The spelled-out intro to neural networks and backpropagation: building micrograd

Andre introduces himself as an experienced trainer of deep neural networks and outlines his goal for the lecture: to demystify the training process of neural networks by building and training a neural network from scratch in a Jupyter notebook, using a library called Micrograd. Micrograd is an autograd engine that facilitates backpropagation, a fundamental algorithm for training neural networks by efficiently calculating the gradient of a loss function with respect to the weights of the network.

Andre explains the concept of Micrograd, an autograd engine he released on GitHub, which implements backpropagation for neural networks. He guides through the step-by-step process of building Micrograd, commenting on its components and demonstrating its capabilities through mathematical expressions. The functionality of Micrograd is illustrated by creating a simple expression graph with two inputs and showing how to perform forward and backward passes to calculate gradients.

The lecture delves into the importance of understanding derivatives and the chain rule in the context of neural network training. Andre defines a scalar-valued function and explores the concept of derivatives at various points, demonstrating numerically how to approximate the derivative of a function. He emphasizes the significance of derivatives in indicating the sensitivity and slope of a function's response to changes in input.

Andre discusses the necessity of visualizing complex mathematical expressions and introduces a method to draw expression graphs using Graphviz, an open-source graph visualization software. He explains how to create nodes and edges for the graph and labels them for clarity. The process of visualizing the forward and backward passes of a mathematical expression is demonstrated, highlighting the computation of gradients for each node in the graph.

In this section, Andre manually implements backpropagation to illustrate the process of calculating gradients for each node in a computation graph. He emphasizes the importance of understanding the chain rule in calculus for combining local derivatives to compute the overall gradient with respect to the output. The process involves setting initial gradients and recursively applying the chain rule to propagate gradients backwards through the graph.

Andre identifies a bug related to gradient accumulation in the backpropagation process, where gradients are not reset after each update, leading to incorrect gradient values. He explains the importance of zeroing the gradients before each backward pass to ensure accurate gradient descent. The fix involves adding a method to reset gradients to zero for all parameters before the backward pass.

The lecture demonstrates how to use the calculated gradients to update the weights and biases of a neural network in a process known as gradient descent. Andre shows how to iteratively perform forward and backward passes, followed by updates to the network's parameters to minimize the loss function. He also discusses the importance of choosing an appropriate learning rate to avoid overshooting or slow convergence.

Andre compares the manual process of training a neural network with the functionalities provided by PyTorch, a production-grade deep learning library. He shows how to implement a neuron, layer, and multi-layer perceptron (MLP) in PyTorch, emphasizing the efficiency and simplicity of using tensors and built-in functions for operations like addition, multiplication, and activation.

The focus shifts to constructing a complete neural network model, starting from individual neurons to layers of neurons and finally to a full multi-layer perceptron (MLP). Andre outlines the process of defining the architecture of an MLP, including the input layer, hidden layers, and output layer, and demonstrates how to perform a forward pass through the network to obtain predictions.

Andre introduces the concept of loss functions as a measure of the neural network's performance, explaining how the mean squared error loss function works. He discusses the process of calculating individual loss components for each prediction and the ground truth, and how to aggregate these components into a total loss value that the network aims to minimize.

The lecture concludes with an iterative optimization process, where Andre demonstrates how to repeatedly perform forward and backward passes, followed by parameter updates to minimize the loss function. He highlights the importance of monitoring the loss and the predictions to ensure the network is converging towards accurate results. The process illustrates the fundamental workflow of training a neural network using gradient descent.