Focus: Training of neural networks, specifically using Micrograd.
Goal: To define and train a neural network, exploring how it works under the hood.
Overview of Micrograd
Micrograd is an autograd engine, short for automatic gradient, that implements backpropagation.
Backpropagation is crucial for efficiently evaluating the gradient of a loss function relative to the weights of a neural network.
Key Concepts
Neural Networks as Mathematical Expressions
Neural networks take input data and weights to produce predictions or loss functions.
They can be likened to complex mathematical expressions.
Understanding Gradients
The gradient provides information about how changes in weights affect the output (loss).
The slope of the function at a point gives insights into how the output responds to small changes in input.
Implementation of Micrograd
Value Object
Core component that wraps scalar values and maintains operation history.
Supports operations like addition, multiplication, and more through operator overloading.
Each operation creates an expression graph.
Forward and Backward Pass
Forward Pass: Compute the value of the output (e.g., g) using .data.
Backward Pass: Initiate backpropagation from the output to calculate gradients using the chain rule.
Example: If g = f(a, b), then gradients g_a and g_b show how g changes with a and b.
Mathematical Operations
Micrograd allows addition, multiplication, power, negation, and other operations to form complex expressions.
Graph Visualization: Tools to visualize how expressions are built and how data flows through the network.
Building a Neural Network
Neurons: Basic units that compute weighted sums of inputs and apply activation functions (e.g., ReLU, tanh).
Layers: Composed of multiple neurons and handle input/output transformations.
Multi-layer Perceptron (MLP): Stacks layers to create a deeper network for complex tasks.
Training Neural Networks
Loss Function: Measures the difference between target outputs and predictions.
Example used: Mean Squared Error.
Optimization: Adjust weights to minimize loss through gradient descent:
Forward pass to calculate outputs and loss.
Backward pass to compute gradients.
Update weights in the direction that reduces loss.
Learning Rate: Affects how significantly to adjust weights; must be tuned for effective training.
Summary of the Lecture
Micrograd provides a straightforward framework to understand neural networks and backpropagation.
Insights into how gradients work and the structure of neural networks can simplify complex concepts in deep learning.
The learning process involves iterating through forward and backward passes, adjusting the weights based on observed gradients to improve prediction accuracy.
Conclusion
Micrograd is a pedagogical tool to grasp neural network training fundamentals.
The lecture emphasized the simplicity and efficiency of understanding neural networks under the hood, preparing for practical applications in frameworks like PyTorch.
Resources
Additional links and discussion forums will be provided in the video description.