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Authors learn embeddings in a Poincaré space rather than Euclidean, better for hierarchical relationships. The reference paper is a good read: Nickel & Kiela '1

Authors learn embeddings in a Poincaré space rather than Euclidean, better for hierarchical relationships. The reference paper is a good read: Nickel & Kiela '17 "Poincaré Embeddings for Learning Hierarchical Representations", https://arxiv.org/abs/1705.08039 https://arxiv.org/abs/1705.08039

darkmighty 7y ago
The use of hyperbolic space to encode hierarchies is absolutely genius (in not small part because it should be obvious), given the properties of hyperbolic space to "expand" around fixed points exponentially, exactly like trees do* . It seems like a continuous generalization of trees essentially. Beautiful. *: https://en.wikipedia.org/wiki/Hyperbolic_space https://en.wikipedia.org/wiki/Hyperbolic_space "Another distinctive property is the amount of space covered by the n-ball in hyperbolic n-space: it increases exponentially with respect to the radius of the ball for large radii, rather than polynomially. (...)"
- zenorogue 7y ago
  Genius because it should be obvious? Yes, it should be obvious for people familiar with both areas, and it is actually known for quite a long time. Hyperbolic geometry is used for visualizing hierarchical data since Lamping-Rao 1995 and Munzner 1998, then there were papers about hyperbolic SOMs (2001 IIRC) and lots of papers about the Hyperbolic Random Graph model for scale-free networks. I would say that the paper linked above introducing "Poincare embeddings" (a rather poor name IMO, BTW) does not feel as impressive if you know the details and the earlier work.
laxatives 7y ago
Kind of disappointed everyone in that field ended up at Facebook. Seems like they aren't even working on this kind of stuff anymore.
- zenorogue 7y ago
  I understand not liking Facebook, but they are in Facebook Research (not like working on improving the ads or something), and they publish their research (rather than keeping it for Facebook uses only), and they still do produce new things. So they just seem to be funded by a private company rather than research grants (i.e., taxes). It is not everyone either, Facebook Research has a team working on this stuff, but there are lots of other people too.
theSage 7y ago
If you want to experiment with these kinds of embeddings, a stabler version using Lorentz embeddings instead of Poincare was written by us at work for internal use. https://github.com/theSage21/lorentz-embeddings https://github.com/theSage21/lorentz-embeddings

darkmighty 7y ago

The use of hyperbolic space to encode hierarchies is absolutely genius (in not small part because it should be obvious), given the properties of hyperbolic space to "expand" around fixed points exponentially, exactly like trees do* . It seems like a continuous generalization of trees essentially. Beautiful. *: https://en.wikipedia.org/wiki/Hyperbolic_space https://en.wikipedia.org/wiki/Hyperbolic_space "Another distinctive property is the amount of space covered by the n-ball in hyperbolic n-space: it increases exponentially with respect to the radius of the ball for large radii, rather than polynomially. (...)"

zenorogue 7y ago
Genius because it should be obvious? Yes, it should be obvious for people familiar with both areas, and it is actually known for quite a long time. Hyperbolic geometry is used for visualizing hierarchical data since Lamping-Rao 1995 and Munzner 1998, then there were papers about hyperbolic SOMs (2001 IIRC) and lots of papers about the Hyperbolic Random Graph model for scale-free networks. I would say that the paper linked above introducing "Poincare embeddings" (a rather poor name IMO, BTW) does not feel as impressive if you know the details and the earlier work.

laxatives 7y ago

Kind of disappointed everyone in that field ended up at Facebook. Seems like they aren't even working on this kind of stuff anymore.

zenorogue 7y ago
I understand not liking Facebook, but they are in Facebook Research (not like working on improving the ads or something), and they publish their research (rather than keeping it for Facebook uses only), and they still do produce new things. So they just seem to be funded by a private company rather than research grants (i.e., taxes). It is not everyone either, Facebook Research has a team working on this stuff, but there are lots of other people too.

theSage 7y ago

If you want to experiment with these kinds of embeddings, a stabler version using Lorentz embeddings instead of Poincare was written by us at work for internal use. https://github.com/theSage21/lorentz-embeddings https://github.com/theSage21/lorentz-embeddings