> The 2D map analogy was a nice stepping stone for building intuition but now we need to cast it aside, because embeddings operate in hundreds or thousands of dimensions. It’s impossible for us lowly 3-dimensional creatures to visualize what “distance” looks like in 1000 dimensions. Also, we don’t know what each dimension represents, hence the section heading “Very weird multi-dimensional space”.5 One dimension might represent something close to color. The king - man + woman ≈ queen anecdote suggests that these models contain a dimension with some notion of gender. And so on. Well Dude, we just don’t know.
nit. This suggests that the model contains a direction with some notion of gender, not a dimension. Direction and dimension appear to be inextricably linked by definition, but with some handwavy maths, you find that the number of nearly orthogonal dimensions within n dimensional space is exponential with regards to n. This helps explain why spaces on the order of 1k dimensions can "fit" billions of concepts.
PaulHoule · 43m ago
Note you don't see arXiv papers where somebody feeds in 1000 male gendered words into a word embedding and gets 950 correct female gendered words. Statistically it does better than chance, but word embeddings don't do very well.
there are a number of graphs where they have about N=20 points that seem to fall in "the right place" but there are a lot of dimensions involved and with 50 dimensions to play with you can always find a projection that makes the 20 points fall exactly where you want them fall. If you try experiments with N>100 words you go endlessly in circles and produce the kind of inconclusively negative results that people don't publish.
The BERT-like and other transformer embeddings far outperform word vectors because they can take into account the context of the word. For instance you can't really build a "part of speech" classifier that can tell you "red" is an adjective because it is also a noun, but give it the context and you can.
In the context of full text search, bringing in synonyms is a mixed bag because a word might have 2 or 3 meanings and the the irrelevant synonyms are... irrelevant and will bring in irrelevant documents. Modern embeddings that recognize context not only bring in synonyms but the will suppress usages of the word with different meanings, something the IR community has tried to figure out for about 50 years.
philipwhiuk · 4m ago
> In https://nlp.stanford.edu/projects/glove/ there are a number of graphs where they have about N=20 points that seem to fall in "the right place" but there are a lot of dimensions involved and with 50 dimensions to play with you can always find a projection that makes the 20 points fall exactly where you want them fall.
Ramsey theory (or 'the Woolworths store alignment hypothesis')
minimaxir · 12m ago
> The BERT-like and other transformer embeddings far outperform word vectors because they can take into account the context of the word.
In addition to being able to utilize attention mechanisms, modern embedding models use a form of tokenization such as BPE which a) includes punctuation which is incredibly important for extracting semantic meaning and b) includes case, without as much memory requirements as a cased model.
The original BERT used an uncased, SentencePiece tokenizer which is out of date nowadays.
PaulHoule · 7m ago
I was working at a startup that was trying to develop foundation models around at time and BPE was such a huge improvement over everything else we'd tried at that time. We had endless meetings where people proposed that we use various embeddings that would lose 100% of the information for out-of-dictionary words and I'd point out that out-of-dictionary words (particularly from the viewpoint of the pretrained model) frequently meant something critical and if we lost that information up front we couldn't get it back.
Little did I know that people were going to have a lot of tolerance for "short circuiting" of LLMs, that is getting the right answer by the wrong path, so I'd say now that my methodology of "predictive evaluation" that would put an upper bound on what a system could do was pessimistic. Still I don't like giving credit for "right answer by wrong means" since you can't count on it.
drc500free · 4m ago
Is this because we can essentially treat each dimension like a binary digit, so we get 2^n directions we can encode? Or am I barking up totally the wrong tree?
kaycebasques · 57m ago
Oh yes, this makes a lot of sense, thank you for the "nit" (which doesn't feel like a nit to me, it feels like an important conceptual correction). When I was writing the post I definitely paused at that part, knowing that something was off about describing the model as having a dimension that maps to gender. As you said, since the models are general-purpose and work so well in so many domains, there's no way that there's a 1-to-1 correspondence between concepts and dimensions.
I think your comment is also clicking for me now because I previously did not really understand how cosine similarity worked, but then watched videos like this and understand it better now: https://youtu.be/e9U0QAFbfLI
I will eventually update the post to correct this inaccuracy, thank you for improving my own wetware's conceptual model of embeddings
OJFord · 40m ago
I would think of it as the whole embedding concept again on a finer grained scale: you wouldn't say the model 'has a dimension of whether the input is king', instead the embedding expresses the idea of 'king' with fewer dimensions than would be needed to cover all ideas/words/tokens like that.
