CNN Architectures: From LeNet to Modern Designs

LeNet-5 Architecture Flow:
┌─────────────────────────────────────────────────────────────────────────────┐
│                                                                             │
│  INPUT (32×32×1)                                                            │
│       │                                                                     │
│       ▼                                                                     │
│  ┌─────────────────┐                                                        │
│  │ C1: CONV 5×5    │  6 filters, stride 1 → Output: 28×28×6                 │
│  │ + tanh          │  Parameters: (5×5×1 + 1) × 6 = 156                     │
│  └────────┬────────┘                                                        │
│           │                                                                 │
│           ▼                                                                 │
│  ┌─────────────────┐                                                        │
│  │ S2: AVGPOOL 2×2 │  stride 2 → Output: 14×14×6                            │
│  │ + trainable     │  Parameters: (1 + 1) × 6 = 12                          │
│  └────────┬────────┘                                                        │
│           │                                                                 │
│           ▼                                                                 │
│  ┌─────────────────┐                                                        │
│  │ C3: CONV 5×5    │  16 filters, sparse connectivity → Output: 10×10×16   │
│  │ + tanh          │  Parameters: 1,516 (varies per filter)                 │
│  └────────┬────────┘                                                        │
│           │                                                                 │
│           ▼                                                                 │
│  ┌─────────────────┐                                                        │
│  │ S4: AVGPOOL 2×2 │  stride 2 → Output: 5×5×16                             │
│  │ + trainable     │  Parameters: (1 + 1) × 16 = 32                         │
│  └────────┬────────┘                                                        │
│           │                                                                 │
│           ▼                                                                 │
│  ┌─────────────────┐                                                        │
│  │ C5: CONV 5×5    │  120 filters → Output: 1×1×120                         │
│  │ + tanh          │  Parameters: (5×5×16 + 1) × 120 = 48,120               │
│  └────────┬────────┘                                                        │
│           │                                                                 │
│           ▼                                                                 │
│  ┌─────────────────┐                                                        │
│  │ F6: FC 120→84   │  Fully Connected → Output: 84                          │
│  │ + tanh          │  Parameters: (120 + 1) × 84 = 10,164                   │
│  └────────┬────────┘                                                        │
│           │                                                                 │
│           ▼                                                                 │
│  ┌─────────────────┐                                                        │
│  │ OUTPUT: RBF     │  Euclidean RBF → Output: 10 classes                    │
│  │                 │  Parameters: 84 × 10 = 840                             │
│  └─────────────────┘                                                        │
│                                                                             │
│  TOTAL TRAINABLE PARAMETERS: ~61,000                                        │
└─────────────────────────────────────────────────────────────────────────────┘

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import numpy as np
 
# LeNet-5 specific tanh activation
def lenet_tanh(x):
    """
    Scaled tanh as used in original LeNet-5.
    A = 1.7159, S = 2/3
    
    Properties:
    - Output range: (-1.7159, +1.7159)  
    - f(1) ≈ 1, f(-1) ≈ -1
    - f'(0) ≈ 1.14 (near-identity for small inputs)
    """
    A = 1.7159
    S = 2.0 / 3.0
    return A * np.tanh(S * x)
 
def lenet_tanh_derivative(x):
    """
    Derivative for backpropagation.
    d/dx [A * tanh(Sx)] = A * S * (1 - tanh²(Sx))
    """
    A = 1.7159
    S = 2.0 / 3.0
    tanh_val = np.tanh(S * x)
    return A * S * (1 - tanh_val ** 2)
 
# Compare with modern ReLU
def relu(x):
    return np.maximum(0, x)
 
def relu_derivative(x):
    return (x > 0).astype(float)
 
