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

TLDRIn this lecture, Andre demonstrates the fundamentals of neural networks and backpropagation through the creation of Micrograd, a lightweight autograd engine. He builds a neural network from scratch in a Jupyter notebook, explaining each component's role in the training process. Andre clarifies complex concepts like gradients and loss functions, illustrating them with intuitive examples. The lecture dives into coding a simple MLP model, showcasing the network's ability to learn from data and improve accuracy through iterative weight tuning, all while emphasizing the simplicity of Micrograd's codebase compared to full-fledged libraries like PyTorch.

### Takeaways

- 📚 The presenter, Andre, has over a decade of experience training deep neural networks and introduces the concept of neural network training 'under the hood'.
- 🌟 The lecture demonstrates building 'micrograd', a library released by Andre on GitHub, which implements backpropagation for neural network training.
- 🔍 Micrograd is an autograd engine, which stands for automatic gradient, and it is used to evaluate the gradient of a loss function with respect to the weights of a neural network.
- 🎯 The core of modern deep neural network libraries like PyTorch or Jax is the backpropagation algorithm, which is also at the heart of micrograd.
- 🌱 The lecture includes a step-by-step guide to building mathematical expressions using micrograd, illustrating how to create and manipulate 'value' objects.
- 📈 Backpropagation is shown to start at the output node and recursively apply the chain rule from calculus to evaluate the derivative of the output with respect to all internal nodes and inputs.
- 🤖 Neural networks are described as mathematical expressions that take input data and weights to produce predictions or loss function outputs.
- 📉 The importance of understanding derivatives in neural network training is emphasized, as they provide information on how inputs affect the output and guide weight adjustments.
- 🔧 The micrograd library is shown to be a simple yet powerful tool for understanding and implementing neural network training with only a few lines of code.
- 👨🏫 The lecture aims to provide an intuitive understanding of how neural networks work and the fundamental role of backpropagation and gradient descent in training them.
- 🔄 The process of training a neural network involves forward passes to calculate predictions, backward passes to calculate gradients, and updates to the weights based on the gradients.

### Q & A

### What is the main focus of the lecture given by Andre?

-The lecture focuses on explaining neural network training, particularly the process of building and training a neural network from scratch using a library called micrograd, which the lecturer developed.

### What is micrograd and why is it significant in the context of this lecture?

-Micrograd is a library released by Andre that implements an autograd engine, which is short for automatic gradient. It is significant because it allows for the efficient evaluation of the gradient of a loss function with respect to the weights of a neural network, which is essential for training neural networks using backpropagation.

### Can you explain the role of backpropagation in training neural networks?

-Backpropagation is an algorithm that calculates the gradient of a loss function with respect to the weights of a neural network. It is used to iteratively tune the weights to minimize the loss function, thereby improving the accuracy of the network.

### How does micrograd represent mathematical expressions in neural networks?

-Micrograd represents mathematical expressions by wrapping numbers in value objects and building an expression graph. It maintains pointers to the value objects, allowing it to track how each value is derived from others, which is crucial for backpropagation.

### What is the purpose of the 'dot' attribute in micrograd's value objects?

-The 'dot' attribute in micrograd's value objects is used to access the actual value of the mathematical expression represented by the value object. It is used during the forward pass to evaluate the output of the network.

### How does micrograd utilize the chain rule from calculus during backpropagation?

-During backpropagation, micrograd starts at the output node and recursively applies the chain rule from calculus, moving backwards through the expression graph. This allows it to evaluate the derivative of the output with respect to all internal nodes and inputs.

### What is the significance of the derivative information provided by micrograd?

-The derivative information provided by micrograd is crucial as it indicates how changes in the inputs or weights affect the output of the neural network. This information is used to adjust the weights in a way that minimizes the loss function, improving the network's performance.

### Why is micrograd described as a scalar-valued autograd engine?

-Micrograd is described as a scalar-valued autograd engine because it operates on individual scalar values, such as negative four or two, rather than on multi-dimensional arrays or tensors. This simplification is used for educational purposes to illustrate the fundamental concepts of backpropagation and neural network training.

### What is the relationship between the mathematical expressions in micrograd and neural networks?

-The relationship between the mathematical expressions in micrograd and neural networks is that neural networks are a specific class of mathematical expressions. They take input data and weights as inputs and produce predictions or loss function values as outputs. Micrograd demonstrates how these expressions can be constructed and differentiated using backpropagation.

### How does Andre demonstrate the power of micrograd with a simple example?

-Andre demonstrates the power of micrograd by building a simple mathematical expression using addition and multiplication, visualizing the expression graph, and then performing a forward pass to calculate the output. He also shows how to run a backward pass manually to calculate the gradients, illustrating the core concepts of backpropagation.

### Outlines

### 🧠 Introduction to Neural Network Training

Andre, an experienced neural network trainer, introduces the concept of neural network training and the inner workings of backpropagation. He plans to demonstrate the training process using a blank Jupiter notebook, guiding viewers through building and training a neural network from scratch. Andre also discusses Micrograd, a library he released on GitHub, which implements backpropagation for efficient loss function gradient evaluation, essential for tuning neural network weights and improving accuracy.

