02/02/2021

Computationally Tractable Riemannian Manifolds for Graph Embeddings

Calin Cruceru, Gary Becigneul, Octavian-Eugen Ganea

Keywords:

Abstract Paper Similar Papers

Abstract: Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases (e.g., hierarchical structures benefit from hyperbolic geometry). However, going beyond embedding spaces of constant sectional curvature, while potentially more representationally powerful, proves to be challenging as one can easily lose the appeal of computationally tractable tools such as geodesic distances or Riemannian gradients. Here, we explore two computationally efficient matrix manifolds, showcasing how to learn and optimize graph embeddings in these Riemannian spaces. Empirically, we demonstrate consistent improvements over Euclidean geometry while often outperforming hyperbolic and elliptical embeddings based on various metrics that capture different graph properties. Our results serve as new evidence for the benefits of non-Euclidean embeddings in machine learning pipelines.

The video of this talk cannot be embedded. You can watch it here:
https://slideslive.com/38948911
(Link will open in new window)
 0
 0
 0
 0
  Share    
This is an embedded video. Talk and the respective paper are published at AAAI 2021 virtual conference. If you are one of the authors of the paper and want to manage your upload, see the question "My papertalk has been externally embedded..." in the FAQ section.

Comments

Post Comment
no comments yet
code of conduct: tbd Characters remaining: 140

Similar Papers

 0
 0
 0
 0
 1:01 
 0
 0
 0
 0
 14:56 
 0
 0
 0
 0
 10:06 
 0
 0
 0
 0
 13:33 
 0
 0
 0
 0
 15:26 
 0
 0
 0
 0
 15:31 
 0
 0
 0
 0
 13:19 
 0
 0
 0
 0
 14:47 
 0
 0
 0
 0
 3:10 
 0
 0
 0
 0
 1:00 
 0
 0
 0
 0
 14:22 
 0
 0
 0
 0
 14:31 
 0
 0
 0
 0
 10:42 
 0
 0
 0
 0
 11:26 
 0
 0
 0
 0
 9:51 
 0
 0
 0
 0
 11:06 
 0
 0
 0
 0
 3:04 
 0
 0
 0
 0
 3:09 
 0
 0
 0
 0
 4:59 
 0
 0
 0
 0
 2:52 
 0
 1
 0
 2
 3:13 
 0
 0
 0
 0
 5:06 
 0
 0
 0
 0
 10:41 
 0
 0
 0
 0
 5:13 
 0
 0
 0
 0
 3:10 
 0
 0
 0
 0
 3:02 
 0
 0
 0
 0
 4:48 
 0
 0
 0
 0
 13:35 
 0
 0
 0
 0
 3:05 
 0
 0
 0
 0
 15:26 
 0
 0
 0
 0
 7:45 
 0
 0
 0
 0
 4:36 
 0
 0
 0
 0
 5:17 
 0
 0
 0
 0
 15:01 
 0
 0
 0
 0
 13:23 
 0
 0
 0
 0
 12:32 
 0
 0
 0
 0
 1:03 
 0
 1
 0
 0
 3:31 
 0
 0
 0
 0
 5:15 
 0
 0
 0
 0
 10:50