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

The Nugget

Neural network training is fundamentally about creating and optimizing mathematical expressions. The core technique involves backpropagation, where gradients are calculated and used to iteratively adjust network weights, minimizing a loss function and thereby improving network predictions.

Make it stick

🧠 Neural network as a mathematical expression: Just a structured way to apply linear algebra for data classification or prediction.
🦾 Backpropagation: Applies the chain rule from calculus to propagate error gradients back through the network layers.
🌱 Gradient descent: Iteratively updating weights in the negative direction of gradients to reduce error.
✨ Loss function: Measures how well neural network predictions match target values; the goal is to minimize this loss.

Micrograd: A minimalistic autograd library showcasing the inner workings of backpropagation by evaluating gradients of loss functions efficiently.
Autograd (Automatic Differentiation): Core aspect of backpropagation, automates the calculation of gradients.
Example Process:
1. Wrap input values within a value object.
2. Build the mathematical expression (e.g., combining various operations like addition, multiplication).
3. Perform a forward pass to compute the output.
4. Execute a backward pass to compute the necessary gradients.

Derivatives indicate how changes in input values affect the output.
Numerical gradient calculation provides an approximate derivative using a small change (h) in input values.
Simple example using (f(x) = 3x^2 - 4x + 5): The derivative indicates the slope, which tells how much the function's value grows or shrinks with small changes in x.

By representing operations on inputs as nodes and edges, a computational graph is formulated.
Visualizing this graph helps understand both forward pass (computing values) and backward pass (computing gradients).

Backpropagation involves propagating gradients from the output layer back to the input nodes using the chain rule.
Gradients are accumulated by traversing the computational graph in reverse order.
Example Backpropagation Steps:
1. Initialize gradients at the final node.
2. Use the chain rule to traverse back, computing and distributing gradients to all preceding nodes.

Neuron: Basic unit with weights and bias, computes weighted sum of inputs passed through an activation function (e.g., tanh).
Layer: Collection of neurons, evaluated independently.
Multi-layer Perceptron (MLP): Consists of multiple layers where the output of one layer serves as the input to the next layer.

Begin with random weights and biases, evaluate network predictions, compute loss, and use gradients to adjust weights iteratively to minimize the loss.
Adjusting learning rates and proper initialization are essential to prevent issues like exploding or vanishing gradients.

"Now specifically what I would like to do is I would like to take you through building of micrograd... it implements backpropagation."
"Micrograd will in the background build out this entire mathematical expression."
"Neural networks are just a mathematical expression... Backpropagation is significantly more general."
"The gradients are telling you how much changing the input values will affect the output."
"The only reason that the previous thing worked is that this is a very simple problem... the gradients ended up accumulating and effectively gave us a massive step size."

This summary contains AI-generated information and may have important inaccuracies or omissions.