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But what is a neural network? | Deep learning chapter 1

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Understanding Neural Networks: Structure and Function

Neural Networks: A Primer
- Human Brain Analogy
  - Effortless recognition of complex patterns (e.g., handwritten digits)
  - Visual cortex processes diverse inputs as same idea
- The Challenge of Programming AI
  - Simple concept (recognizing a '3') becomes difficult for traditional programming
  - Highlights the need for Machine Learning and Neural Networks
- Relevance and Importance
  - Present and future of technology
What is a Neural Network?
- Inspired by the Brain
  - Neurons: Units holding numbers between 0 and 1
  - Activation: The numerical value held by a neuron
- Layered Structure
  - Input Layer
    - Represents pixels of the input image (e.g., 28x28 = 784 neurons)
    - Activation represents grayscale value (0 for black, 1 for white)
  - Output Layer
    - 10 neurons, each representing a digit (0-9)
    - Activation indicates confidence in the digit recognition
  - Hidden Layers
    - Intermediate layers between input and output
    - Responsible for complex pattern recognition
    - Example: Two hidden layers with 16 neurons each (arbitrary choice)
- Information Flow
  - Activations in one layer determine activations in the next
  - Loosely analogous to biological neuron firing
The Process of Recognition
- Trained Network Behavior
  - Input image activates input layer neurons
  - Pattern of activations propagates through layers
  - Output layer's brightest neuron indicates the recognized digit
- Hope for Hidden Layers: Hierarchical Feature Detection
  - Recognizing digits by combining components
  - Example: '9' has a loop and a line
  - Potential role of hidden layers:
    - Second-to-last layer: Detects subcomponents (e.g., a loop)
    - Second layer: Detects fundamental features (e.g., edges)
  - Generalizability: Useful for other image recognition tasks
  - Broader applications: Speech parsing, abstract thought
How Activations Propagate: The Math
- Core Mechanism: Combining Layer Activations
  - Goal: Combine pixels into edges, edges into patterns, patterns into digits
- Detecting Patterns (e.g., an edge in a specific region)
  - Parameters: Weights and Biases
    - Weights: Numbers associated with connections between neurons
      - Represent the importance of a connection
      - Organized into a grid (green for positive, red for negative)
    - Weighted Sum: Sum of activations from the previous layer multiplied by their respective weights
    - Bias: An additional number added to the weighted sum
      - Represents a threshold for neuron activation
- Squishing Output: Activation Functions
  - Goal: Output activation between 0 and 1
  - Sigmoid Function (Logistic Curve)
    - Squishes any real number into the [0, 1] range
    - Input 0 maps to 0.5, very negative to 0, very positive to 1
  - Output Activation: A measure of how positive the weighted sum is, after applying the sigmoid
Network Complexity
- Number of Parameters
  - Weights and biases for each connection
  - Example: 784 neurons * 16 neurons/layer * 2 hidden layers + output layer connections
  - Total: Approximately 13,000 weights and biases
- "Learning" Defined
  - Finding the correct settings for all weights and biases
  - Enables the network to solve the intended problem
- Manual Tuning (Thought Experiment)
  - Satisfying to understand what parameters mean
  - Aids in debugging and improving the network
Notation for Connections
- Vector Representation
  - Activations of a layer organized into a column vector
- Matrix Representation
  - Weights organized into a matrix
  - Matrix-vector product computes weighted sums efficiently
- Bias Vector
  - Biases organized into a vector and added to the matrix-vector product
- Applying Activation Function
  - Applied element-wise to the resulting vector
- Compact Expression
  - sigmoid(W * a + b)
  - W: Weight matrix, a: Activation vector, b: Bias vector
The Network as a Function
- Neurons as Functions
  - Take previous layer outputs, produce a value between 0 and 1
- Entire Network as a Function
  - Input: 784 pixel values
  - Output: 10 digit probabilities
  - Complex function with ~13,000 parameters
Future Steps: Learning
- How the network learns appropriate weights and biases from data
- Deeper dive into what the specific network is doing
Discussion on Activation Functions
- Sigmoid Function
  - Early choice, inspired by biological analogy
  - Can be difficult to train ("old school")
- ReLU (Rectified Linear Unit)
  - Modern choice, widely used
  - max(0, a) where a is the weighted sum
  - Easier to train, especially for deep networks
  - Simplification of biological activation (either off or on)