Introduction to Backpropagation in Machine Learning

Key Concepts

• Backpropagation: Fundamental algorithm underpinning modern machine learning.
  • Common to various ML systems like GPT, AlphaFold, etc.
  • Foundation of ML field despite multitude of architectures and training data.

History

• Origins: Unclear but principles date back to the 17th century (Leibniz).
• Sepo Linna: Modern form proposed in 1970.
• 1986 Milestone: David Rumelhart, Geoffrey Hinton, Ronald Williams' paper.
  • Applied to multi-layer perceptrons.
  • Demonstrated effectiveness in solving problems and capturing representations.

Understanding Backpropagation

Basic Concept

• Problem Example: Fitting a curve to data points (X, Y) on a plane.
  • Aim: Find best-fitting curve y(x) using polynomial of degree 5.
  • Define coefficients (k0, k1, ..., k5).
  • Objective: Minimize “loss” (square distance between data points and curve).

Loss Function

• Loss (L): Function measuring quality of fit.
  • Loss depends on coefficients: L(k0, k1, ..., k5).
  • Goal: Find configuration of ki that minimizes loss.

Curve Fitter 6000 (Imaginary Machine)

• Manual Approach: Adjust knobs (coefficients) to minimize loss.
  • Inefficient and subjective.

Calculus and Derivatives

Introduction to Derivatives

• Concept: Measures rate of change of function.
  • Used to determine how adjustments affect output (loss).
  • Derivative Example: Function f(x), its derivative f'(x) is slope of tangent.
• Gradient Descent: Iterative process to find minimum loss using derivatives.

Scalars to Vectors

• From one-dimensional to multi-dimensional functions.
  • Use partial derivatives and gradient vectors.
  • Gradient Vector: Points to steepest ascent; used to find descent direction.

Mathematical Foundation

Simple Functions and Rules

• Building Blocks: Known derivatives for linear, polynomial, exponential functions, etc.
• Chain Rule: Essential for combining functions (core of backpropagation).
  • Enables derivative computations for complex functions.

Backpropagation Mechanics

• Computational Graph: Representation of loss calculation.
  • Nodes as basic operations (add, multiply).
  • Forward and backward pass (gradient propagation).
• Backward Pass: Calculate gradient by applying chain rule.
• Gradient Descent Iteration: Adjust coefficients, recalculate loss, and repeat.

Beyond Machine Learning: Brain Learning

• Question: Is backpropagation a good model for biological learning?
• Next Video: Exploration of synaptic plasticity and learning in biological brains.

Conclusion

• Stay tuned for the next part focusing on biological relevance and brain’s learning algorithms.