- 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.

- 🧠
**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:
- Wrap input values within a value object.
- Build the mathematical expression (e.g., combining various operations like addition, multiplication).
- Perform a forward pass to compute the output.
- 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:
- Initialize gradients at the final node.
- 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.