Brief Summary
This video explains the inner workings of neural network training by building a simplified autograd engine called Micrograd from scratch. It covers the concepts of derivatives, backpropagation, and gradient descent, illustrating them with practical examples. The video also compares Micrograd to PyTorch, a production-ready deep learning library, highlighting the similarities and differences in their implementation.
- Key takeaways: Neural networks are mathematical expressions that can be trained using backpropagation and gradient descent. Micrograd is a simplified autograd engine that demonstrates the core concepts of neural network training. PyTorch is a production-ready deep learning library that provides efficient implementations of these concepts.
Introduction
The video introduces the concept of neural network training and its underlying mechanisms. It explains that the goal is to iteratively tune the weights of a neural network to minimize a loss function, thereby improving the network's accuracy. Backpropagation, a core algorithm for efficient gradient evaluation, is highlighted as a key component of modern deep learning libraries like PyTorch and JAX.
Micrograd Overview
Micrograd is introduced as a simplified autograd engine that implements backpropagation. It allows users to build mathematical expressions and calculate their derivatives with respect to input variables. The video demonstrates how Micrograd can be used to build an expression graph with two inputs (a and b) and a single output (g), and then calculate the derivatives of g with respect to a and b.
Derivative of a Simple Function with One Input
The video explains the concept of derivatives and their significance in understanding the behavior of functions. It uses a simple function f(x) = 3x^2 - 4x + 5 as an example and demonstrates how to calculate the derivative numerically using the definition of the derivative. The derivative is interpreted as the slope of the function at a given point, indicating how the function responds to small changes in the input.
Derivative of a Function with Multiple Inputs
The video extends the concept of derivatives to functions with multiple inputs. It uses a function d(a, b, c) = a * b + c as an example and demonstrates how to calculate the derivatives of d with respect to a, b, and c numerically. The derivatives are interpreted as the sensitivity of the output d to small changes in each input variable.
Starting the Core Value Object of Micrograd and its Visualization
The video begins building the core data structure of Micrograd, the Value object. This object wraps a scalar value and stores information about its children (the values that produced it), the operation that created it, and its gradient. The video also introduces a visualization function, drawdot, which creates a graph representation of the expression graph built using Value objects.
Manual Backpropagation Example #1: Simple Expression
The video demonstrates manual backpropagation through a simple expression graph. It starts with the output node (l) and calculates the derivatives of l with respect to all the intermediate nodes (f, d, c, e, b, a) using the chain rule. The gradient of each node represents the derivative of the output with respect to that node, indicating how changing that node affects the output.
Preview of a Single Optimization Step
The video briefly previews the concept of gradient descent, which involves nudging the input variables in the direction of their gradients to minimize the output value. It demonstrates how nudging the input variables in the direction of their gradients can lead to a decrease in the output value.
Manual Backpropagation Example #2: A Neuron
The video demonstrates manual backpropagation through a simple neuron model. It calculates the derivatives of the neuron's output (o) with respect to its inputs (x1, x2), weights (w1, w2), and bias (b). The gradients are interpreted as the sensitivity of the output to changes in each input, weight, and bias.
Implementing the Backward Function for Each Operation
The video starts implementing the backward function for each operation in Micrograd. This function calculates the local derivatives of the operation and chains them with the global derivative to propagate the gradient back to the input nodes. The backward functions for addition, multiplication, and tanh are implemented.
Implementing the Backward Function for a Whole Expression Graph
The video implements the backward function for the entire expression graph. It uses topological sort to order the nodes in the graph so that the backward pass can be performed in the correct order. The backward function iterates through the nodes in reverse topological order, calling the backward function for each node to propagate the gradient.
Fixing a Backprop Bug When One Node is Used Multiple Times
The video addresses a common backpropagation bug that occurs when a node is used multiple times in an expression graph. The bug arises because the gradient is overwritten when the backward pass is performed on the node multiple times. The solution is to accumulate the gradients by using the plus equals operator instead of directly setting the gradient.
Breaking Up a Tanh, Exercising with More Operations
The video breaks down the tanh function into its atomic components (exponentiation, addition, subtraction, division) and implements the backward functions for these operations. This exercise demonstrates that the level of abstraction at which operations are implemented is flexible, as long as the local derivatives are known.
Doing the Same Thing but in PyTorch: Comparison
The video compares Micrograd to PyTorch, a production-ready deep learning library. It shows how to perform the same operations in PyTorch using tensors and demonstrates that the core concepts of backpropagation and gradient descent are similar in both libraries. PyTorch, however, provides more efficient implementations due to its use of tensors and parallel operations.
Building Out a Neural Net Library (Multi-Layer Perceptron) in Micrograd
The video starts building a neural network library in Micrograd. It defines the Neuron, Layer, and MLP classes, which represent individual neurons, layers of neurons, and multi-layer perceptrons, respectively. The video demonstrates how to create and forward an MLP with multiple layers.
Creating a Tiny Dataset, Writing the Loss Function
The video creates a tiny dataset with four examples and defines a loss function, mean squared error, to measure the performance of the neural network. The loss function calculates the difference between the network's predictions and the desired targets, providing a measure of the network's accuracy.
Collecting All of the Parameters of the Neural Net
The video implements a function to collect all the parameters (weights and biases) of the neural network. This function is used to update the parameters during gradient descent.
Doing Gradient Descent Optimization Manually, Training the Network
The video demonstrates manual gradient descent optimization. It iteratively performs the forward pass, calculates the loss, backpropagates the loss to calculate gradients, and updates the parameters in the direction of their gradients. This process is repeated until the loss converges to a minimum value.
Summary of What We Learned, How to Go Towards Modern Neural Nets
The video summarizes the key concepts covered in the lecture, including the nature of neural networks as mathematical expressions, the role of backpropagation and gradient descent in training, and the importance of zeroing gradients before each backward pass. It also discusses how the concepts learned in the video can be applied to more complex neural networks with billions of parameters.
Walkthrough of the Full Code of Micrograd on Github
The video provides a walkthrough of the full code of Micrograd on Github, explaining the different components and their functionalities.
Real Stuff: Diving into PyTorch, Finding Their Backward Pass for Tanh
The video dives into the PyTorch codebase to find the backward pass implementation for the tanh function. It highlights the complexity of production-ready libraries and the challenges of finding specific code pieces.
Conclusion
The video concludes by summarizing the key takeaways and encouraging viewers to explore the links provided in the video description for further learning and discussion. It also hints at a potential follow-up video to address common questions.
