Question: Suppose you had a neural network with linear activation functions. That is , for each unit the output is some constant c times the weighted

Suppose you had a neural network with linear activation functions. That is

,

for each unit the output is some constant c times the weighted sum of the inputs.

Assume that the network has one hidden layer. For a given assignment to the weights w

,

write down equations for the value of the units in the output layer as a function of w and the input layer x

,

without any explicit mention of the output of the hidden layer. Show that there is a network with no hidden units that computes the same function.

Repeat the calculation in part

(

),

but this time do it for a network with any number of hidden layers.

Suppose a network with one hidden layer and linear activation functions has n input and output nodes and h hidden nodes. What effect does the transformation in part

(

)

to a network with no hidden layers have on the total number of weights? Discuss the case h

< <

.

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Problem Breakdown and Solution In this problem we are tasked with analyzing a neural network with linear activation functions Well explore the equations of the output units in terms of the input layer ... View full answer

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