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

Andre introduces the lecture by outlining his decade-long experience with neural networks, particularly emphasizing the under-the-hood mechanics of neural network training. He plans to demonstrate building and training a neural network from scratch using a Jupyter notebook and Micrograd, an autograd engine he developed. The focus is to understand automatic differentiation, backpropagation, and their intuitive aspects through step-by-step code explanations, culminating in the manipulation and understanding of Micrograd’s functionality.

Andre dives deeper into explaining backpropagation, the core algorithm behind training neural networks by efficiently calculating gradients. He uses Micrograd to illustrate this by constructing and manipulating mathematical expressions. The discussion includes transforming simple mathematical inputs through various operations, emphasizing the process's intuitive grasp by calculating gradients. This example serves to clarify how neural networks, though complex, fundamentally rely on basic calculus and simple operations that Micrograd can handle.

The focus shifts to understanding derivatives in the context of neural training, where Andre employs basic calculus to explore how minor changes in inputs affect the output. This segment is crucial for appreciating how gradients are used to adjust neural network parameters during training. He uses simple numerical methods to estimate derivatives and explains the concept of the chain rule in calculus, which is pivotal in backpropagation for linking changes across multiple layers and operations within neural networks.

Andre continues with more complex examples to illustrate Micrograd’s utility in building and manipulating expression graphs. He constructs a multi-input mathematical expression, introducing the concept of 'value objects' in Micrograd that encapsulate data and operations. This part is rich with demonstrations on visualizing these expressions and understanding the backward pass, which calculates gradients with respect to all inputs, demonstrating the powerful capabilities of Micrograd in managing and understanding deep learning computations.

The discussion progresses to implementing fundamental operations such as addition and multiplication in Micrograd. Andre explains the importance of each operation and sets up the computational groundwork for building more complex neural network structures. He meticulously details the implementation of automatic differentiation within Micrograd, illustrating how gradients flow through operations and how these operations contribute to the neural network's learning process.

Andre employs a graphical representation to make the flow of data and the process of backpropagation through a neural network intuitive. He introduces functions for visualizing these graphs, thereby making it easier to understand how operations are interconnected and how gradients are propagated backward through the network. This visualization is key to grasping how adjustments to the network’s weights are computed, which directly impacts the network’s performance.

This part of the lecture delves into the specifics of how the gradient is calculated using the chain rule, a fundamental concept in calculus that is extensively used in training neural networks. Andre explains the multiplication of local derivatives to compute the gradient with respect to each node in the network, illustrating the process with clear examples and demonstrating how to apply these concepts in Micrograd to efficiently train neural networks.

Andre expands Micrograd's functionality by introducing more complex mathematical operations like exponentiation and division, explaining the mathematical reasoning behind these operations and their implementation. This extension is crucial for supporting a wider range of neural network architectures and functionalities, demonstrating the versatility and depth of Micrograd as a tool for understanding and building neural networks.

The final steps in building the neural network involve integrating multiple layers and activation functions, specifically discussing how multi-layer perceptrons (MLPs) are constructed. Andre covers the hierarchical nature of these models, from individual neurons to layers, and finally to a complete network, using Micrograd to illustrate these concepts vividly. This comprehensive overview ties together all the concepts discussed and shows the practical application of Micrograd in constructing and training complex neural network models.