Micrograd is an autograd engine that implements backpropagation to efficiently evaluate the gradient of a loss function and tune the weights of a neural network.

How can Micrograd be used?

Micrograd allows you to build out mathematical expressions and calculate the derivative of the output with respect to the inputs.

How many lines of code does Micrograd require?

Micrograd is a powerful yet simple autograd engine that enables neural network training with only 150 lines of code.

How can the derivative of a function be calculated?

The derivative of a function with respect to its inputs can be calculated by taking a small value of h and fixing the inputs at a certain point, then printing the slope which is the difference between the outputs divided by h.

What is the chain rule in calculus?

The chain rule in calculus allows us to calculate the derivative of a sum expression, which is the local influence of c on d.

Learn Neural Networks & Backpropagation with Python & PyTorch

Name: Learn Neural Networks & Backpropagation with Python & PyTorch
Uploaded: 2023-02-08 18:21:44
Description: Using Python and PyTorch, we can create and train a neural network with a forward pass, backward pass, and gradient descent update.

This article is a summary of a YouTube video "The spelled-out intro to neural networks and backpropagation: building micrograd" by Andrej Karpathy

TLDR Using Python and PyTorch, we can create and train a neural network with a forward pass, backward pass, and gradient descent update.

Backpropagation and its importance in neural network training

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Backpropagation allows us to evaluate the derivative of the output with respect to the inputs, giving us important information about how the inputs affect the output through the mathematical expression.
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Back propagation involves calculating the gradient along all intermediate values, including the derivative of the loss function with respect to the weights of a neural network.
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Backpropagation allows for optimization of neural networks by recursively applying the chain rule backwards through the computation graph.
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The backward function can be customized to propagate gradients and chain rule at each node, making it possible to compute complex neural networks.
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The trick used in deep learning to improve neural net performance is to calculate a single number that measures the total performance, called the loss.
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Backpropagation allows us to calculate the gradient for every single parameter in the neural network, giving us the ability to nudge them a tiny amount based on the gradient information to minimize loss.

Micrograd and its role in building and optimizing neural networks

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Building micrograd allows for an intuitive understanding of how neural network training works under the hood, which is crucial for developing more advanced AI technologies.
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Micrograd is what you need to train your networks and everything else is just efficiency, and it only consists of 100 lines of code for the autograd engine and a neural network library built on top of it.
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With micrograd, it's possible to backpropagate all the way through an entire MLP and into the weights of all the neurons.
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Implementing an actual training loop involves a forward pass, backward pass, and gradient descent update, which can be iterated to optimize the model's loss.
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Neural nets can have billions or even trillions of parameters, making them capable of solving extremely complex problems.

Q&A

What is Micrograd?

— Micrograd is an autograd engine that implements backpropagation to efficiently evaluate the gradient of a loss function and tune the weights of a neural network.
How can Micrograd be used?

— Micrograd allows you to build out mathematical expressions and calculate the derivative of the output with respect to the inputs.
How many lines of code does Micrograd require?

— Micrograd is a powerful yet simple autograd engine that enables neural network training with only 150 lines of code.
How can the derivative of a function be calculated?

— The derivative of a function with respect to its inputs can be calculated by taking a small value of h and fixing the inputs at a certain point, then printing the slope which is the difference between the outputs divided by h.
What is the chain rule in calculus?

— The chain rule in calculus allows us to calculate the derivative of a sum expression, which is the local influence of c on d.

Timestamped Summary

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00:00
Micrograd is a powerful yet simple autograd engine that enables neural network training with only 150 lines of code.
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19:52
Using Python, we can create expression graphs to calculate derivatives of functions with respect to variables.
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39:35
Using the chain rule, we can calculate the derivative of a sum expression and use manual backpropagation to influence the output of a two-layer neural network.
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58:46
Multiplying the local derivative with the global derivative, and using the chain rule, allows for the propagation of gradients through 10h for back propagation.
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1:15:21
Implementing a backward pass for a two-dimensional neuron with a 10h requires breaking up the 10h into an expression, using an intermediate variable and exponentiation, and propagating all dependencies before calling the backward function.
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1:37:29
PyTorch enables us to build complex mathematical expressions and neural networks, with a neuron class that takes in inputs, multiplies them with weights, adds a bias, and passes the result through a non-linearity to get an output.
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1:52:36
We successfully trained a neural net by implementing a training loop with a forward pass, backward pass, and gradient descent update to minimize the loss.
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2:10:17
We built up a neural network using PyTorch's forward and backward passes to correctly minimize loss and predict outputs.