Predictive Analytics $-$ MDA$611$

PBL Week $10$

Neural Networks

Give a neural network with the following structure: $1$ input neuron, $4$ neurons in the hidden layer, $1$ output neuron.

The output of the hidden layer is fed to a sigmoid function $($S$($z$)=1/(1+$e$^(-$z$)))$ to produce the binary output at the output neuron, where z is the input to the output neuron.

The weights between the input neuron and the neurons in the hidden layer have the following values: w$11=3,$ w$12=2,$ w$13=1,$ w$14=0\mathrm{.}5$

The weights between neurons in the hidden layer and the output neuron are: w$21=+2,$ w$22=0\mathrm{.}5,$ w$23=3,$ w$24=+1$

There is no bias input in both layers.

Questions:

Q$1.$ Roughly sketch the structure of this neural network, including nodes, weights, etc.

Q$2.$ If the number $3$ is given to the input neuron, what will be the output at the output neuron?