Convolutional Neural Networks (CNNs) Lecture Notes

Introduction

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• Focus of the lecture: Convolutional Neural Networks (CNNs) after discussing Feedforward Networks.

Overview of CNNs

• Previous discussions covered origins of deep learning and feedforward networks.
• Introduction to a popular architecture: Convolutional Neural Networks.
• Example used: Number recognition.
• Resource provided by Adam Harley for interactive experimentation with CNNs.

Key Differences Between Feedforward and Convolutional Networks

• Feedforward networks build layers of abstraction but often appear random.
• CNNs show clearer layers of abstraction.

Network Structure

• Input: Individual pixels of the image.
• Output: Patterns classified (numbers 0 to 9).
• Layers involved:
  • 2 Convolutional layers
  • 2 Pooling layers
  • 2 Fully connected layers

Input Details

• Image stored as a matrix of pixel values (Matrix = Channel).
• Typical digital images have 3 channels (RGB).
• Simplified assumption: Single channel (luminance) with pixel values ranging from 0 (dark) to 255 (bright).
• Other information can be represented similarly (e.g., speech as a matrix of frequency values).

Convolutional Layer Explained

• Named after the convolutional operator (dot product of functions).
• Implemented as a feature detector (filter/kernel).
• Kernel: A small matrix that moves across the input image, producing a feature map.
• Example: Kernels detecting edges, corners, shapes.
• Importance of non-linearity (ReLU) applied to feature maps.

Kernels and Feature Maps

• Initial kernels detect simple patterns (edges, shapes).
• Each convolutional layer can have multiple kernels.
• Example: First layer has 6 kernels detecting basic patterns.
• Higher layers incorporate more complex kernels for detecting shapes and structures.

Pooling Layers

• Purpose: Downsample feature maps to reduce overfitting and speed up calculations.
• Type used: Max pooling.
• Kernel slides across feature maps to save the largest pixel value.
• Result: Retains important features while reducing spatial size.

Layer Abstraction in CNNs

• Repeat convolutional and pooling layers to build more abstraction.
• Higher layers detect complex features by combining lower-level features.
• Example: 16 kernels in a later layer detect more intricate structures.

Classifier in CNNs

• Fully connected layers classify the high-level abstracted features.
• Example structure: First layer with 120 neurons, second layer with 100 neurons.
• Adam Harley emphasizes how weights and biases are adjusted during backpropagation and gradient descent.

Generalizations and Overlooked Details

• Generalizations made for simplicity:
  • Hyperparameters (kernel size, stride, pooling types).
  • Specifics of tuning kernel coefficients during learning.
• Additional resources mentioned for deeper understanding.

Limitations and Future Discussions

• CNNs excel at image classification but struggle with tasks like natural language processing (which requires memory).
• Future videos will cover networks designed for language processing.

Learning Resources

• Brilliant.org offers courses on deep learning and CNNs.
• Courses provide intuitive explanations and problem-solving opportunities.
• Promotion for 20% off annual premium subscription for early sign-ups.

Conclusion

• Encourage support for content and topic suggestions.
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