Lecture Notes: Neural Networks and Activation Functions

Introduction

• Neural Networks: Systems designed to mimic the human brain.
• Purpose: Transform data to uncover patterns, much like the Pythagorean theorem unravels geometric relationships.

Importance of Data Transformation

• Raw data is often not suitable for direct use by algorithms.
• Data Transformation: Essential for effective learning, prediction, and problem-solving.
• Pre-processing Steps:
  • Normalization: Scaling data to a standard range.
  • Feature Extraction: Identifying important patterns or features.
  • Encoding Categorical Variables: Converting non-numeric data to a numeric format.

Role of Activation Functions

• Activation Functions: Introduce non-linearities into the network, crucial for modeling complex relationships.
• Without them, networks would only learn linear relationships, limiting pattern recognition capabilities.

Common Activation Functions

Rectified Linear Unit (ReLU)

• Functionality: Transfers positive input values unchanged; converts negatives to zero.
• Advantages:
  • Simple and efficient computation.
  • Faster learning compared to sigmoid or tanh functions.
  • Avoids the Vanishing Gradient problem.
• Drawbacks:
  • Dying Neurons: Neurons stop learning due to zero outputs.
  • Sensitive to outliers.

Leaky ReLU

• Difference from ReLU: Allows negative inputs to pass with a small slope.
• Advantage: Mitigates dying neurons by keeping small positive outputs for negative inputs.

Sigmoid Function

• Output Range: Transforms inputs to a range between 0 and 1.
• Drawbacks:
  • Vanishing Gradient Issue: Makes deep network layers less sensitive to training.

Vanishing Gradient Problem

• Explanation: Gradients diminish as they move backward through deep layers, akin to whispered instructions losing volume.
• Solutions:
  • Use different activation functions.
  • Carefully initialize weights.
  • Ensure strong gradient signals during training.

Conclusion

• Choosing Activation Functions: Critical for addressing dying neurons and vanishing gradients.
• Task-Specific Selection: Choose the most suitable activation function based on the task requirements.

Understanding these aspects ensures better learning outcomes in neural networks.