The roadmap from ops to GPT

This deep dive has a sequence, and that sequence is not cosmetic. It is dependency order.

You do not want attention before vectors, learning before gradients, or gradients before computational graphs. Each stage gives language and structure to the next one. This lesson is the map of that order.

Why the Order Matters

If we shuffled the topics of this course, the later sections would become harder than they need to be. The roadmap exists to prevent that.

We start with small visible computations because later ideas depend on them. Once you see the dependency order, the course stops looking like a random topic list and starts looking like a built path.

From Operations to Learning

We begin with scalar values, elementary operations, expressions, and dependency graphs. That gives us a picture of computation as structure, not just arithmetic. Once the graph exists, we can ask not only what value was produced, but also what depends on what and how influence moves through the system.

That opens the door to gradients. Local derivatives, chain rule on a graph, reverse-mode autodiff, and gradient accumulation explain how the system can measure how earlier values affect later results. Then we turn that into learning through parameters, updates, and optimization.

Without this stage, training feels like a black box. With it, learning becomes a mechanical process.

From Learning to Representation

Once we understand learning at the scalar level, we move into larger numerical structures: vectors, matrices, embeddings, and projections. The values are no longer single scalars, but the core ideas still carry over. Computations still compose, parameters can still be learned, and gradients still guide updates.

This stage explains how symbols become usable numerical representations, and why later attention mechanisms have something meaningful to operate on.

From Representation to GPT Behavior

After representations come the mechanisms that make GPT feel like GPT: attention, multi-step information mixing, transformer blocks, language modeling, the training loop, and the inference loop.

By this point, those ideas should land as extensions of earlier machinery rather than as alien new magic. You can connect the visible interface of a GPT to the internal computations that make that interface possible.

You do not need to master the whole map in advance. The point is to know where you are, why this lesson comes before the next one, and what later ideas the current lesson is preparing you for.

Tiny Checkpoint

Answer briefly:

1. Why do computational graphs come before gradients?
2. Why do gradients come before optimization?
3. Why do vectors and embeddings come before attention?