### 📚 Understanding Micrograd and Automatic Gradient

The lecture delves into the details of Micrograd, an autograd engine that facilitates backpropagation, a fundamental algorithm in training modern deep neural networks. Andre explains the process of building mathematical expressions with Micrograd, showcasing its capabilities through various operations such as addition, multiplication, and exponentiation. He emphasizes the importance of understanding the derivative information provided by the gradients, which is crucial for tweaking the inputs to improve the output.

### 🔍 Derivative Insights and Numerical Approximations

Andre explores the concept of derivatives, explaining their significance in understanding the sensitivity and slope of a function at a specific point. He demonstrates how to numerically approximate derivatives using small increments and discusses the importance of avoiding excessively small values to prevent issues with floating-point arithmetic. The lecture also covers the evaluation of derivatives for more complex functions involving multiple inputs.

### 🌟 Building Expression Graphs and Visualizing Neural Networks

The script describes the construction of expression graphs using Micrograd, which are essential for visualizing the flow of operations in a neural network. Andre introduces a method to visualize these graphs, providing an intuitive understanding of how inputs are transformed through various operations to produce an output. This visual representation is crucial for understanding the forward pass in neural network training.

### 🚀 Implementing Backpropagation Manually

Andre walks through the process of manually implementing backpropagation, starting from the output and moving backwards through the expression graph. He illustrates how to calculate the gradient of the loss function with respect to each variable and operation in the graph, emphasizing the importance of this process in training neural networks to minimize the loss function.

### 🔧 Coding the Backward Pass and Gradient Accumulation

The script transitions into the coding phase, where Andre begins to implement the backward pass functionality within the Micrograd library. He discusses the importance of gradient accumulation, ensuring that gradients are correctly updated during the backpropagation process. This step is crucial for adjusting the weights of the neural network during training.

### 🌱 Growing Neural Networks with Micrograd

Andre demonstrates how to use Micrograd to build more complex neural network structures, such as multi-layer perceptrons. He explains the process of defining neurons, layers, and the entire neural network architecture, highlighting the simplicity of Micrograd's codebase. The lecture also touches on the efficiency of neural network training in production environments, contrasting it with the pedagogical approach used in Micrograd.

### 🔄 The Power of Automatic Backpropagation

The script covers the automation of the backpropagation process, which is essential for efficiently training neural networks. Andre discusses the implementation of the backward function in Micrograd, which automates the gradient calculation and propagation through the neural network. This automation is a significant step towards making neural network training practical for complex problems.

### 🔬 Debugging and Testing Neural Network Code

Andre highlights the importance of debugging and testing neural network code, pointing out a common mistake of not resetting gradients before the backward pass. He demonstrates how this can lead to incorrect gradient accumulation and emphasizes the need for careful implementation to ensure the neural network trains as expected.

### 🌐 Comparing Micrograd with PyTorch

The lecture concludes with a comparison between Micrograd and PyTorch, a production-grade deep learning library. Andre shows how Micrograd's implementation aligns with PyTorch's API and functionality, demonstrating the power and flexibility of neural network code. He also discusses the challenges of working with large codebases and the importance of understanding the underlying principles of neural network training.

### Mindmap

### Keywords

### 💡Neural Networks

### 💡Backpropagation

### 💡Micrograd

### 💡Autograd

### 💡Value Object

### 💡Forward Pass

### 💡Loss Function

### 💡Gradient

### 💡Derivative

### 💡Tensor

### Highlights

Introduction to the process of building Micrograd, a library that simplifies understanding of neural network training.

Micrograd is an autograd engine that implements backpropagation for efficient gradient evaluation in neural networks.

Backpropagation is essential for iteratively tuning neural network weights to minimize loss functions.

Building mathematical expressions with Micrograd involves creating a graph of operations from inputs to outputs.

The forward pass in neural networks calculates the output value of an expression given the inputs.

Backward pass initializes backpropagation, applying the chain rule to evaluate derivatives of the output with respect to inputs and weights.

Micrograd's value objects wrap numbers and track their transformation through mathematical operations.

Derivatives provide critical information on how inputs affect the output, guiding weight adjustments in neural networks.

Visualizing expression graphs helps understand the flow of data and gradients in neural network training.

Implementing basic operations like addition and multiplication is crucial for constructing complex neural network expressions.

The chain rule is fundamental to backpropagation, allowing the calculation of gradients for complex expressions.

Micrograd demonstrates that neural network training can be achieved with as little as 150 lines of code.

The importance of understanding derivatives for optimizing neural networks through gradient descent.

Practical demonstration of numerically approximating derivatives to understand function sensitivity at specific points.

Building a neural network from scratch using Micrograd involves defining neurons, layers, and the network architecture.

Loss functions, such as mean squared error, are used to quantify the performance of neural networks and guide optimization.

The necessity of resetting gradients to zero before each backward pass to prevent accumulation of gradient values.

Micrograd supports complex operations like exponentiation and division, expanding the range of expressible neural network functions.

Training a neural network involves iterative forward and backward passes, updating weights to minimize the loss.

Challenges in finding specific implementations within large, complex codebases like PyTorch, highlighting the simplicity of Micrograd.

The process of registering new operations in PyTorch to extend its functionality, similar to operations defined in Micrograd.