Essay
Embeddings for Product Managers
October 2025 · 6 min read · Glen Cornell
You don't need the math. You need one mental model: your product's content, and your users, can become points in a space where distance means similarity. Almost everything useful about embeddings falls out of that.
In 2013, a group of researchers showed something that still sounds like a magic trick. Take the word "king." Represent it as a list of numbers. Subtract the numbers for "man," add the numbers for "woman," and look at what you land nearest to. You land on "queen."
The canonical result from word2vec (2013). Once words are points in space, the step from 'man' to 'woman' runs roughly parallel to the step from 'king' to 'queen'. You can do math on meaning.
Arithmetic. On words. The model was called word2vec, and the result wasn't a parlor trick. It was a window into one of the most useful ideas in modern software, and one most product people still treat as somebody else's department. It shouldn't be. The intuition is simple, and once you have it, you start seeing product opportunities you couldn't see before.
What an embedding actually is
An embedding turns a thing into a point in space. A word, a sentence, a support ticket, a product, a user, anything. The point lives in a space with a lot of dimensions, hundreds or thousands, which sounds intimidating but doesn't need to be. The only rule that matters is this: things that are similar end up near each other, and things that are different end up far apart.
That's it. The whole concept is a map. On a real map, cities that are close together are geographically near. In an embedding space, things that are close together are similar in meaning. The "king minus man plus woman" trick works because the model arranged words so that the direction you walk to get from "man" to "woman" is roughly the same direction that takes you from "king" to "queen." Meaning became geometry. And once meaning is geometry, you can measure it, sort by it, and do math on it.
Why this is a product concern, not an ML detail
Here's the part PMs miss. Embeddings aren't a niche technique buried in the ML team's backlog. They're the quiet machinery under a surprising amount of what users already love, and an even larger amount of what they're about to expect.
each dot is a customer message; color is what it's actually about
Illustrative. Messages about the same thing cluster together even when they share no words. 'Where's my package' and 'hasn't arrived yet' land next to each other. That clustering is what lets software work with meaning instead of keywords.
Picture every customer message your product receives, turned into a point. Messages about billing cluster in one region. Messages about shipping cluster in another. The clustering happens on its own, from meaning, not from shared keywords. "Where is my package," "it still hasn't arrived," and "tracking says delivered but it's not here" all land in the same neighborhood, even though they barely share a word.
Look at what that one picture gives you for free. Search that understands intent instead of matching strings. Recommendations, because "similar" is just "nearby." Automatic grouping of tickets, reviews, or feedback into themes. Deduplication, because near-identical things sit on top of each other. Classification, because a new point inherits the label of its neighbors. Every one of these is the same operation underneath: find what's close.
The intuition that pays off most
If you take one thing from this, take the difference between keyword search and semantic search, because it's the clearest example of what embeddings change.
Old search matched characters. If a customer typed "how do I get my money back" and your help doc said "refund policy," the search found nothing, because the strings don't overlap. You'd have to anticipate every phrasing and stuff in synonyms by hand. Anyone who's run a help center knows that game, and knows you always lose it.
Semantic search matches meaning. "How do I get my money back" lands right next to "refund policy" in the space, because the model knows they're about the same thing, so the right document surfaces with zero shared words. This is why search inside good products suddenly got dramatically better. It stopped guessing at your keywords and started understanding your intent. The big recommendation engines, the ones behind your music discovery and your video feed, have run on exactly this for years: represent everything as points, serve up the nearby ones.
This is also how AI "reads your documents"
Embeddings are having a moment for one specific reason. They're how you give a language model the right context to answer a question about your data.
The pattern, called retrieval-augmented generation, is less complicated than the acronym. Embed all your documents into the space ahead of time. When a question comes in, embed the question too, find the handful of document chunks nearest to it, and hand just those to the model along with the question. The model answers using material it was never trained on, because you retrieved the relevant pieces and put them in front of it. That retrieval step, "find the nearest chunks," is pure embedding math. Every "chat with your docs" feature you've seen is doing this underneath.
It's worth seeing the through-line. The hard part of working with these models is getting the right context in front of them at the right moment. Embeddings are the main tool the industry uses to do that. They are how software decides what's relevant.
What to actually keep in your head
You don't need the math, but a few honest caveats will keep you from over-trusting the magic.
Similar is not the same as correct. Embeddings find what's related, not what's true. Two confidently wrong answers can sit right next to each other.
They inherit the world they learned from. The same arrangement that gives you "king minus man plus woman equals queen" also encodes the stereotypes in the training text. The geometry reflects the data, warts and all, which matters the moment you use it on people.
They're only as good as what you feed them and how you cut it up. If you embed a giant document as one point, you lose the ability to retrieve the relevant paragraph. How you chunk and what model you choose are real product decisions with real quality consequences, not plumbing to wave off.
And "similar" is defined by the model. Different embedding models draw the map differently. Switching models can quietly change what your product considers related, which is the kind of thing that breaks search in ways nobody can explain for a week.
The mental model is the deliverable
I'll close where I started, because the takeaway is small and it travels.
Your product's content and your users can become points in a space where distance means similarity. That single idea unlocks search that understands intent, recommendations, clustering, dedup, classification, and the retrieval that makes AI useful on your own data. It even crosses media: there are models that put text and images in the same space, so you can search photos by describing them.
You don't have to implement any of it. But the PM who carries this intuition asks better questions and spots opportunities the one who treats AI as a magic box walks right past. Embeddings turn meaning into geometry. Once you can see the map, you start noticing all the places your product could be using it, and isn't.