Lecture Notes on Micrograd and Neural Networks

Introduction

• Speaker: Andre, with over a decade of experience in deep neural networks.
• Objective: Understand the inner workings of neural network training, specifically through the library Micrograd.

Overview of Micrograd

• Definition: Micrograd is an autograd engine, implementing backpropagation to evaluate the gradient of a loss function efficiently.
• Importance of Backpropagation: Core algorithm for modern deep learning libraries (e.g., PyTorch, JAX).

Building Micrograd

• Starting Point: Blank Jupyter notebook.
• Value Object: Key component to wrap scalar values and build mathematical expressions.
  • Supports operations like addition, multiplication, exponentiation, etc.
• Expression Graph: Micrograd constructs a graph of operations and retains pointers to input values.

Forward and Backward Pass

• Forward Pass: Calculate the output of an expression (e.g., g = f(a, b)).
• Backward Pass: Initializes backpropagation to compute gradients using the chain rule.
  • Example: Compute a.grad and b.grad to understand how changes in inputs affect the output.

Mathematical Expressions and Neural Networks

• Neural Networks as Expressions: They can be seen as complex mathematical expressions built from simple operations.
• Understanding Derivatives: Derivatives tell how sensitive a function's output is to changes in its inputs.
• Scalar Values vs. Tensors: Micrograd operates at a scalar level for pedagogical purposes, while real neural networks use tensors for efficiency.

Code Implementation

• Micrograd Size: The core backpropagation engine is around 100 lines of code, demonstrating that neural networks can be understood at a fundamental level with a simplified approach.
• **Structure of Micrograd:
  • engine.py: Contains the core functionality (value object, gradients, backward method).
  • nn.py: Defines neurons, layers, and multi-layer perceptrons (MLPs).

Neural Network Training

• Basic Steps:
  1. Forward pass to compute predictions.
  2. Compute loss (e.g., mean squared error).
  3. Backward pass to compute gradients.
  4. Update weights using gradient descent.
• Learning Rate: A hyperparameter that controls the step size during weight updates.

Key Concepts

• Chain Rule: Essential for understanding backpropagation. It allows gradients to be computed for complex nested functions.
• Topological Sorting: Ensures that nodes in a computational graph are processed in the correct order during backpropagation.
• Efficiency and Scaling: Micrograd is educational; production-level libraries like PyTorch optimize for performance using tensors and parallelism.

Summary

• Final Thoughts: Micrograd provides a simple and effective way to understand the principles behind neural networks and backpropagation.
• Real-World Applications: Techniques learned through Micrograd are applicable in training complex models in libraries like PyTorch.
• Encouragement to Explore Further: Suggested resources, forums, and discussions for continued learning.