Linear Neurons The following is a network of linear neurons- that is, neurons whose output is identical
Question:
Linear Neurons The following is a network of linear neurons- that is, neurons whose output is identical to their net input, x w (in other words, their output function that translates net input into output is simply the identity function). These neurons do not receive any "dummy inputs (biases or offsets). The numbers in the circles indicate the output of a neuron, and the labels of connections indicate the value of the corresponding weight.
(a) Just as a warm-up exercise, compute the output of the hidden layer and the output-layer neurons for the given input (2, 1).
(b) Only mandatory for CS670: Show that a network of linear neurons, such as this one, always computes a linear function, regardless of its number of layers and neurons. Hint: A function y fx) is linear if and only if it can be expressed as y- Ax for some matrix A.
(c) Only mandatory for CS670: Given that our three-layer network computes a linear function, we suddenly notice that our network is wastefully large. It must be possible to compute exactly the same function with a two-layer network. Draw such a network, including all of its weights, that only consists of an input layer and an output layer and computes the same function as the network shown above. In the network above, determine how the output of each output-layer neuron depends on the two network inputs, and then you should be able to find the correct weights for the two-layer network. There is a more elegant way of deriving the solution that is related to (b), but any correct solution gets full points, regardless of your approach.
Basic Business Statistics
ISBN: 978-0321870025
13th edition
Authors: Mark L. Berenson, David M. Levine, Kathryn A. Szabat