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F21BC: Explain the Role of Activation Functions in Neural Networks - IT Assignment Help
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Assignment Task:
Explain the role of activation functions in neural networks.
A feedforward neural network has two input nodes, one hidden layer with three hidden neurons, and one output node. The activation functions for all hidden and output neurons are the same linear function in the following form: g(x)=c*x, where “c” is a constant. Please explain why this neural network is a linear classifier (you should use mathematical equations with analysis to illustrate this).
For the same neural network as in (b), if we replace the activation function for the output neuron with the sigmoid function, will this neural network still be a linear classifier? Please present your analysis and use mathematical equations to illustrate your ideas.
Consider the following neural network, where x1, x2 are input, y1, y2 are output, and vij and wij are weight values with vij representing the weight from input node j to hidden node i, and wij representing the weight from hidden node j to output node i. For instance, v21 represents the weight from input node 1 to hidden node 2.
The bias has been omitted in the above network; please draw a new graph to complete the above network by considering the bias (you don’t need to assign initial weights for the bias).
Consider the same neural network in (d). For a training sample with input x1=1, x2=2, calculate the output of the network if the activation function g() in the hidden layer and the output layer is the identity relation: a=g(a). Please ignore the bias in this case for ease of calculation.
(3)
(5)
(4)
(3)
(5)
Q2
(a)
(b)
(c)
(d)
(e)
Explain why deep learning is still needed for many complicated problems even though the universal approximation theorem states that a shallow neural network can approximate any continuous functions?
You are training a multilayer perceptron using backpropagation, and after many epochs you find that the loss function is very small, but it is oscillating within a very small range. What might be the reason for this and how will you deal with this situation?
In the context of backpropagation, explain what characteristics an activation function should have in order to achieve effective training of neural networks.
When training a neural network with backpropagation, the learning rate is first set to be a larger value, and then it is gradually decreased during the learning process. Explain the reason and draw a graph to illustrate this (2 marks for explaining the reason and 2 marks for the graph).
In a convolution neural network, suppose there are 6 filters of size 3 x 3 and stride 1 (the step size of the filter) in the first layer. If an input of dimension 10 x 10 x 3 is passed through this layer, what are the dimensions of the data which the next layer will receive? Draw a graph to illustrate your ideas (three marks for calculating the dimensions, and three marks for the graph).
Note: the input dimension 10 x 10 x 3 means the input images have three channels (RGB), and the convolution operation needs to be adapted to the three channel situation.
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