So the distinction between a direction and a dimension expressing 'gender' is that maybe gender isn't 'important' (or I guess high-information-density) enough to be an entire dimension, but rather is expressed by a linear combination of two (or more) yet more abstract dimensions.
benatkin · 9m ago
> Machine learning (ML) has the potential to advance the state of the art in technical writing. No, I’m not talking about text generation models like Claude, Gemini, LLaMa, GPT, etc. The ML technology that might end up having the biggest impact on technical writing is embeddings.
This is maybe showing some age as well, or maybe not. It seems that text generation will soon be writing top tier technical docs - the research done on the problem with sycophancy will likely result something significantly better than what LLMs had before the regression to sycophancy. Either way, I take "having the biggest impact on technical writing" to mean in the near term. If having great search and organization tools (ambient findability and such) is going to steal the thunder from LLMs writing really good technical docs, it's going to need to happen fast.
daxfohl · 19m ago
Wait, but if gender was composed of say two dimensions, then there'd be no way to distinguish between "the gender is different" and "the components represented by each of those dimensions are individually different", right?
aaronblohowiak · 44m ago
>nearly orthogonal dimensions within n dimensional space
nit within a nit: I believe you intended to write "nearly orthogonal directions within n dimensional space" which is important as you are distinguishing direction from dimension in your post.
osigurdson · 39m ago
You can't visualize it but you can certainly compute the euclidean distance. Tools like UMAP can be used to drop the dimensionality as well.
minimaxir · 1m ago
Speaking of UMAP, a new update to the cuML library (https://github.com/rapidsai/cuml) released last month allows UMAP to feasibly be used on big data without shenanigans/spending a lot of money. This opens up quite a few new oppertunities and I'm getting very good results with.
To be clear, when I said "embeddings are underrated" I was only arguing that my fellow technical writers (TWs) were not paying enough attention to a very useful new tool in the TW toolbox. I know that the statement sounds silly to ML practitioners, who very much don't "underrate" embeddings.
I know that the post is light on details regarding how exactly we apply embeddings in TW. I have some projects and other blog posts in the pipeline. Short story long, embeddings are important because they can help us make progress on the 3 intractable challenges of TW: https://technicalwriting.dev/strategy/challenges.html
rybosome · 46m ago
Thanks for the write-up!
I’m curious how you found the quality of the results? This gets into evals which ML folks love, but even just with “vibes” do the results eyeball as reasonable to you?
milindsoni · 2m ago
I was using transformer.js to generate and use embeddings with small models in the browser itself, its quite useful to implement any kind of semantic search.
jbellis · 59m ago
Great to see embeddings getting some love outside the straight-up-ML space!
I had a non-traditional use case recently, as well. I wanted to debounce the API calls I'm making to gemini flash as the user types his instructions, and I decided to try a very lightweight embeddings model, light enough to run on CPU and way too underpowered to attempt vector search with. It works pretty well! https://brokk.ai/blog/brokk-under-the-hood
jasonjmcghee · 22m ago
Another very cool attribute of embeddings and embedding search is that they are resource cheap enough that you can perform them client side.
You can even build and statically host indices like hnsw for embeddings.
I put together a little open source demo for this here https://jasonjmcghee.github.io/portable-hnsw/ (it's a prototype / hacked together approximation of hnsw, but you could implement the real thing)
Long story short, represent indices as queryable parquet files and use duckdb to query them.
Depending on how you host, it's either free or nearly free. I used Github Pages so it's free. R2 with cloudflare would only cost the size what you store (very cheap- no egress fees).
qq99 · 8m ago
I was wondering about this. I was hesitant to add embedding-based search to my app because I didn't want to incur the latency to the embedding API provider blocking every search on initial render. Granted, you can cache the embeddings for common searches. OTOH, I also don't want to render something without them, perform the embedding async, and then have to reify the results list once the embedding arrives. Seems hard to sensibly do that from a UX perspective.
To render locally, you need access to the model right? I just wonder how good those embeddings will be compared to those from OpenAI/Google/etc in terms of semantic search. I do like the free/instant aspect though
> I don’t know. After the model has been created (trained), I’m pretty sure that generating embeddings is much less computationally intensive than generating text.
