Show HN: Semantic Calculator (king-man+woman=?)
105 nxa 117 5/14/2025, 7:54:31 PM calc.datova.ai ↗
I've been playing with embeddings and wanted to try out what results the embedding layer will produce based on just word-by-word input and addition / subtraction, beyond what many videos / papers mention (like the obvious king-man+woman=queen). So I built something that doesn't just give the first answer, but ranks the matches based on distance / cosine symmetry. I polished it a bit so that others can try it out, too.
For now, I only have nouns (and some proper nouns) in the dataset, and pick the most common interpretation among the homographs. Also, it's case sensitive.
The prompt I used:
> Remember those "semantic calculators" with AI embeddings? Like "king - man + woman = queen"? Pretend you're a semantic calculator, and give me the results for the following:
The more I think about it the less surprised I am, but my initial thoughts were quite simply "now way" - surely an approximation of an NLP model made by another NLP model can't beat the original, but the LLM training process (and data volume) is just so much more powerful I guess...
Your embedding model is literally the translation layer converting the text to numbers. The transformers are the main processing unit of the embeddings. You can even see some self-reflection in the model as the transformer is composed of attention and a MLP sub-network. The attention mechanism generates the interrelational dependence of the data and the MLP projects up into a higher dimension before coming down so that this can untangle these relationships. But the idea is that you just repeat this process over and over. The attention mechanism has the benefit over CNN models because it has a larger receptive field, so can better process long range relationships (long range being across the input data) where CNNs bias for local relationships.
(what I meant to say is that it doesn't do embedding math "LIKE" the OP — not that it doesn't do embedding math at all.)
To clarify some of the issues:
I think you are misunderstanding the architecture of these models. The embedding sub-network is the translation of text to numeric tokens. You'll find mention of the embedding sub-networks in both the GPT3[3] and GPT4 papers. Though they are given lower importance than other works. While much smaller than the main network, don't forget that embedding networks are still quite large. For the smaller models they constitute a significant part of the total parameter count[4]After the embedding sub-network is your main transformer network. The purpose of this network is to perform embedding math! It is just that the goal is to do significantly more complicated math. Remember, these are learnable mappings (see Optimal Transport). We're just breaking it down into their two main intermediate mappings. But the embeddings still end up being a bottleneck. It is your literal gateway from words to numbers.
[0] https://en.wikipedia.org/wiki/Mass_noun
[1] https://www.merriam-webster.com/dictionary/data
[2] https://www.sciotoanalysis.com/news/2023/1/18/this-data-or-t...
[3] https://arxiv.org/abs/2005.14165
[4] https://arxiv.org/abs/2303.08774
[4] https://www.lesswrong.com/posts/3duR8CrvcHywrnhLo/how-does-g...
The rant about network architecture misses my point, which is that an LLM does not just do a linear transformation and a similarity search. Sure, in the most abstract sense it still just computes an output embedding from two input embeddings, but only in a very distant, pedantic way. (Actually, to be VERY pedantic, that would not even be true, because ChatGPT's tokenizer embeds tokens, not words. The in- and output of the model is more than just the semantic embedding of words; using two different but semantically equivalent words may result in different outputs with a transformer LLM, but not in a word semantics model.)
I just thought it was cool that ChatGPT is so good at it.
You're right that there's subjectivity but not infinitely so. There is a bound to this and that's both required for language to work and for us to build these models. I did agree that the data one was tricky so not really going to argue, I was just pointing out a critical detail given that the models learn through pattern matching rather than a dictionary. It's why I made the comment about humans. As for ruler minus crown, I gave my explication, would you care to share yours? I'd like to understand your point of view so I can better my interpretation of the results, because frankly I don't understand. What is the semantic relationship being changed if not the attribute of ruler?
The architecture part was a miscommunication. I hope you understand how I misunderstood you when you said "this doesn't do embedding math like OP!". It is clear I'm not alone either.
To be pedantic, people generally refer to the tokenization and embedding simply as embedding. It's the common verbiage. This is because with BPE you are performing these steps simultaneously and the term is appropriate given the longer usage in math.I was just trying to help you understand a different viewpoint.
(some might say all an LLM does is embeddings :)
Curious tool but not what I would call accurate.
Is the famous example everyone uses when talking about word vectors, but is it actually just very cherry picked?
I.e. are there a great number of other "meaningful" examples like this, or actually the majority of the time you end up with some kind of vaguely tangentially related word when adding and subtracting word vectors.
(Which seems to be what this tool is helping to illustrate, having briefly played with it, and looked at the other comments here.)
