Recent publications:

  • Poincaré embeddings for learning hierarchical representations, NIPS’17, paper, slides, code

(Word embeddings for link prediction, impressive results in low dimension)

(improving on empirical results of Poincaré embeddings by theoretically grounding entailment)

  • Representation trade-off for hyperbolic embeddings, ICML’18, paper, code

(hyperbolic MDS, bounds for dimensionality-precision trade-off, combinatorial embedding method)

  • Learning continuous hierarchies in the Lorentz model of hyperbolic geometry, ICML’18, paper

(learning to embed hypernymy from similarity data, advantages of the Lorentz model over the Poincaré model)

  • Embedding text in hyperbolic spaces, ACL’18 (workshop), paper

(adaption in hyperbolic spaces of word2vec, skip-thought, …)

  • Hyperbolic neural networks, NIPS’18, paper, code

(matrix multiplication, bias translation, pointwise non-linearities, softmax, RNN, GRU)

Preprints:

  • Neural embeddings of graphs in hyperbolic space, paper

(Embedding graphs using negative sampling, computing similarity measure involving hyperbolic distance to 0)

  • Hyperbolic attention networks, paper

(attention mechanism, transformer, relation networks, message passing networks, …)

  • Large-margin classification in hyperbolic space, paper, code

(SVM in hyperbolic space)

  • Skip-gram word embeddings in hyperbolic space, paper, code

(adaptation of word2vec to the hyperboloid model)

  •  Hyperbolic recommender systems, paper

(Obtains state-of-the-art results with a simple method embedding users and item in the Poincaré ball)

 

 

 

 

A few other applications of hyperbolic geometry:

Complex networks:

      • 2007: Geographic routing using hyperbolic space, paper
      • 2008: Efficient navigation in scale-free networks embedded in hyperbolic metric spaces, paper
      • 2010: Resilient routing for sensor networks using hyperbolic embedding of universal covering space, paper
      • 2010: Hyperbolic geometry of complex networks, paper
      • 2010: Sustaining the Internet with hyperbolic mapping, Nature, paper
      • 2016: An experimental investigation of hyperbolic routing with a smart forwarding plane in NDN, paper
      • 11/17: Machine learning meets complex networks via coalescent embedding in the hyperbolic space, Nature, paper
      • 12/17: An improved hyperbolic embedding algorithm, paper

Bio-informatics:

      • 2002: Geometry of the space of phylogenetic trees, paper
      • 2004: Visualising very large phylogenetic trees in three dimensional hyperbolic space, paper

Visualization:

      • 1995: A focus+context technique based on hyperbolic geometry for visualizing large hierarchies, paper
      • 1995: Visualizing the structure of the World Wide Web in 3D hyperbolic space, paper
      • 2000: Visualizing large hierarchical clusters in hyperbolic space, paper

 

Theory of hyperbolic geometry:

      • 1987: Hyperbolic groups, Gromov, pdf
      • 1997: Hyperbolic geometry, Cannon et al., book
      • 2005: A course on geometric group theory, Bowditch, pdf
      • 2008: A Gyrovector space approach to hyperbolic geometry, Ungar, book
      • 2013: Hyperbolic geometry, Parkkohnen, pdf

 

Other blog posts

Hyperbolic Embeddings with a Hopefully Right Amount of Hyperbole

Implementing Poincaré Embeddings

Poincaré Embeddings for Representing Hierarchical Data

 

Free online software

Play with 2D hyperbolic spaces

Make hyperbolic tiling of images