Step-by-Step Neural Network Training

In this extensive video, Andrej Karpathy provides a detailed, step-by-step explanation of backpropagation and the training of neural networks, assuming only basic knowledge of Python and a basic recollection of high school calculus. The video starts with an overview of micrograd, a minimalistic autograd engine that Andrej developed. Micrograd allows the construction and differentiation of mathematical expressions, which are essential for training neural networks. The video then delves into the core concepts of derivatives and backpropagation, explaining how the derivative of a simple function can be computed and how this extends to functions with multiple inputs. Andrej builds a value object class that can handle basic arithmetic operations and tracks the computational graph for backpropagation. Using this value object, he demonstrates manual backpropagation on simple expressions and a neuron, explaining how the chain rule is applied recursively through the computational graph. The video then transitions to implementing more complex operations like exponentiation and division, and shows how to break down a tanh function into atomic operations. Andrej also compares this manual implementation with PyTorch, showing how the same operations can be performed using this popular deep learning library. The video culminates in building a multi-layer perceptron (MLP), training it on a simple dataset using gradient descent, and visualizing the computational graph. Throughout, Andrej emphasizes the importance of understanding the underlying mechanics of neural networks and backpropagation, providing a solid foundation for more advanced studies in deep learning.