الشبكات الالتفافية (CNN)

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import load_sample_image

photo = load_sample_image("china.jpg").mean(axis=2)[::3, ::3]   # grayscale, smaller

vertical_edges = np.array([[-1, 0, 1],
                           [-1, 0, 1],
                           [-1, 0, 1]])    # a 3x3 filter

def convolve(img, kernel):
    h, w = img.shape[0] - 2, img.shape[1] - 2
    out = np.zeros((h, w))
    for i in range(h):
        for j in range(w):
            out[i, j] = np.sum(img[i:i + 3, j:j + 3] * kernel)  # slide & dot
    return out

fig, axes = plt.subplots(1, 2, figsize=(9, 3.2))
axes[0].imshow(photo, cmap="gray"); axes[0].set_title("original")
axes[1].imshow(np.abs(convolve(photo, vertical_edges)), cmap="gray"); axes[1].set_title("vertical edges")
for ax in axes: ax.axis("off")
plt.tight_layout()
plt.show()

import torch
from torch import nn
from sklearn.datasets import load_digits
from sklearn.model_selection import train_test_split

torch.manual_seed(0)
digits = load_digits()                       # 1797 images, 8x8, digits 0-9
X = torch.tensor(digits.images / 16.0, dtype=torch.float32).unsqueeze(1)  # (N, 1, 8, 8)
y = torch.tensor(digits.target)
X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size=0.25, random_state=0)

model = nn.Sequential(
    nn.Conv2d(1, 16, kernel_size=3, padding=1), nn.ReLU(),   # 16 learned filters
    nn.MaxPool2d(2),                                         # 8x8 -> 4x4
    nn.Conv2d(16, 32, kernel_size=3, padding=1), nn.ReLU(),
    nn.MaxPool2d(2),                                         # 4x4 -> 2x2
    nn.Flatten(),
    nn.Linear(32 * 2 * 2, 10),                               # 10 classes
)
loss_fn = nn.CrossEntropyLoss()              # multi-class (softmax inside)
opt = torch.optim.Adam(model.parameters(), lr=0.01)

for epoch in range(30):
    model.train()
    for i in range(0, len(X_tr), 64):
        opt.zero_grad()
        loss_fn(model(X_tr[i:i + 64]), y_tr[i:i + 64]).backward()
        opt.step()

model.eval()
with torch.no_grad():
    preds = model(X_te).argmax(dim=1)
print(f"test accuracy: {(preds == y_te).float().mean():.1%}")
print("first 10 predictions:", preds[:10].tolist())
print("true labels:         ", y_te[:10].tolist())