(Btw, not saying wordvecs / embeddings aren't extremely useful, just talking about this simplistic arithmetic)
India - Asia + Europe = Italy
Japan - Asia + Europe = Netherlands
China - Asia + Europe = Soviet-Union
Russia - Asia + Europe = European Russia
calculation + machine = computer
I'll have to mediate on that.
actor - man + woman = actress
garden + person = gardener
rat - sewer + tree = squirrel
toe - leg + arm = digit
100%
And, worse, most latent spaces are decidedly non-linear. And so arithmetic loses a lot of its meaning. (IIRC word2vec mostly avoided nonlinearity except for the loss function). Yes, the distance metric sort-of survives, but addition/multiplication are meaningless.
(This is also the reason choosing your embedding model is a hard-to-reverse technical decision - you can't just transform existing embeddings into a different latent space. A change means "reembed all")
https://neal.fun/infinite-craft/
It provides a panel filled with slowly moving dots. Right of the panel, there are objects labeled "water", "fire", "wind", and "earth" that you can instantiate on the panel and drag around. As you drag them, the background dots, if nearby, will grow lines connecting to them. These lines are not persistent.
And that's it. Nothing ever happens, there are no interactions except for the lines that appear while you're holding the mouse down, and while there is notionally a help window listing the controls, the only controls are "select item", "delete item", and "duplicate item". There is also an "about" panel, which contains no information.
[0] https://youtu.be/8-ytx84lUK8
Are you using word2vec for these, or embeddings from another model?
I also wanted to add some flavor since it looks like many folks in this thread haven't seen something like this - it's been known since 2013 that we can do this (but it's great to remind folks especially with all the "modern" interest in NLP).
It's also known (in some circles!) that a lot of these vector arithmetic things need some tricks to really shine. For example, excluding the words already present in the query[1]. Others in this thread seem surprised at some of the biases present - there's also a long history of work on that [2,3].
[1] https://blog.esciencecenter.nl/king-man-woman-king-9a7fd2935...
[2] https://arxiv.org/abs/1905.09866
[3] https://arxiv.org/abs/1903.03862
The dictionary is based on https://wordnet.princeton.edu/, no word2vec. It's just a plain lookup among precomputed embeddings (with mxbai-embed-large). And yes, I'm excluding words that are present in the query because.
It would be interesting to see how other models perform. I tried one (forgot the name) that was focused on coding, and it didn't perform nearly as well (in terms of human joy from the results).
> a drug (such as opium or morphine) that in moderate doses dulls the senses, relieves pain, and induces profound sleep but in excessive doses causes stupor, coma, or convulsions
https://www.merriam-webster.com/dictionary/narcotic
So we can see some element of losing time in that type of drug. I guess? Maybe I’m anthropomorphizing a bit.
blue + red = yellow (87%) -- rgb, neat
black + {red,blue,yellow,green} = white 83% -- weird
[1]: https://github.com/GrantMoyer/word_alignment
Other stuff that works: key, door, lock, smooth
Some words that result in "flintlock": violence, anger, swing, hit, impact
I built a game[0] along similar lines, inspired by infinite craft[1].
The idea is that you combine (or subtract) “elements” until you find the goal element.
I’ve had a lot of fun with it, but it often hits the same generated element. Maybe I should update it to use the second (third, etc.) choice, similar to your tool.
[0] https://alchemy.magicloops.app/
[1] https://neal.fun/infinite-craft/
Also, if it gets buried in comments, proper nouns need to be capitalized (Paris-France+Germany).
I am planning on patching up the UI based on your feedback.
Or maybe they would all be completely inscrutable and man-woman would be like the 50th strongest result.
Good to understand this bias before blindly applying these models (Yes- doctor is gender neutral - even women can be doctors!!)
That could be seen as trying to find the true "meaning" of a word.
Can not personally find the connection here, was expecting father or something.
High dimension vector is always hard to explain. This is an example.
I’ve been unable to find it since. Does anyone know which site I’m thinking of?
paleolith + cat = Paleolithic Age
paleolith + dog = Paleolithic Age
paleolith - cat = neolith
paleolith - dog = hand ax
cat - dog = meow
Wonder if some of the math is off or I am not using this properly
Getting to cornbread elegantly has been challenging.
woman + intelligence = man (77%)
Oof.
hacker - code = professional golf
Accurate.
man+vagina=woman (ok that is boring)
https://en.m.wikipedia.org/wiki/Isle_of_Man
Edit: these must be capitalized to be recognized.
I think you need to disable auto-capitalisation because on mobile the first word becomes uppercase and triggers a validation error.
great idea, but I find the results unamusing
(Goshawks are very intense, gyrs tend to be leisurely in flight.)
Very few papers that actually say something meaningful are left unnoticed, but as soon as you say something generic like "language models can do this", it gets featured in "AI influencer" posts.
queen - woman + man = drone
Navratilova - woman + man = Lendl
female + age = male
rice + fish + raw = meat
hahaha... I JUST WANT SUSHI!
this is pretty fun
hmm...
six (84%)
Close enough I suppose