An embedding is generated after a single pass through the model, so functionally it's the equivalent of generating a single token from an text generation model.
energy123 · 11m ago
I might be wrong but aren't embedding models usually bidirectional and not causal, so the attention mechanism itself is more expensive.
breadislove · 7m ago
yes exactly
jacobr1 · 1h ago
I may have missed it ... but were any direct applications to tech writers discussed in this article? Embeddings are fascinating and very important for things like LLMs or semantic search, but the author seems to imply more direct utility.
kaycebasques · 50m ago
> were any direct applications to tech writers discussed in this article
No, it was supposed to be a teaser post followed up by more posts and projects exploring the different applications of embeddings in technical writing (TW). But alas, life happened, and I'm now a proud new papa with a 3-month old baby :D
I do have other projects and embeddings-related posts in the pipeline. Suffice to say, embeddings can help us make progress on all 3 of the "intractable" challengs of TW mentioned here: https://technicalwriting.dev/strategy/challenges.html
PaulHoule · 1h ago
Semantic search and classification and clustering. For the first, there is a substantial breakthrough in IR every 10 years or so you take what you can get. (I got so depressed reading TREC proceedings which seemed to prove that "every obvious idea to improve search relevance doesn't work" and it wasn't until I found a summary of the first ten years that I learned that the first ten years had turned up one useful result, BM2.5)
As for classification, it is highly practical to put a text through an embedding and then run the embedding through a classical ML algorithm out of
This works so consistently that I'm considering not packing in a bag-of-words classifier in a text classification library I'm working on. People who hold court on Huggingface forums tends to believe you can do better with fine-tuned BERT, and I'd agree you can do better with that, but training time is 100x and maybe you won't.
20 years ago you could make bag-of-word vectors and put them through a clustering algorithm
I'd disagree with the bit that it takes "a lot of linear algebra" to find nearby vectors, it can be done with a dot product so I'd say it is "a little linear algebra"
sansseriff · 43m ago
It would be great to semantically search through literature with embeddings. At least one person I know if is trying to generate a vector database of all arxiv papers.
The big problem I see is attribution and citations. An embedding is just a vector. It doesn't contain any citation back to the source material or modification date or certificate of authenticity. So when using embeddings in RAG, they only serve to link back to a particular page of source material.
Using embeddings as links doesn't dramatically change the way citation and attribution are handled in technical writing. You still end up citing a whole paper or a page of a paper.
I think GraphRAG [1] is a more useful thing to build on for technical literature. There's ways to use graphs to cite a particular concept of a particular page of an academic paper. And for the 'citations' to act as bidirectional links between new and old scientific discourse. But I digress
I built an rss aggregator with semantic search using embeddings. The main usage was being able to categorise based on any randomly created category. So you could have arbitrary categories
I really enjoy working with embedding. They’re truly fascinating as a representation of meaning - but also a very cheap and effective way to perform very cheap things like categorisation and clustering.
btbuildem · 57m ago
How would you approach using them in a specialized discipline (think technical jargon, acronyms etc) where traning a model from scratch is practically impossible because everyone (customers, solution providers) fiercely guards their data?
A generic embedding model does not have enough specificity to cluster the specialized terms or "code names" of specific entities (these differ across orgs but represent the same sets of concepts within the domain). A more specific model cannot be trained because the data is not available.
Quite the conundrum!
lblume · 1h ago
Semantic search seems like a more promising usecase than simple related articles. A big problem with classical keyword-based search is that synonyms are not reflected at all. With semantic search you can search for what you mean, not what words you expect to find on the site you are looking for.
PaulHoule · 58m ago
A case related to that is "more like this" which in my mind breaks down into two forks:
(1) Sometimes your query is a short document. Say you wanted to know if there were any patents similar to something you invented. You'd give a professional patent searcher a paragraph or a few paragraphs describing the invention, you can give a "semantic search engine" the paragraph -- I helped build one that did about as well as the professional using embeddings before this was cool.
(2) Even Salton's early works on IR talked about "relevance feedback" where you'd mark some documents in your results as relevant, some as irrelevant. With bag-of-words this doesn't really work well (it can take 1000 samples for a bag-of-words classifier to "wake up") but works much better with embeddings.