# Demonstration
x = np.linspace(-3, 3, 100)
 
print("At x=0:")
print(f"  LeNet tanh(0) = {lenet_tanh(0):.4f}")
print(f"  LeNet tanh'(0) = {lenet_tanh_derivative(0):.4f}")  # ≈ 1.14
print(f"  ReLU(0) = {relu(0):.4f}")
print(f"  ReLU'(0) = undefined (typically 0)")
 
print("
At x=1:")
print(f"  LeNet tanh(1) = {lenet_tanh(1):.4f}")  # ≈ 0.96
print(f"  ReLU(1) = {relu(1):.4f}")

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import torch
import torch.nn as nn
import torch.optim as optim
from torchvision import datasets, transforms
from torch.utils.data import DataLoader
 
class ModernLeNet5(nn.Module):
    """
    Modern implementation of LeNet-5 with contemporary best practices:
    - ReLU instead of tanh
    - Max pooling instead of average pooling
    - Softmax output instead of RBF
    - Batch normalization (optional modern addition)
    """
    def __init__(self, num_classes=10):
        super(ModernLeNet5, self).__init__()
        
        # C1: Convolutional layer 1
        self.conv1 = nn.Conv2d(
            in_channels=1, 
            out_channels=6, 
            kernel_size=5, 
            stride=1, 
            padding=2  # Same padding to preserve 32×32 → 32×32
        )
        
        # S2: Subsampling (now max pooling)
        self.pool1 = nn.MaxPool2d(kernel_size=2, stride=2)
        
        # C3: Convolutional layer 2
        self.conv2 = nn.Conv2d(
            in_channels=6, 
            out_channels=16, 
            kernel_size=5
        )
        
        # S4: Subsampling
        self.pool2 = nn.MaxPool2d(kernel_size=2, stride=2)
        
        # C5: Convolutional layer 3 (acts like FC at this scale)
        self.conv3 = nn.Conv2d(
            in_channels=16, 
            out_channels=120, 
            kernel_size=5
        )
        
        # F6: Fully connected layer
        self.fc1 = nn.Linear(120, 84)
        
        # Output: Fully connected (replaces RBF)
        self.fc2 = nn.Linear(84, num_classes)
        
        # Activation function (modern: ReLU)
        self.relu = nn.ReLU()
        
    def forward(self, x):
        # C1 + S2
        x = self.relu(self.conv1(x))
        x = self.pool1(x)
        
        # C3 + S4
        x = self.relu(self.conv2(x))
        x = self.pool2(x)
        
        # C5
        x = self.relu(self.conv3(x))
        
        # Flatten
        x = x.view(x.size(0), -1)
        
        # F6
        x = self.relu(self.fc1(x))
        
        # Output (no activation - raw logits for CrossEntropyLoss)
        x = self.fc2(x)
        
        return x
 
# Training setup
def train_lenet():
    # Data preprocessing
    transform = transforms.Compose([
        transforms.Resize((32, 32)),  # LeNet expects 32×32
        transforms.ToTensor(),
        transforms.Normalize((0.1307,), (0.3081,))  # MNIST mean, std
    ])
    
    train_dataset = datasets.MNIST(
        root='./data', train=True, download=True, transform=transform
    )
    train_loader = DataLoader(train_dataset, batch_size=64, shuffle=True)
    
    # Model, loss, optimizer
    model = ModernLeNet5(num_classes=10)
    criterion = nn.CrossEntropyLoss()  # Modern: cross-entropy
    optimizer = optim.SGD(
        model.parameters(), 
        lr=0.01, 
        momentum=0.9,  # Adding momentum
        weight_decay=1e-4  # L2 regularization
    )
    
    # Learning rate scheduler
    scheduler = optim.lr_scheduler.StepLR(optimizer, step_size=10, gamma=0.1)
    
    # Training loop
    model.train()
    for epoch in range(20):
        total_loss = 0
        for batch_idx, (data, target) in enumerate(train_loader):
            optimizer.zero_grad()
            output = model(data)
            loss = criterion(output, target)
            loss.backward()
            optimizer.step()
            total_loss += loss.item()
        
        scheduler.step()
        print(f"Epoch {epoch+1}: Loss = {total_loss/len(train_loader):.4f}")
    
    return model
 
# Demonstrate parameter count
model = ModernLeNet5()
total_params = sum(p.numel() for p in model.parameters())
print(f"Total parameters: {total_params:,}")  # ≈ 61,706

