Consider a single layer ANN as in below with logistic sigmoid activation function and square error loss function. The inputs are given as $x=[0\mathrm{.}5,-1,0\mathrm{.}75{]}^T.$ The weights and bias are randomly initialized as $w_0=[0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}4{]}^T$ and $b=0\mathrm{.}3.$ Whereas the corresponding output is $y=1.$ Let the learning rate $=0\mathrm{.}1,$ answer the following:

$.$Find the output using the forward propagation Find the gradient $.$Find the updated weights and bias Find the updated loss function

Inputs Weights