The thing is that embeddings are "hunchy" and not really the right data structure to represent things like "people who are between 5 feet and 6 feet tall and have been on more than 1000 airplane flights in their life" (knowledge graph/database sorts of queries) or "the thread that links the work of Derrida and Badiou" (could be spelled out logically in some particular framework but doing that in general seems practically intractable)
kgeist · 1h ago
In my benchmarks for a service which is now running in production, hybrid search based on both keywords and embeddings performed the best. Sometimes you need exact keyword matches; other times, synonyms are more useful. Hybrid search combines both sets of results into a single, unified set. OpenSearch has built-in support for this approach.
jbellis · 57m ago
they're both useful
search is an active "I'm looking for X"
related articles is a passive "hey thanks for reading this article, you might also like Y"
I like that this looks like a very ethical and "fair" use of the LLM technology
charcircuit · 17m ago
How are they underrated when they have been been used by the top sites for over a decade? The author doesn't really explain why he thinks they are underrated despite being behind almost every search and recommendation users receive on their computers.
nit. This suggests that the model contains a direction with some notion of gender, not a dimension. Direction and dimension appear to be inextricably linked by definition, but with some handwavy maths, you find that the number of nearly orthogonal dimensions within n dimensional space is exponential with regards to n. This helps explain why spaces on the order of 1k dimensions can "fit" billions of concepts.
In
https://nlp.stanford.edu/projects/glove/
there are a number of graphs where they have about N=20 points that seem to fall in "the right place" but there are a lot of dimensions involved and with 50 dimensions to play with you can always find a projection that makes the 20 points fall exactly where you want them fall. If you try experiments with N>100 words you go endlessly in circles and produce the kind of inconclusively negative results that people don't publish.
The BERT-like and other transformer embeddings far outperform word vectors because they can take into account the context of the word. For instance you can't really build a "part of speech" classifier that can tell you "red" is an adjective because it is also a noun, but give it the context and you can.
In the context of full text search, bringing in synonyms is a mixed bag because a word might have 2 or 3 meanings and the the irrelevant synonyms are... irrelevant and will bring in irrelevant documents. Modern embeddings that recognize context not only bring in synonyms but the will suppress usages of the word with different meanings, something the IR community has tried to figure out for about 50 years.
Ramsey theory (or 'the Woolworths store alignment hypothesis')
In addition to being able to utilize attention mechanisms, modern embedding models use a form of tokenization such as BPE which a) includes punctuation which is incredibly important for extracting semantic meaning and b) includes case, without as much memory requirements as a cased model.
The original BERT used an uncased, SentencePiece tokenizer which is out of date nowadays.
Little did I know that people were going to have a lot of tolerance for "short circuiting" of LLMs, that is getting the right answer by the wrong path, so I'd say now that my methodology of "predictive evaluation" that would put an upper bound on what a system could do was pessimistic. Still I don't like giving credit for "right answer by wrong means" since you can't count on it.
I think your comment is also clicking for me now because I previously did not really understand how cosine similarity worked, but then watched videos like this and understand it better now: https://youtu.be/e9U0QAFbfLI
I will eventually update the post to correct this inaccuracy, thank you for improving my own wetware's conceptual model of embeddings
So the distinction between a direction and a dimension expressing 'gender' is that maybe gender isn't 'important' (or I guess high-information-density) enough to be an entire dimension, but rather is expressed by a linear combination of two (or more) yet more abstract dimensions.
This is maybe showing some age as well, or maybe not. It seems that text generation will soon be writing top tier technical docs - the research done on the problem with sycophancy will likely result something significantly better than what LLMs had before the regression to sycophancy. Either way, I take "having the biggest impact on technical writing" to mean in the near term. If having great search and organization tools (ambient findability and such) is going to steal the thunder from LLMs writing really good technical docs, it's going to need to happen fast.
nit within a nit: I believe you intended to write "nearly orthogonal directions within n dimensional space" which is important as you are distinguishing direction from dimension in your post.
For large datasets (as the UMAP algorithm scales in exponential compute), you will need to use the GPU-accelerated UMAP from cuML. https://docs.rapids.ai/api/cuml/stable/api/#umap
The post was previously discussed 6 months ago: https://news.ycombinator.com/item?id=42013762
To be clear, when I said "embeddings are underrated" I was only arguing that my fellow technical writers (TWs) were not paying enough attention to a very useful new tool in the TW toolbox. I know that the statement sounds silly to ML practitioners, who very much don't "underrate" embeddings.
I know that the post is light on details regarding how exactly we apply embeddings in TW. I have some projects and other blog posts in the pipeline. Short story long, embeddings are important because they can help us make progress on the 3 intractable challenges of TW: https://technicalwriting.dev/strategy/challenges.html
I’m curious how you found the quality of the results? This gets into evals which ML folks love, but even just with “vibes” do the results eyeball as reasonable to you?
