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Comment by brigadier132 | Hacker News Reader

The vectors are literally constructed so that cosine similarity is semantic similarity.

> second unstated assumption is that the vector index can accurately identify the top K vectors by cosine similarity, and that's not true either

Its not unstated, its called ANN for a reason

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> The vectors are literally constructed so that cosine similarity is semantic similarity.

Are they? A learned embedding doesn't guarantee this and a positional embedding certainly doesn't. Our latent embeddings don't either unless you are inferring this through the dot product in the attention mechanism. But that too is learned. There are no guarantees that the similarities that they learn are the same things we consider as similarities. High dimensional space is really weird.

And while we're at it, we should mention that methods like t-SNE and UMAP are clustering algorithms not dimensional reduction. Just because they can find ways to cluster the data in a lower dimensional projection (epic mapping) doesn't mean that they are similar in the higher dimensional space. It all depends on the ability to unknot in the higher dimensional space.

It is extremely important to do what the OP is doing and consider the assumptions of the model, data, and measurements. Good results do not necessarily mean good methods. I like to say that you don't need to know math to make a good model, but you do need to know math to know why your model is wrong. Your comment just comes off as dismissive rather than actually countering the claims. There's plenty more assumptions than OP listed too. But their assumptions don't mean the model won't work, it just means what constraints the model is working under. We want to understand the constraints/assumptions if we want to make better models. Large models have advantages because they can have larger latent spaces and that gives them a lot of freedom to unknot data and move them around as they please. But that doesn't mean the methods are efficient.

Do you know how embedding models are trained?

Yes. My comment is about the geometry of higher dimensions and their meanings. These are not the same as in {2,3}D

There are embeddings that are trained to reflect similarity, for example SentenceBERT, where the training process pushes pairs of similar sentences (as defined by whoever built the dataset) to have closer embeddings and dissimilar sentences to be further apart.

As the OP points out, Cosine similarity doesn't always equate to relevance. As I was expanding upon, things get really messy as the dimensions increase and your intuition about how vectors relate to one another goes out the window, and fast. Distributional mass is not uniform. Rate of originality increases. And of course, there is no guarantees that latent dimensions align with human meaningful semantic features. There's no pressure to align basis vectors with human perceived semantics. My argument isn't about that there isn't a similarity pressure it's that similarity in high dimensions means different things then similarities in low dimensions. For example, in high dimensions most of a unit cube's mass lies outside the unit sphere, while in 2 or 3 dimensions the unit cube is always contained inside with room to spare. High dimensions are weird and that's what my comment is about because many people are using their lower dimensional intuition for ML.

To be fair… semantic similarity isn’t the same as relevance either.

They are related, and we frequently assume they are close enough that it doesn’t matter, but they are different.

I disagree, the embeddings are what are used by the llms themselves to produce relevant output and the output is relevant ergo the embeddings do produce relevant output via similarity search

Not if you're using ANN. In some cases that will be very similar to exhaustive search but in other cases you'll get results that you don't want. You also need embeddings that distribute things mostly evenly across the embedding space (not all will).

You probably aren’t using an LLM for your text embeddings for document retrieval (they don’t perform as well as specialist embedding models[0]), and even if they did, you have an embedding about a bare document, without any context of what you are trying to get out of it. If you were to add your context in and then get an embedding, you would get a different answer. As your query gets specific, irrelevant aspects of the embedding space can overwhelm the similarity function, leading to irrelevant answers that are still semantically similar.

[0] https://huggingface.co/spaces/mteb/leaderboard

The recent SILO-LM paper has a slightly different approach: rather than using input embeddings and prompting the LLM with documents, it searches the database according to the LLM's output embedding and uses KNN search to skew the output embedding vector before token generation. Done that way round, using LLM embeddings outperforms RAG, allegedly.

They did it with a custom language model. I really want to give this a try with llama2 embeddings but haven't had the bandwidth yet (and llama2's embedding vectors are inconveniently huge, but that's a different problem).

Interesting! I’ll have to look into that.

Consider the extreme case: when I ask a question about X, then a page with just the questions about X will get the highest similarity. But what I want in terms of relevance for the answer is a page with a little bit about X and lots of surrounding context that answers the question. By definition the extra context will likely lower the similarity.

That's interesting.

Are there any good sources to learn more about that?

This is kind of a moot argument, semantic similarity is higher dimensionality than cosine similarity can capture.

If I'm using vectors for question/answer, then:

"What is a cat"

and

"What is a dog"

Should be more dissimilar than the documents answering either.

If I'm using it for FAQ filtering then they should be more similar.

I've had decent results using a doc2query style approach:

    1. Ask an LLM to return a list of questions answered by the document
    2. Store the embeddings of the questions along with a document ID
    3. On user query, get the embedding of the user query
    4. KNN cosine similarity search the user embedding vs. the corpus of question embeddings
    5. Return the highest ranked documents

You can tweak this approach depending on your use case, so that in step 1 you generate embeddings that are more similar to the types of things you want returned in step 5. If you want the answer to "What is a cat" to be similar to "What is a dog," you'd prompt/finetune the LLM in step 1 to generate broad questions that would encompass both; if you want them to be very different, you'd do the opposite and avoid generalities.

You just reinvented a 2 year old technique with a more expensive pipeline and missed performance gains (from the cross-encoder step):

https://www.sbert.net/examples/domain_adaptation/README.html https://arxiv.org/abs/2112.07577

I'm aware of more efficient ways to do it! (Hence referencing e.g. doc2query.) But you have to train a model, whereas with an LLM you can get a working version in 5mins of work.

But with even less work you can just pick up a model that was pre-trained using GPL and get great results.

I'm able to pull messy results directly from internet sources and re-rank on the fly with a quantized e5 model small enough to fit in a serverless function.

You don't need a vector database to do all this stuff, people who are paid off people using vector databases are the ones who are hyping them up the most.

Oh, I wasn't suggesting using a vector DB. Personally I just iterate through the corpus and check cosine similarity with a for loop.

If by "quantized e5 model small enough to fit in a serverless function" you mean e5-small-v2, FYI it actually underperforms just calling OpenAI for embeddings (text-embedding-ada-002) on the HuggingFace MTEB benchmarks. And that definitely doesn't negate using a doc2query-style approach to preprocess the documents before running them through the pretrained embedding model if you're comparing e.g. questions to answers, rather than raw document-to-document similarity. (Of course a custom trained model will be more efficient! In fact, the original doc2query paper in 2019 used a custom trained model for step 1, as did many enhancements on it e.g. doc-t5-query. What's neat is that with the advent of really good pretrained LLMs, you can get results approximating that without training your own models in like ~5mins of work.)

I guess this really boils down to your usecase: if you can have a result for your user with fully predictable latency (my biggest beef with non-Azure OpenAI), no additional round trip, and increased configurability, does MTEB performance move the needle?

Considering the LLM is still doing the final pass, and the latency from the LLM is based on output length, I find the UX to be significantly improved just doing reranking in-process.

I think there's been a bit of whiplash, where people went from gatekeeping "hard ML", to "I can shove this all at a REST API", but there's a golden path laying in between for use-cases where UX matters.

I even fall back to old school NLP (like ML-less, glorified wordlist POS taggers) for LLM tasks and end up with significantly improved performance for almost 0 additional effort

yes - but calculating the consine similarity for all the candidates is prohibitively expensive.

hence heuristic.

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