The Forward Pass in Python

A neural network stacks layers. The hidden layer is the layer from the last lesson: it turns each row's 2 inputs into 3 numbers between 0 and 1. The output layer, a single neuron, reads those 3 numbers as its inputs and gives one answer per row. Sending the inputs through every layer, in order, is the forward pass.

The shapes chain together: X is (4, 2) and W1 is (2, 3), so the hidden layer is (4, 3). W2 is (3, 1), one weight for each hidden neuron, so the output is (4, 1): one answer per row.

Returning two values: a function can give back two results separated by a comma, and two names before the = take them in order. Here the second result is built from the first, the way the output layer is built from the hidden one:

def double_and_square(n):
    doubled = n * 2
    squared = doubled ** 2
    return doubled, squared

d, s = double_and_square(3)
print(d, s)   # 6 36

A column as a row: in a[:, 0], the part before the comma picks rows and the part after picks columns, and : means all of them. So np.array([[7], [8]])[:, 0] gives back the flat array [7 8].

Your code must print these lines:

W1 shape: (2, 3) W2 shape: (3, 1)
out: [0.736 0.704 0.877 0.816]

After them, the check prints the shapes of hidden and out, the hidden table, and what forward gives for the single row [1, 1].

Your task: write a function forward(X) that runs the hidden layer, then the output layer, and returns both results; call it on X and print the network's four answers.

Assignment
Follow the Coding Tutorial to write forward, run it on X and print the output column.

Hint
Inside forward, the output layer reads hidden, not X: (4, 3) @ (3, 1). Wrap each layer's sum in sigmoid(…), and round the answers with np.round(…, 3).