micrograd: understanding backpropagation through a tiny implementation

Automatic differentiation can feel abstract when it is hidden inside a large framework. A small implementation exposes the data structure, the local derivative rules, and the order in which gradients are propagated.

Each scalar value can point to the values that produced it and retain the local operation. The forward pass builds a directed acyclic graph that can later be traversed in reverse.

Every supported operation contributes a local derivative. Backpropagation does not require a new global symbolic derivative for the whole network; it composes these local rules using the chain rule.

Starting from the final scalar objective, the backward pass propagates how much the objective changes with respect to each intermediate value. Gradients from multiple downstream paths are accumulated.

A compact neural-network layer can then be built from these scalar values. A neuron computes a weighted sum plus bias, followed by an activation; the autograd engine supplies gradients for the parameters.

• Backpropagation is repeated application of the chain rule on a computation graph.
• A framework's automatic differentiation still rests on explicit local derivative rules.
• A tiny implementation is useful for understanding, but it does not replace optimized tensor libraries for production-scale workloads.
• Understanding the scalar mechanism helps explain why matrix and tensor implementations need careful batching, memory, and numerical design.

This explainer sits between mathematical lessons on gradients and larger Transformer mechanics. The same habit applies throughout: start with the mathematical operation, make the data flow explicit, then inspect what the software implementation adds.