$13.$ In the neural network below, wa$=-1,$ wb$=2,$ and the remaining connection weights are all equal to $1.$ Assume that each neuron directly $$fires$$ with strength equal to the sum of the input signals it receives $($i$.$e$.$ no bias terms, no activation functions$).$ When the top input neuron$$s input is $-1\mathrm{.}5$ and the bottom$$s is $3,$ we want the network to output $0,$ but the network currently outputs something different. Assuming we can only change the connection weights of wa and wb$,$ determine whether each one should be increased or decreased to push the network$$s output closer to the correct value, and explain why. Hint: Calculate the output of the network first, then work backwards.

$14.$ Give an example of a situation where autocorrect assisted by a language model would perform better than if it simply looked for the closest word to what a user typed.

NOTE: Can you please provide the mathematical work you do in order to answer the questions especially for question $13.$