Consider a feed$-$forward netw

ork that has two inputs, two outputs and three neurons in a single

hidden layer. The network is shown in Figure $1($on the next page$)$ and the activation function for

all the neurons is a logistic function, i$.$e$.$ unipolar binary.

Presented with an input vector of

x $=[+1,$ x$1,$ x$2]$T $=[1,1,0]$T

the actual output was

y $=[$y$1,$ y$2]$T $=[0\mathrm{.}6027,0\mathrm{.}4507]$T

but the target output was

$[1,0]$T$.$

Carry out the calculations requested below $($in the context of backpropagation learning using the

generalized delta rule $($no momentum$)$ for the network, given the following values:

whid$1-0=0\mathrm{.}77$ whid$2-0=0\mathrm{.}07$ whid$3-0=0\mathrm{.}23$ wout$1-0=0\mathrm{.}00$ wout$2-0=0\mathrm{.}00$

whid$1-1=-1\mathrm{.}01$ whid$2-1=-0\mathrm{.}30$ whid$3-1=-0\mathrm{.}44$ wout$1-1=0\mathrm{.}14$ wout$2-1=-0\mathrm{.}44$

whid$1-2=1\mathrm{.}05$ whid$2-2=-0\mathrm{.}22$ whid$3-2=0\mathrm{.}25$ wout$1-2=-0\mathrm{.}30$ wout$2-2=-0\mathrm{.}10$

wout$1-3=1\mathrm{.}09$ wout$2-3=0\mathrm{.}09$

Hidden layer outputs for the input vector given above are:

z$1=0\mathrm{.}4403$ z$2=0\mathrm{.}4428$ z$3=0\mathrm{.}4477$

$($a$)$ Find $$out$-1.$

$($b$)$ Calculate $$wout$1-2,$ using a learning rate of $0\mathrm{.}7.$

$($c$)$ Obtain $$hid$-2.$

$($d$)$ Calculate $$whid$2-1,$ using a learning rate of $0\mathrm{.}7.$