To find $H2_{\text{in}}$ using an Artificial Neural Network (ANN) with backpropagation, we'll need to calculate the input to the node $h_2$ in the hidden layer. The calculation involves summing up the weighted inputs from $i_1$ and $i_2$.

From the image, we have:

• $i_1$ is connected to $h_2$ with a weight of $0.12$.
• $i_2$ is connected to $h_2$ with a weight of $0.08$.
• The bias for $h_2$, denoted as $B_1$, is given as $0.31$.

The formula for $H2_{\text{in}}$ is:

$H2_{\text{in}} = (i_1 \times 0.12) + (i_2 \times 0.08) + B_1$

To proceed, I would need the values of $i_1$ and $i_2$ (the input layer values). If these are given, I can substitute them and compute $H2_{\text{in}}$.

Please provide the values of $i_1$ and $i_2$ if available, or let me know if you need help with another part of this process.

Would you like more detailed steps on backpropagation, or have any other specific questions? Here are some questions that might further enhance your understanding:

1. How is the backpropagation algorithm used to adjust weights in neural networks?
2. What role do biases play in neural network computations?
3. How does the activation function affect the value calculated in each layer?
4. What is the significance of the weights between layers?
5. Why do we add bias terms to the weighted sum of inputs?

Tip: In neural networks, each layer's input is computed as the weighted sum of the previous layer's outputs plus a bias, which allows the model to capture complex patterns.