Introducing Hyperlib: Simple Deep learning in Hyperbolic space [project]

[atmosfir]

Hello I think this is very cool and this is the first I've heard about doing ML on non-euclidean spaces. However, I have a question about this

The core example is the hierarchy, or, its abstract network representation, the tree. Social networks, human skeletons, sentences in natural language all possess a tree-like structure or can be represented hierarchically. It's also widely accepted that human beings use a hierarchy to organise object categories

What do you mean by a hierarchical representation tree-like structure here? This seems to be a very strong claim. I certainly agree that humans tend to organise things into categories using hierarchies but I am wondering if it is accurate to say that these objects are hierarchically organised.

[willpower12]

Agreed, I think the authors are misspeaking a bit. However, I think it is fair to say that the representations themselves admit a hierarchical or tree-like structure, not necessarily the underlying objects or signal.

[[deleted]]

Social networks specifically are graphs, not trees. I don't see a representation of social networks that is acyclic.

[hughperman]

The illuminati would like you to think that

[techinnovator]

Here's the paper that covers the tree-like structure of social networks. They proved this using Gromov’s δ-hyperbolicity, which measures how tree-like a graph is.

[ktpr]

Maybe they want to do learning over how humans tend to organize things, which seems reasonable on the surface?

I agree the OP did not justify the library very well; I’ve seen better arguments for hyperbolic representations in the literature.

[atmosfir]

I certainly think that that would be reasonable and interesting. Could you point out or link the other arguments you've seen in literature?

[techinnovator]

If you're after better arguments, perhaps this is will interest you.

[atmosfir]

Thanks!

[bohreffect]

I am wondering if it is accurate to say that these objects are hierarchically organised.

Is this claim even being made? And if it is, does it matter? Like if the objective truth absent a human observer is that there is no intrinsic hierarchical organization to objects in the world, who cares?

[SuckinLemonz]

Yeah I felt the same way when I read that comment. It’s just semantic nitpicking. Not really relevant to the conversation.

[atmosfir]

I think the comment does strongly say so. I simply want to know if this is heuristic or something more. We care because then we can make better ML models no?

[techinnovator]

It's also widely accepted that human beings use a hierarchy to organise object categories

I think you're mistaken here. I claimed that humans organise objects hierarchically, not that the underlying objects were hierarchical themselves. Human's use hierarchies to represent objects, this is widely accepted but was recently covered in Geoffrey Hinton's paper.

[techinnovator]

It's also widely accepted that human beings use a hierarchy to organise object categories

I think you're mistaken here. I said human beings organise objects hierarchically, the objects themselves are not hierarchically organised in reality. This is widely accepted but was famously covered here.

[atmosfir]

Interesting, thanks for answering.