Recent publications:

(chronological order)

  • 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

(adapting to hyperbolic spaces word2vec, skip-thought, …)

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

  • Poincaré Wasserstein Auto-Encoders, NIPS’18 (workshop), paper

(non-spherical Gaussian in Poincaré model, rejection sampling, …)

  • Poincaré GloVe: hyperbolic word embeddings, ICLR’19, paper

(adapting GloVe to the Poincare model, delta-hyperbolicities, connection to Gaussian embeddings, …)

(adapting Adam, Adagrad, Amsgrad to Riemannian spaces, experiments on hyperbolic taxonomy embedding, …)

  • Hyperbolic attention networks, ICLR’19, paper

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

  • Learning mixed-curvature representations in product spaces, ICLR’19, paper

(representing graphs in products of spheres, hyperbolic and Euclidean spaces, discrete sectional curvature, …)

 

 

 

Preprints:

(chronological order)

2018
  • Neural embeddings of graphs in hyperbolic space, paper
  • Large-margin classification in hyperbolic space, paper, code
  • Skip-gram word embeddings in hyperbolic space, paper, code
  • Hyperbolic recommender systems, paper
  • Lorentzian distance learning, paper
  • Riemannian TransE: multi-relational graph embedding in non-Euclidean space, paper
  • Adversarial auto-encoders with constant curvature latent manifolds, paper
2019
  • Hierarchical representations with Poincaré Variational Auto-Encoders, paper
  • Hyperbolic Heterogeneous Information Network Embedding, paper
  • Inferring concept hierarchies from text corpora via hyperbolic embeddings, paper

 

 

 

 

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