Recent publications:
(chronological order)
(Word embeddings for link prediction, impressive results in low dimension)
 Hyperbolic entailment cones for learning hierarchical embeddings, ICML’18, paper, slides 1, slides 2, code, poster
(improving on empirical results of Poincaré embeddings by theoretically grounding entailment)
(hyperbolic MDS, bounds for dimensionalityprecision tradeoff, 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, skipthought, …)
(matrix multiplication, bias translation, pointwise nonlinearities, softmax, RNN, GRU)
 Poincaré Wasserstein AutoEncoders, NIPS’18 (workshop), paper
(nonspherical Gaussian in Poincaré model, rejection sampling, …)
 Poincaré GloVe: hyperbolic word embeddings, ICLR’19, paper
(adapting GloVe to the Poincare model, deltahyperbolicities, connection to Gaussian embeddings, …)
 Riemannian adaptive optimization methods, ICLR’19, paper, pytorchgeoopt
(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 mixedcurvature 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
 Largemargin classification in hyperbolic space, paper, code
 Skipgram word embeddings in hyperbolic space, paper, code
 Hyperbolic recommender systems, paper
 Lorentzian distance learning, paper
 Riemannian TransE: multirelational graph embedding in nonEuclidean space, paper
 Adversarial autoencoders with constant curvature latent manifolds, paper
2019
 Hierarchical representations with Poincaré Variational AutoEncoders, paper
A few other applications of hyperbolic geometry:
Complex networks:


 2007: Geographic routing using hyperbolic space, paper
 2008: Efficient navigation in scalefree 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

Bioinformatics:
Visualization:
Theory of hyperbolic geometry:
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