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"""
Complete LeNet-5 Implementation
Both historical (original design) and modern (contemporary best practices) versions.
"""
 
import torch
import torch.nn as nn
import torch.nn.functional as F
import numpy as np
 
class HistoricalLeNet5(nn.Module):
    """
    Faithful recreation of the original LeNet-5 (LeCun et al., 1998)
    
    Key differences from modern CNNs:
    - Scaled tanh activation: 1.7159 * tanh(2/3 * x)
    - Trainable pooling with coefficient and bias
    - Sparse connectivity in C3 (simplified here to full connectivity)
    - RBF output layer (replaced with Euclidean distance)
    """
    
    def __init__(self, num_classes=10):
        super(HistoricalLeNet5, self).__init__()
        
        # C1: 32×32×1 → 28×28×6
        self.c1 = nn.Conv2d(1, 6, kernel_size=5, stride=1, padding=0)
        
        # S2: Trainable subsampling (simplified to avg pool + learnable scale)
        self.s2_pool = nn.AvgPool2d(kernel_size=2, stride=2)
        self.s2_weight = nn.Parameter(torch.ones(6))
        self.s2_bias = nn.Parameter(torch.zeros(6))
        
        # C3: 14×14×6 → 10×10×16
        self.c3 = nn.Conv2d(6, 16, kernel_size=5, stride=1, padding=0)
        
        # S4: Trainable subsampling
        self.s4_pool = nn.AvgPool2d(kernel_size=2, stride=2)
        self.s4_weight = nn.Parameter(torch.ones(16))
        self.s4_bias = nn.Parameter(torch.zeros(16))
        
        # C5: 5×5×16 → 1×1×120
        self.c5 = nn.Conv2d(16, 120, kernel_size=5, stride=1, padding=0)
        
        # F6: 120 → 84
        self.f6 = nn.Linear(120, 84)
        
        # Output: 84 → num_classes (simplified from RBF)
        self.output = nn.Linear(84, num_classes)
        
        # Initialize weights
        self._initialize_weights()
    
    def _initialize_weights(self):
        """Xavier-like initialization as described in the original paper"""
        for m in self.modules():
            if isinstance(m, nn.Conv2d):
                fan_in = m.kernel_size[0] * m.kernel_size[1] * m.in_channels
                std = 1.0 / np.sqrt(fan_in)
                nn.init.normal_(m.weight, mean=0, std=std)
                if m.bias is not None:
                    nn.init.zeros_(m.bias)
            elif isinstance(m, nn.Linear):
                fan_in = m.in_features
                std = 1.0 / np.sqrt(fan_in)
                nn.init.normal_(m.weight, mean=0, std=std)
                if m.bias is not None:
                    nn.init.zeros_(m.bias)
    
    def scaled_tanh(self, x):
        """Original LeNet activation: A * tanh(S * x)"""
        A = 1.7159
        S = 2.0 / 3.0
        return A * torch.tanh(S * x)
    
    def trainable_subsample(self, x, weight, bias):
        """
        Trainable subsampling as in original LeNet.
        output = tanh(weight * avg_pool(x) + bias)
        """
        # weight and bias are per-channel
        pooled = F.avg_pool2d(x, kernel_size=2, stride=2)
        # Reshape weight and bias for broadcasting: (1, C, 1, 1)
        w = weight.view(1, -1, 1, 1)
        b = bias.view(1, -1, 1, 1)
        return self.scaled_tanh(w * pooled + b)
    
    def forward(self, x):
        # C1 + activation
        x = self.scaled_tanh(self.c1(x))
        
        # S2: trainable subsample
        x = self.trainable_subsample(x, self.s2_weight, self.s2_bias)
        
        # C3 + activation
        x = self.scaled_tanh(self.c3(x))
        
        # S4: trainable subsample
        x = self.trainable_subsample(x, self.s4_weight, self.s4_bias)
        
        # C5 + activation
        x = self.scaled_tanh(self.c5(x))
        
        # Flatten
        x = x.view(x.size(0), -1)
        
        # F6 + activation
        x = self.scaled_tanh(self.f6(x))
        
        # Output
        x = self.output(x)
        
        return x
 
 
class ModernLeNet5(nn.Module):
    """
    Modern implementation of LeNet-5 with contemporary best practices.
    
