The next module is a big one, the machine behind every language model, so let us make sure this one is fully set before we climb. Here is the whole of embeddings in three plain beats.

A word is a position. Not a label, a place in a space of hundreds of sliders, sitting near the words it behaves like. That is what an embedding is.

Relationships became directions. Because every word had to sit near its relatives all at once, the space arranged itself so that shared relationships point the same way. That is why king minus man plus woman lands on queen: a relationship turned into a move you can make.

Meaning depends on the sentence. A single fixed position blurs words like "bank" that mean several things, so the real systems recompute each word's position from the words around it, every time.

That last beat is the door into the next module. Recomputing a word's position by letting it weigh every other word in the sentence is not free, it needs a specific machine. That machine is the transformer, and building it is where we go next.

If "a word is a position, relationships are directions, and context shifts the position" feels solid, you are ready. If it feels shaky, the earlier slides in this chapter are worth a second pass before you go on. There is no rush.