The Essence of Neural Networks (As Explained by Karpathy)

Hi there! I'm Shrijith Venkatrama, founder of Hexmos. Right now, I’m building LiveAPI, a tool that makes generating API docs from your code ridiculously easy.

In this post - I share a few key points from Karpathy's introduction to neural networks.

• A neural network is "just" a mathematical expression that transforms input data into predictions (our output).
• It can be represented as a graph.
• Each node in this graph is essentially a Value object.
• In micrograd, this Value is simply a static integer or float. In more advanced libraries, it can be a vector or tensor.
• However, whether you use integers, floats, vectors, or tensors, the fundamental principles remain the same.
• The real question is: How do we determine the value at each node to construct a meaningful mathematical expression?
• This is precisely what "training" a neural network is about.
• Training involves refining the Value at each node so that the input-output mapping aligns with our expectations across a broad set of inputs.
• But how is training achieved? The key technique is called "backpropagation."
• At each node, we can perform backpropagation using autograd.
• A crucial concept here is the "loss function," which quantifies how close or far the actual output of the neural network is from the ideal output.
• The objective of training is to minimize this loss.
• This is done using the "chain rule" to compute derivatives such as dg/da and dg/db (the derivative of the output with respect to the inputs).
• We also compute derivatives for all intermediate nodes—dg/dc, dg/dd, dg/de, dg/df, and so on.
• These derivatives tell us how the inputs and intermediate nodes influence the final output.

Reference:

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