MLP neural network has a layer dimensions 2x2x1 dimensions.
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- 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, ws, w" = (0.5, 1,2)" 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: 21 2 w3 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 8° for the output layer. (d) Compute the net gradient vector 8* for the hidden layer.Computer Science A neural network of 2 convolutional layers each with 16 filters, kernel size = 2, stride = 1, and valid padding, suppose the shape of a single input image is (3, 32, 32) (channels, height, width). What will be the shape of the output of this network?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
- The following figure is a diagram of a small convolutional neural network that converts a 16x16 image into 4 output values (16x16 - 4x12x12 → 4x6x6 6x1). The network has the following layers/operations from input to output: convolution with 4 filters, max pooling, ReLu (after pooling), and finally a fully-connected layer (with no hidden layer). For this network we will not be using any bias/offset parameters. Please answer the following questions about this network. 16x16 Convolution 4 filters 5x5 Stride 1 4@12x12 max pooling 2x2 Stride 2 4@6x6 6x1 fully- connectedWe consider a neural network with 100 neurons in the input layer and 10 neurons in the hidden layer and these two layers are fully connected between, how many weight parameters do we have between these two layers?Consider a convolutional neural network which takes as input a 50-by-50 black-and-white image. The first convolutional layer uses 12 filters that are 7-by-7, with stride 3 and zero padding of width 1. Compute the width of this layer. Answer:
- Consider a convolutional neural network which takes as input a 42-by-54 color image (i.e. with three channels R, G, B). The first convolutional layer has 16 filters that are 6-by-6, with stride 2 and no zero-padding. Compute the number of: * weights per filter in this layer (including bias): * neurons in this layer: * connections into the neurons in this layer: * independent parameters in this layer: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.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 ]
- 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.The cost function of a general neural network is defined as J(ŷ,y) = m // [4 (9(0), y(1) The loss function L(ŷ), y() is defined by the logistic loss function Ly, y) = [ylogy) + (1-y)log (1 - ¹)] Please list the stochastic gradient descent update rule, batch gradient descent update rule, and mini-batch gradient descent update rule. Explain the main difference of these three update rules.Consider a general neural network with K − 1 hidden layers (K weight matrices). All input units, output units, and hidden units have a dimension of D. Assume we have N input vectors. How many scalar multiplications do we need to compute the forward pass? Also, draw the network.