    Changes from original:
    - ReLU activation (faster training, no vanishing gradients)
    - Max pooling (better performance)
    - He initialization (optimal for ReLU)
    - Optional batch normalization
    - Dropout for regularization
    """
    
    def __init__(self, num_classes=10, use_batchnorm=True, dropout_rate=0.5):
        super(ModernLeNet5, self).__init__()
        
        self.use_batchnorm = use_batchnorm
        
        # Feature extractor
        self.features = nn.Sequential(
            # C1
            nn.Conv2d(1, 6, kernel_size=5, stride=1, padding=2),
            nn.BatchNorm2d(6) if use_batchnorm else nn.Identity(),
            nn.ReLU(inplace=True),
            nn.MaxPool2d(kernel_size=2, stride=2),
            
            # C2/C3
            nn.Conv2d(6, 16, kernel_size=5, stride=1, padding=0),
            nn.BatchNorm2d(16) if use_batchnorm else nn.Identity(),
            nn.ReLU(inplace=True),
            nn.MaxPool2d(kernel_size=2, stride=2),
            
            # C5
            nn.Conv2d(16, 120, kernel_size=5, stride=1, padding=0),
            nn.ReLU(inplace=True),
        )
        
        # Classifier
        self.classifier = nn.Sequential(
            nn.Dropout(dropout_rate),
            nn.Linear(120, 84),
            nn.ReLU(inplace=True),
            nn.Dropout(dropout_rate),
            nn.Linear(84, num_classes),
        )
        
        # He initialization for ReLU
        self._initialize_weights()
    
    def _initialize_weights(self):
        for m in self.modules():
            if isinstance(m, nn.Conv2d):
                nn.init.kaiming_normal_(m.weight, mode='fan_out', nonlinearity='relu')
                if m.bias is not None:
                    nn.init.zeros_(m.bias)
            elif isinstance(m, nn.BatchNorm2d):
                nn.init.ones_(m.weight)
                nn.init.zeros_(m.bias)
            elif isinstance(m, nn.Linear):
                nn.init.kaiming_normal_(m.weight, mode='fan_out', nonlinearity='relu')
                if m.bias is not None:
                    nn.init.zeros_(m.bias)
    
    def forward(self, x):
        x = self.features(x)
        x = x.view(x.size(0), -1)
        x = self.classifier(x)
        return x
 
 
# Utility functions for comparison
def count_parameters(model):
    """Count trainable parameters"""
    return sum(p.numel() for p in model.parameters() if p.requires_grad)
 
def compare_models():
    """Compare historical and modern implementations"""
    historical = HistoricalLeNet5()
    modern = ModernLeNet5()
    modern_no_bn = ModernLeNet5(use_batchnorm=False)
    
    print("LeNet-5 Model Comparison")
    print("=" * 50)
    print(f"Historical LeNet-5:    {count_parameters(historical):>8,} parameters")
    print(f"Modern (with BN):      {count_parameters(modern):>8,} parameters")
    print(f"Modern (without BN):   {count_parameters(modern_no_bn):>8,} parameters")
    
    # Test forward pass
    dummy_input = torch.randn(1, 1, 32, 32)
    
    print("
Forward pass shapes:")
    print(f"  Input:  {dummy_input.shape}")
    print(f"  Historical output: {historical(dummy_input).shape}")
    print(f"  Modern output:     {modern(dummy_input).shape}")
 
if __name__ == "__main__":
    compare_models()