إزاي الشبكة بتتعلم

import numpy as np

X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
y = np.array([[0], [1], [1], [0]])            # XOR

rng = np.random.default_rng(1)
W1, b1 = rng.normal(size=(2, 4)), np.zeros(4)  # hidden layer: 4 neurons
W2, b2 = rng.normal(size=(4, 1)), np.zeros(1)  # output layer
sigmoid = lambda z: 1 / (1 + np.exp(-z))
lr = 0.5

for epoch in range(5001):
    # ---- forward ----
    h = np.tanh(X @ W1 + b1)
    p = sigmoid(h @ W2 + b2)
    loss = np.mean((p - y) ** 2)

    # ---- backward (chain rule, layer by layer) ----
    d_out = 2 * (p - y) / len(X) * p * (1 - p)
    d_W2, d_b2 = h.T @ d_out, d_out.sum(axis=0)
    d_h = d_out @ W2.T * (1 - h ** 2)            # derivative of tanh
    d_W1, d_b1 = X.T @ d_h, d_h.sum(axis=0)

    # ---- update ----
    W2 -= lr * d_W2; b2 -= lr * d_b2
    W1 -= lr * d_W1; b1 -= lr * d_b1

    if epoch % 1000 == 0:
        print(f"epoch {epoch:4}: loss = {loss:.4f}")

print("predictions:", p.round(2).ravel())