0
$\begingroup$

I got a 'homework' to solve from college but I have no idea how to do it ...
Can anyone get it?

A neural network with the following structure is given: one input neuron, four elements in the hidden layer, one output neuron. The output neuron is bipolar, the neurons in the hidden layer are linear. The weights between the input neuron and the neurons in the hidden layer have the following values: w11 = -3, w12 = 2, w13 = -1, w14 = 0.5, while between neurons in the hidden layer and the starting neuron:: w21 = +2, w22 = -0.5, w23 = -3, w24 = +1 (no threshold input in both layers). What will the network response be like if the number 3 is given to the input neuron?

$\endgroup$
2
$\begingroup$

Given that the neurons are linear in the hidden layer of the Neural Network, so the output is just the dot product of the weights and the input. To put things in perspective generally we use an activation function(sigmoid, signum, etc) which is applied to the dot product.

Hence for an input of 3 inputs to node 1 of hidden layer is -3 * 3 = 9, to node 2 is 2 * 3= 6 to node 3 is -1 * 3 = -3 to node 4 is 0.5 *3 = 1.5 (basically i have performed dot product). Since neurons are linear no activation function is applied and is directly propagated to the next layer, the output layer.

Contribution of all the hidden nodes to the output layer is the dot product of the weights with the output of hidden layer that is 9*2 + -0.5*6 + -3*-3 + 1*1.5 = 25.5 (check for any calculation errors). And finally the output layer is bipolar hence an activation function (probably sigmoid) is applied to it. Since for sigmoid function sigmoid(z) > 0.5 if z>0 hence the output will be 1 as z = 25.5 as per convention.

Note: This is not a site for school problems. Since you are new here it is better to know that, and the problem was pretty straightforward too.

$\endgroup$
  • $\begingroup$ Thanks for your help but you have make a little mistake in calculations: -3 * 3 is not 9 only -9 :) So finally it will be -9*2 + -0.5*6 + -3*-3 + 1*1.5 = -4,5 $\endgroup$ – Paul Jan 25 '18 at 13:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.