Is the cosine distance bound in the docs correct?

[Guillermo_Ripa]

Description

In the docs, there’s a note that says vectors are normalized for cosine similarity, and then we use dot product.

Wouldn’t that mean that the cosine distance ends up being -1 <= distance <= 1? Or do we do 1 - dot(a,b) in the code?

I’m asking because we found negative distance using cosine when returning them in metadata.

[DudaNogueira]

hi @Guillermo_Ripa !!

That’s an interesting question.

I will need to ask internally for more context on this.

I’ll get back with more info. Thanks!

[andrewisplinghoff]

The cosine distance should never be negative, it is defined as 1 - dot(a,b) in the code:

weaviate/weaviate/blob/598b4db26ba52c77f7777996ac100f48cd895431/adapters/repos/db/vector/hnsw/distancer/cosine_dist.go#L44

Here in the tests you can also see the expected distance measures, e.g. opposing vectors lead to cosine distance 2:

weaviate/weaviate/blob/598b4db26ba52c77f7777996ac100f48cd895431/adapters/repos/db/vector/hnsw/distancer/cosine_dist_test.go#L66-L68

Could you give us an example where there was a negative cosine distance calculated?

[Guillermo_Ripa]

Thanks @DudaNogueira and @andrewisplinghoff for the code snippets! That’s really helpful.

The distance was a -1e-5, so I brushed it off as a floating point error. But it got me looking into docs.

The code snippet and the unit test puts my doubt to rest. thank you

[DudaNogueira]

Great!! Thanks for jumping in, @andrewisplinghoff !

That was the code that our team pointed me to

Thanks!!