fixed at 0, and let the weight matrices between the input and hidden, and hidden and output layers, respectively, be: W = (w1, w2, w3) = (1, 1, –1) W = (w , w̟, wɔ" = (0.5, 1,2)" %3D Assume that the hidden layer uses ReLU, whereas the output layer uses sigmoid activation. Assume SSE error. Answer the following questions, when the input is x = 4 and the true response is y =0: 22 ws 23 Figure 25.13. Neural network for Q1. (a) Use forward propagation to compute the predicted output. (b) What is the loss or error value? (c) Compute the net gradient vector 8º for the output layer. (d) Compute the net gradient vector 8 for the hidden layer.

Q1. Consider the neural network in Figure 25.13. Let bias values be fixed at 0, and let the weight matrices between the input and hidden, and hidden and output layers, respectively, be: W = (w1, w2, w3) = (1, 1, –1) W = (w , w̟, wɔ" = (0.5, 1,2)" %3D Assume that the hidden layer uses ReLU, whereas the output layer uses sigmoid activation. Assume SSE error. Answer the following questions, when the input is x = 4 and the true response is y =0: 22 ws 23 Figure 25.13. Neural network for Q1. (a) Use forward propagation to compute the predicted output. (b) What is the loss or error value? (c) Compute the net gradient vector 8º for the output layer. (d) Compute the net gradient vector 8 for the hidden layer.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter20: Queuing Theory

Section20.10: Exponential Queues In Series And Open Queuing Networks

Problem 6P

See similar textbooks

Similar questions

(i). Consider a 3-layer perceptron neural network consisting of 1 input neuron, 2hidden neurons with sigmoid activation functions, and 1 output neuron with linearactivation function. Assuming v1 and v2 represent the connection weights fromthe hidden neurons to the output neuron, v0 represents the bias for the outputneuron, w11 and w21 represent the connection weights from the input neuron tothe hidden neurons, and w10 and w20 represent the biases for the 2 hiddenneurons. Let x represent the input to the neural network and y represent the outputfrom the neural network.Suppose the vector of neural network weights is:w = [v0 v1 v2 w10 w11 w20 w21]T = [0 0.1 0.5 0 -1 1 0.2]T. Calculate the output y if input x = 0. Calculate y again for x = 1. (ii). For the same neural network as in (1), calculate the derivative of y with respect the neural network weight parameters v0, v1, v2 , w10 , w11 , w20, and w21 for x = 0. Calculate the derivatives again for x = 1.
Consider a fully-connected artificial neural network with one hidden layer, i.e., a multilayer perceptron (MLP), which has 5 inputs, 3 neurons in the hidden layer, and 1 output neuron. The relation between the output y and the inputs x = [x1, . . . , x5] is given by y(x) = f (w, φ(x)), where φ(x) = [φ1(x), φ2(x), φ3(x)] 1. Draw the diagram that shows the inputs, nuerons, connections, correspond-ing weight parameters, and activation functions. 2. Explain the relation y(x) = f (w, φ(x)): write the explicit relation, explainthe role of functions f and φ(x), and state examples of functions.
Give an example of how a neural network with a large number of layers could present a problem.In the next paragraphs, discuss overfitting and how to avoid it.
Draw a feed forward neural network with 3 input neurons, 1 hidden layer including 2 neurons and 2 output neurons. Consider all the weights as -1 and thresholds 0. Run your network to find the output for the vector [1 -1 1]. Use activation function as hard limiter.
Find the total number Q of tunable parameters in a general L-hidden-layer neural network, in terms of variables expressed in the layer sizes below 1 layer_sizes= [N, U_1, ., U_L, C] (b) Based on your answer in part (a), explain how the input dimension N and number of data points P each contributes to Q. How is this different from kernel methods
using python and neural networks. where/how here can i add a for loop to test having 1 to 100 neurons in one single hindden layer? acti = ['logistic', 'tanh', 'relu', 'identity'] neural = MLPClassifier(activation=acti[0], solver='lbfgs', max_iter=200, hidden_layer_sizes=(6))
Define the neural network a fully connected network with two hidden layers with Nh1 and Nh2 features, respectively. The hidden layers should use relu activation and the final layer should not have any activation. a linear network with no hidden layer. We will use this network to study the benefit of depth, or equivalently using a non-linear network instead of a linear network. The final layer should not have any activation class NeuralNet(N.Module): # YOUR CODE HERE class LinearNet(N.Module): #YOUR CODE HERE
Two layers neural networks consist of 3 input neurons and one output neuron. The input vector is (x1, x2, x3) where x3 is always =1.0. x1, x2 and the desired output d are given by the table below. When using the initial weight vector w = (1.0, 1.0, -3.0) there was an error as shown in the figure. The equation for the decision boundary was: x1*1 + x2*1 - 1*3=0. , (i.e. net = x1*w1+x2*w2+x3*w3), f(net) is the sign of net What are the new values of the vector w after the first input (1,1,1), note that input x3 is always 1.0? What are the new values of the vector w after the second input (9.4, 6.4, 1.0)? Suggest a vector w such that the total error is ZERO for the 10 points.
giving the following weight matrix for a vector quantization neural network: w = [ 0.6000 0.6300 0.8000 0.5000 1.0000 -0.7000] and given the following input x= [0.3 , 0.5] decide the winning node and hence update the weight matrix given a training rate of 0.1
Draw a geed forward neural network with 3 input neurons, 1 hidden layer including 3 neurons and 1 output neuron. Consider all the weights as -1 and thresholds 0. Find output for vector [1 -1 1 ]
Given the flowing neural network, each circle represents a neuron whose thresholdvalue is recorded inside the circle. The lines connecting the circles represent connectionsbetween neurons. Two connected neurons associate the same weight which is recordednext to the line connecting the neurons. What is the output when both inputs are 1s?
Give an example of a difficulty that develops when a neural network has several layers.Discuss overfitting and how to prevent it in the following paragraphs.