I had a non-traditional use case recently, as well. I wanted to debounce the API calls I'm making to gemini flash as the user types his instructions, and I decided to try a very lightweight embeddings model, light enough to run on CPU and way too underpowered to attempt vector search with. It works pretty well! https://brokk.ai/blog/brokk-under-the-hood
ONNX models can be loaded and executed with transformer.js https://github.com/huggingface/transformers.js/
You can even build and statically host indices like hnsw for embeddings.
I put together a little open source demo for this here https://jasonjmcghee.github.io/portable-hnsw/ (it's a prototype / hacked together approximation of hnsw, but you could implement the real thing)
Long story short, represent indices as queryable parquet files and use duckdb to query them.
Depending on how you host, it's either free or nearly free. I used Github Pages so it's free. R2 with cloudflare would only cost the size what you store (very cheap- no egress fees).
To render locally, you need access to the model right? I just wonder how good those embeddings will be compared to those from OpenAI/Google/etc in terms of semantic search. I do like the free/instant aspect though
An embedding is generated after a single pass through the model, so functionally it's the equivalent of generating a single token from an text generation model.
No, it was supposed to be a teaser post followed up by more posts and projects exploring the different applications of embeddings in technical writing (TW). But alas, life happened, and I'm now a proud new papa with a 3-month old baby :D
I do have other projects and embeddings-related posts in the pipeline. Suffice to say, embeddings can help us make progress on all 3 of the "intractable" challengs of TW mentioned here: https://technicalwriting.dev/strategy/challenges.html
As for classification, it is highly practical to put a text through an embedding and then run the embedding through a classical ML algorithm out of
https://scikit-learn.org/stable/supervised_learning.html
This works so consistently that I'm considering not packing in a bag-of-words classifier in a text classification library I'm working on. People who hold court on Huggingface forums tends to believe you can do better with fine-tuned BERT, and I'd agree you can do better with that, but training time is 100x and maybe you won't.
20 years ago you could make bag-of-word vectors and put them through a clustering algorithm
https://scikit-learn.org/stable/modules/clustering.html
and it worked but you got awful results. With embeddings you can use a very simple and fast algorithm like
https://scikit-learn.org/stable/modules/clustering.html#k-me...
and get great clusters.
I'd disagree with the bit that it takes "a lot of linear algebra" to find nearby vectors, it can be done with a dot product so I'd say it is "a little linear algebra"
The big problem I see is attribution and citations. An embedding is just a vector. It doesn't contain any citation back to the source material or modification date or certificate of authenticity. So when using embeddings in RAG, they only serve to link back to a particular page of source material.
Using embeddings as links doesn't dramatically change the way citation and attribution are handled in technical writing. You still end up citing a whole paper or a page of a paper.
I think GraphRAG [1] is a more useful thing to build on for technical literature. There's ways to use graphs to cite a particular concept of a particular page of an academic paper. And for the 'citations' to act as bidirectional links between new and old scientific discourse. But I digress
[1] https://microsoft.github.io/graphrag/
https://github.com/aws-samples/rss-aggregator-using-cohere-e...
Unfortunately I no longer work at AWS so the infrastructure that was running it is down.
https://aws.amazon.com/blogs/machine-learning/use-language-e...
https://github.com/aws-samples/rss-aggregator-using-cohere-e...
I really enjoy working with embedding. They’re truly fascinating as a representation of meaning - but also a very cheap and effective way to perform very cheap things like categorisation and clustering.
A generic embedding model does not have enough specificity to cluster the specialized terms or "code names" of specific entities (these differ across orgs but represent the same sets of concepts within the domain). A more specific model cannot be trained because the data is not available.
Quite the conundrum!
(1) Sometimes your query is a short document. Say you wanted to know if there were any patents similar to something you invented. You'd give a professional patent searcher a paragraph or a few paragraphs describing the invention, you can give a "semantic search engine" the paragraph -- I helped build one that did about as well as the professional using embeddings before this was cool.
(2) Even Salton's early works on IR talked about "relevance feedback" where you'd mark some documents in your results as relevant, some as irrelevant. With bag-of-words this doesn't really work well (it can take 1000 samples for a bag-of-words classifier to "wake up") but works much better with embeddings.
The thing is that embeddings are "hunchy" and not really the right data structure to represent things like "people who are between 5 feet and 6 feet tall and have been on more than 1000 airplane flights in their life" (knowledge graph/database sorts of queries) or "the thread that links the work of Derrida and Badiou" (could be spelled out logically in some particular framework but doing that in general seems practically intractable)
search is an active "I'm looking for X"
related articles is a passive "hey thanks for reading this article, you might also like Y"
Very little maths and lots of dogs involved.