Do you really need a vector database?

2023-04-12 22:31:02

Spoiler alert: the reply is perhaps! Though, my inclusion of the phrase “truly” betrays my bias.

Vector databases are having their day proper now. Three completely different vector DB corporations have raised cash on valuations as much as $700 million (paywall link). Surprisingly, their rise in reputation shouldn’t be for his or her “authentic” function in advice programs, however reasonably as an auxillary software for Giant Language Fashions (LLMs). Many on-line examples of mixing embeddings with LLMs will present you ways they retailer the embeddings in a vector database.

Whereas that is nice and fast for a Proof of Idea, there may be all the time a price to introducing new infrastructure, particularly when that infrastructure is a database. I’ll speak somewhat about that price on this weblog put up, however I’m primarily focused on whether or not there’s even a tangible profit to start with.

Why a vector database?

I feel I’ll skip over the compulsory rationalization of embeddings. Others have done this significantly better than me. So, let’s assume you understand what embeddings are and that you’ve got plans to embed some issues (in all probability paperwork, photographs, or “entities” for a advice system). Individuals sometimes use a vector database in order that they will shortly discover the most related embeddings to a given embedding. Perhaps you’ve embedded a bunch of photographs and wish to discover different canine that look much like a given canine. Or, you embed the textual content of a search question and wish to discover the highest 10 paperwork which are most much like the question. Vector databases allow you to do that in a short time.

Pre-meditated calculation

Vector databases are capable of calculate similarity shortly as a result of they’ve already pre-calculated it. Er, to be truthful, they’ve roughly pre-calculated it. For $N$ entities, it takes $O(N^{2})$ calculations to calculate the similarity between each single merchandise and each different merchandise. In the event you’re Spotify and have over 100 million tracks, then this generally is a fairly massive calculation! (Fortunately, it’s no less than embarrassingly parallel). Vector databases will let you commerce off some accuracy in change for pace, such that you may tractably calculate the (roughly) most related entities to a given entity.

Do that you must pre-calculate similarity between each entity, although? I consider this like batch versus streaming for information engineering, or batch prediction vs real-time inference for ML fashions. One good thing about batch is that it makes real-time easy. One draw back of batch is that you must compute every little thing, whether or not or not you really need it.

For measuring similarities, you are able to do this calculation in real-time. For $N$ whole entities, the time complexity for calculating the highest $ok$ most related entities to a given entity is $O(N)$. This comes from a pair assumptions: we’ll use cosine similarity for our similarity metric, and we’ll assume the embeddings have already been normalized. Then, for an embedding dimension $d lt lt N$, it’s $O(Nd)$ to calculate the similarity between a given embedding and all different $N$ embeddings. To search out the highest $ok$ most related entities, now we have so as to add one other $O(N + ok log(ok))$. This all nets out to roughly $O(N)$.

In numpy, the “real-time” calculation takes 3 traces of code:

# vec -> 1D numpy array of form D
# mat -> 2D numpy array of form N x D
# ok -> variety of most related entities to seek out.
similarities = vec @ mat.T
partitioned_indices = np.argpartition(-similarities, kth=ok)[:k]
top_k_indices = np.argsort(-similarities[partitioned_indices])

Proof-based claims

Relying in your measurement of $N$ and your latency necessities, $O(N)$ might be very affordable! To show my level, I put collectively somewhat benchmark. All of the code for the benchmark might be discovered at this nn-vs-ann GitHub repo.

For my benchmark, I randomly initialize $N$ embeddings with 256 dimensions apiece. I then measure the time it takes to pick the highest 5 “nearest neighbor” (aka most related) embeddings to a given embedding. I carry out this benchmark for a variety of $N$ values utilizing two completely different approaches:

numpy is the “real-time” calculation that performs the total accuracy, non-precomputed nearest neighbors calculation.
hnswlib makes use of hnswlib to pre-calculate approximate nearest neighbors.

The outcomes are proven under, with each axes on log scales. It’s laborious to see after we’re coping with log-log scales, however numpy scales linearly with $N$. The latency is roughly 50 milliseconds per million embeddings. Once more, relying in your $N$ and latency necessities, 50 ms for 1 million embeddings may be completely nice! Moreover, you get to avoid wasting your self the complication of standing up a vector database and ready the ~100 seconds to index these million embeddings.

However that’s not truthful

Eyyyyy, you bought me! I’ve glossed over and ignored plenty of elements on this argument. Listed here are a pair counterarguments that could be related:

The numpy strategy requires me to carry every little thing in reminiscence which isn’t scalable.
How do you even productionize this numpy strategy? Pickle an array? That sounds horrible, after which how do you replace it?
What about the entire different advantages of a vector database, reminiscent of metadata filtering?
What if I actually do have a whole lot of embeddings?
Shouldn’t you cease hacking issues and simply use the precise software for the job?

Permit me to now counter my very own counterarguments:

1. The numpy strategy requires me to carry every little thing in reminiscence which isn’t scalable.

Sure, though vector databases additionally require holding issues in reminiscence (I feel?). Additionally, you’ll be able to purchase very excessive reminiscence machines these days. Additionally additionally, you’ll be able to reminiscence map your embeddings if you wish to commerce reminiscence for time.

2. How do you even productionize this numpy strategy? Pickle an array? That sounds horrible, after which how do you replace it?

I’m glad you requested! I actually did productionize this strategy at a startup I labored at. Each day, I educated a contrastive studying picture similarity mannequin to study good picture representations. I wrote out the picture embeddings as JSON to S3. I had an API that calculated essentially the most related photographs for an enter picture utilizing the numpy methodology within the benchmark. That API had an async background job that might examine for brand new embeddings on S3 once in a while. When it discovered new embeddings, it simply loaded them into reminiscence.

3. What about the entire different advantages of a vector database, reminiscent of metadata filtering?

Sure, and this is the reason you must perhaps simply use your present database (and even augment it!) or a tried-and-true doc database like Elasticsearch reasonably than a vector database. Relatedly, if that you must filter by varied metadata, are you already storing that metadata in your “common” database? If that’s the case, it’s going to be annoying to must sync that information over to a brand new system. I’m definitely not a fan of this.

4. What if I actually do have a whole lot of embeddings?

Then yeah, you may simply have to make use of a specialised vector DB (though I do suppose that Elasticsearch supports approximate nearest neighbors). One factor I might double examine is that you may’t cut back your search to an affordable variety of embeddings previous to performing your similarity calculations. For instance, for those who’re looking for essentially the most related shirts to a given shirt, you don’t must calculate similarities for non-shirts!

5. Shouldn’t you cease hacking issues and simply use the precise software for the job?

Like most issues, my guess is that the precise software for the job might be the software you’re already utilizing. And that software might be postgres, or Elasticsearch if you really want it.

Courageous new world

My arguments may all be absolutely moot, provided that we’re transferring to a world of enormous, open-ended LLMs that want entry to, like, all of Wikipedia with a purpose to reply questions. For these functions, vector DBs certainly do make sense. I’m extra focused on non-open ended LLMs, although, and I do surprise how a lot these would require vector databases. Let’s see what occurs! On the tempo issues are going, I can’t predict the afternoon, so I’ll simply attempt to savor my lunch.

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