7.1 CNN architecture: convolutional layers, pooling, and fully connected layers

Convolutional Neural Networks (CNNs) are powerful image processing tools. They use convolutional layers to extract features, pooling layers to reduce dimensions, and fully connected layers for final classification or regression. These components work together to analyze visual data effectively.

CNN architecture design involves arranging layers and fine-tuning hyperparameters. The structure typically includes alternating convolutional and pooling layers, followed by fully connected layers. Careful consideration of factors like network depth, filter sizes, and regularization techniques optimizes performance.

CNN Architecture Components

Convolutional Layers

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• Extract features from input data and apply filters to detect patterns
• Filters (kernels) slide across input data as learnable parameters
• Feature maps result from applying filters to input
• Stride determines step size for filter movement
• Zero-padding controls output size
• Convolution operation: $output = \sum (input * filter) + bias$
• Activation functions include ReLU, Leaky ReLU, and ELU enhance non-linearity

Pooling Layers

• Reduce spatial dimensions, decrease computational complexity, provide translation invariance
• Max pooling selects maximum value in pooling window
• Average pooling calculates average value in pooling window
• Global pooling applies operation across entire feature map
• Window size and stride affect pooling behavior
• Dimensionality reduction preserves important features

Fully Connected Layers

• Perform final classification or regression, combining features from previous layers
• Neurons fully connected to previous layer, multiple layers possible
• Mathematical operation: $output = activation(weights * input + bias)$
• Softmax activation for multi-class classification, sigmoid for binary classification
• Flattening converts 2D feature maps to 1D vector
• Dropout prevents overfitting by randomly deactivating neurons during training

CNN Architecture Design

Layer Arrangement and Interaction

• Typical structure: input layer, alternating convolutional and pooling layers, fully connected layers, output layer
• Early layers extract features, later layers combine them
• Skip connections allow information to bypass layers, mitigating vanishing gradient problem
• Deeper networks capture complex features, wider networks capture diverse features

Hyperparameter Considerations

• Number of layers impacts model complexity and capacity
• Smaller filters capture fine-grained features, larger filters capture broader patterns
• Learning rate affects convergence speed and stability
• Batch size influences training speed and generalization
• Regularization techniques (L1/L2, data augmentation) prevent overfitting
• Optimization algorithms (SGD, Adam, RMSprop) affect training dynamics