Please answer the question at the bottom what is the gradient descent update to w$(1,2)[1]$ with a learning rate of a$.$ Please write it in terms of xi yi and oi and the weights. sigmoid function is the activation function for h$1,$ h$2,$ h$3$ and o

Q$2)$

Let $x=\{x^{(1)},$cdots,$x^{(m)}\}$ be a dataset of $m$ samples with $2$ features, i$.$e $x^{(i)}in{R}^2.$ The samples are classified into $2$ categories with labels $y^{(i)}in\{0,1\}.$ A scatter plot of the dataset is shown in the following figure:

The examples in class $1$ are marked as $"x"$ and examples in class $0$ are marked as $"$o$".$ We want to perform binary classification using a simple neural network with the architecture shown in the following figure:

Denote the two features $x_1$ and $x_2^{},$ the three neurons in the hidden layer $h_1,h_2,$ and $h_3,$ and the output neuron as $o.$ Let the weight from $x_i$ to $h_j$ be $w_{i,j}^{[1]}$ for iin$\{1,2\},$jin$\{1,2,3\},$ and the weight from $h_j$ to $o$ be $w_j^{[2]}.$ Finally, denote the intercept weight for $h_j$ as $w_{0,j}^{[1]},$ and the intercept weight for $o$ as $w_0^{[2]}.$ For the loss function, we'll use average squared loss instead of the usual negative log$-$likelihood:

$l=\frac{1}{m}{\displaystyle \underset{i=1}{\overset{m}{}}}(o^{(i)}-y^{(i)}{)}^2$

where $o^{(i)}$ is the result of the output neuron for example $i.$

Suppose we use the sigmoid function as the activation function for $h_1,h_2,h_3,$ and $o.$ What is the gradient descent update to $w_{1,2}^{[1]},$ assuming we use a learning rate of $?$ Your answer should be written in terms of $x^{(l)},o^{(i)},y^{(i)},$ and the weights.