Convolutional Neural Networks (CNN) are a type of deep learning model widely used in image processing, object recognition, and computer vision. Compared to traditional artificial neural networks, CNN have fewer parameters and can effectively learn local features, making them a preferred choice for these tasks.

The Basics of Convolutional Neural Networks

At the core of CNN are artificial neural networks, which are models inspired by the functioning of the human brain. The main goal of these networks is to perform learning, interpret the learned information, and make autonomous decisions based on the interpretations. Artificial neural networks generally consist of three layers:

1. Input Layer: This is where the features are fed into the system. The number of nodes in this layer is equal to the number of features needed to best represent the data.

2. Hidden Layer: This layer transforms the values received from the input layer by applying certain coefficients. For example, threshold conditions can be applied at these nodes to produce a specific number of outputs.

3. Output Layer: In this layer, predictions or interpretations are made based on the findings from the hidden layer.

Historically, artificial neural networks were first introduced by Warren S. McCulloch and Walter Pitts in 1943. However, due to the limited computing power at the time, the potential of these models was not fully realized. By the 2000s, significant advancements in computing power led to increased success and popularity of neural networks. Despite this, the human brain, which serves as the inspiration for these models, contains approximately 100 billion neurons. Fully replicating this structure with current technology is not yet possible, but continuous advancements are being made.

Key Components of CNN

^{A convolutional neural network structure}

Convolutional Layer

The convolutional layer is the most important component of a CNN. It extracts local features from the input image using filters (kernels). Each filter scans a specific region of the image and performs a multiplication operation with the pixels in that region to create a feature map.

1. Filter (Kernel): These are usually 3x3 or 5x5 matrices used to detect features like edges, corners, or textures.

2. Stride: This determines how much the filter moves across the image. For example, a stride of 1 means the filter moves one pixel at a time.

3. Padding: This involves adding zero values around the edges of the image to preserve its size.

^{Convolution operation example (Created with artificial intelligence.)}

Pooling Layer

In CNN architectures, pooling layers are often placed between convolutional layers. The purpose of pooling is to reduce the number of parameters when images are too large, thereby shrinking the image while preserving important information. There are two main types of pooling: max pooling and average pooling.

^{Pooling layer example (Credit: Mayank Jain)}

1. Max Pooling: This method reduces the spatial dimensions of the input data by selecting the maximum value within a specific window. It helps extract dominant features while maintaining rotational and positional invariance.

^{Max Pooling (Credit: Afshine Amidi ve Shervine Amidi, CNN Handbook)}

^{Average Pooling (Credit: Afshine Amidi ve Shervine Amidi, CNN Handbook)}

Fully Connected Layer

The final step in CNN occurs in the fully connected layer. In this layer, all nodes and neurons in one layer are connected to the next layer. Although computationally complex and prone to overfitting, this layer plays a crucial role in learning. After applying a flattening operation to the data, the neural network performs the learning process.

^{Flatting example (Credit: Rubiscode.net)}

^{Working Logic of Fully Connected Layer (Credit: teknoloji.org)}

The Learning Process of CNN

The learning process of CNN involves the model learning meaningful features from input data and optimizing weights to make more accurate predictions. This process consists of forward propagation, loss calculation, backpropagation, optimization, and weight update steps.

Forward Propagation

Forward propagation is the process of passing input data through the CNN layers to produce an output prediction. The steps are as follows:

1. Input Layer: The input is usually an image, such as a 28x28 pixel handwritten digit or a 224x224x3 colored image.

2. Convolutional Layers: The input image is processed using filters (kernels) in the convolutional layer. Each filter scans a specific region of the image and creates a feature map.

3. Activation Function: After convolution, an activation function (usually ReLU) is applied to the feature map to introduce non-linearity.

4. Pooling Layer: The pooling layer reduces the size of the feature map, often using max pooling to select the maximum value in a window.

5. Fully Connected Layer: The features from the convolutional and pooling layers are fed into the fully connected layer, which combines them for classification or regression tasks.

6. Output Layer: Finally, the output layer (e.g., softmax) produces the model's predictions, such as classifying an image into a specific category.

Loss Calculation

The outputs from forward propagation are compared with the ground truth values using a loss function. Common loss functions include:

1. Cross-Entropy Loss: Used for classification tasks.

2. Mean Squared Error (MSE): Used for regression tasks.

The loss function measures the model's performance and is used to optimize the model.

Backpropagation

Backpropagation is an optimization process used to minimize the model's errors. It calculates the gradients of the loss function and updates the model's parameters (filters and weights). The steps are:

1. Gradient Calculation: The gradient of the loss function with respect to each parameter is calculated.

2. Chain Rule: Backpropagation uses the chain rule to propagate gradients backward through the layers.

3. Gradient Update: The gradients are used to update the filters and weights.

Parameter Update

The gradients calculated during backpropagation are used to update the model's parameters using optimization algorithms like Gradient Descent. This step minimizes the model's errors.

1. Gradient Descent: This method updates the parameters in the opposite direction of the gradients. The update rule is:

Where:

• θ: Model parameters (filters and weights),
• η: Learning rate,
• ∇L(θ): Gradient of the loss function.

2. Optimization Algorithms: Advanced algorithms like Momentum and Adam (Adaptive Moment Estimation) can also be used to improve learning efficiency.

Advantages of CNN

1. Parameter Efficiency: CNN use fewer parameters compared to fully connected layers, making them faster to train and less memory-intensive.

2. Local Feature Learning: CNN can effectively learn local features in images.

3. Scale and Transformation Invariance: Pooling layers make CNN more robust to scale and transformation changes.

Applications of CNN

CNN are widely used in the following areas:

1. Image and video understanding

2. Recommendation/prediction systems

3. Image classification

4. Image segmentation

5. Medical image processing

6. Natural language processing

7. Brain-computer interfaces

8. Time series analysis