Backpropagation

import numpy as np

# ─── Forward pass ─────────────────────────────────────────
def sigmoid(x):
    return 1.0 / (1.0 + np.exp(-x))

# Dữ liệu & mục tiêu
x = np.array([0.6, 0.9])
y = 0.8

# Trọng số khởi tạo (tương ứng mạng 2-3-1 trong bài)
W1 = np.array([[0.15, -0.20],
               [0.25,  0.30],
               [-0.10, 0.40]])    # (3, 2)
W2 = np.array([0.35, -0.30, 0.50])  # (3,)

# Forward
z1 = W1 @ x                 # (3,)
h  = sigmoid(z1)            # (3,)
z2 = W2 @ h                 # scalar
y_hat = sigmoid(z2)
loss = 0.5 * (y - y_hat) ** 2
print(f"ŷ = {y_hat:.4f}, loss = {loss:.5f}")

# ─── Backward pass (chain rule bằng tay) ──────────────────
dL_dy      = -(y - y_hat)                 # ∂L/∂ŷ
dy_dz2     = y_hat * (1 - y_hat)          # σ'(z2)
dL_dz2     = dL_dy * dy_dz2               # scalar

dL_dW2     = dL_dz2 * h                   # (3,)
dL_dh      = dL_dz2 * W2                  # (3,)

dh_dz1     = h * (1 - h)                  # σ'(z1), (3,)
dL_dz1     = dL_dh * dh_dz1               # (3,)
dL_dW1     = np.outer(dL_dz1, x)          # (3, 2)

# ─── Gradient descent update ──────────────────────────────
lr = 0.8
W1 -= lr * dL_dW1
W2 -= lr * dL_dW2

# Forward lại để xem loss đã giảm
h  = sigmoid(W1 @ x)
y_hat = sigmoid(W2 @ h)
new_loss = 0.5 * (y - y_hat) ** 2
print(f"Sau 1 bước: ŷ = {y_hat:.4f}, loss = {new_loss:.5f}")

import torch
import torch.nn as nn
import torch.optim as optim

# Mạng 2-3-1
model = nn.Sequential(
    nn.Linear(2, 3),
    nn.Sigmoid(),
    nn.Linear(3, 1),
    nn.Sigmoid(),
)

x = torch.tensor([0.6, 0.9])
y = torch.tensor([0.8])

# Loss & optimizer
loss_fn = nn.MSELoss()
optimizer = optim.SGD(model.parameters(), lr=0.8)

# Vòng lặp huấn luyện
for step in range(50):
    # Forward
    y_hat = model(x)
    loss = loss_fn(y_hat, y)

    # Backward — TỰ ĐỘNG tính gradient cho MỌI tham số
    optimizer.zero_grad()    # xóa gradient cũ
    loss.backward()          # ← đây là backprop
    optimizer.step()         # w <- w - lr * grad

    if step % 10 == 0:
        print(f"Step {step:3d} | loss = {loss.item():.5f}")

# Xem gradient của từng weight sau backward()
for name, param in model.named_parameters():
    print(f"{name}: shape={tuple(param.shape)}, "
          f"last grad norm={param.grad.norm().item():.4f}")