You are expecting too much out of this basic approach. The "simple" similarity search in word2vec (used in https://semantle.com/ if you haven't seen it) is based on _multiple_ embeddings like this one (it's a simple neural network not a simple embedding).

This is a simple example where it scores their frequency. If you scored every word by their frequency only you might have embeddings like this:

  act: [0.1]
  as:  [0.4]
  at:  [0.3]
  ...

That's a very simple 1D embedding, and like you said would only give you popularity. But say you wanted other stuff like its: Vulgarity, prevalence over time, whether its slang or not, how likely it is to start or end a sentence, etc. you would need more than 1 number. In text-embedding-ada-002 there are 1536 numbers in the array (vector), so it's like:

  act: [0.1, 0.1, 0.3, 0.0001, 0.000003, 0.003, ... (1536 items)]
  ...

The numbers don't mean anything in-and-of-themselves. The values don't represent qualities of the words, they're just numbers in relation to others in the training data. They're different numbers in different training data because all the words are scored in relation to each other, like a graph. So when you compute them you arrive at words and meanings in the training data as you would arrive at a point in a coordinate space if you subtracted one [x,y,z] from another [x,y,z] in 3D.

So the rage about a vector db is that it's a database for arrays of numbers (vectors) designed for computing them against each other, optimized for that instead of say a SQL or NoSQL which are all about retrieval etc.

So king vs prince etc. - When you take into account the 1536 numbers, you can imagine how compared to other words in training data they would actually be similar, always used in the same kinds of ways, and are indeed semantically similar - you'd be able to "arrive" at that fact, and arrive at antonyms, synonyms, their French alternatives, etc. but the system doesn't "know" that stuff. Throw in Burger King training data and talk about French fries a lot though, and you'd mess up the embeddings when it comes arriving at the French version of a king! You might get "pomme de terre".

King doesn’t need to appear commonly with prince. It just needs to appear in the same context as prince.

It also leaves out the old “tf idf” normalization of considering how common a word is broadly (less interesting) vs in that particular document. Kind of like a shittier attention. Used to make a big difference.

It doesn't even work as described for popularity - one word starts at 49,999 and one starts at 0.

Yeah, that is a poorly written description. I think they meant that each word gets a unique index location into an array, and the value at that word's index location is incremented whenever the word occurs.

It's a document embedding, not a word embedding.

Maybe the idea is to order your vocabulary into some kind of “semantic rainbow”? Like a one-dimensional embedding?