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Hyperbolic neural networks - 2018

Hyperbolic Neural Networks

Research Paper on Hyperbolic Neural Networks

Research Area:  Machine Learning

Abstract:

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean geometry, firstly because of the absence of corresponding hyperbolic neural network layers. Here, we bridge this gap in a principled manner by combining the formalism of Möbius gyrovector spaces with the Riemannian geometry of the Poincaré model of hyperbolic spaces. As a result, we derive hyperbolic versions of important deep learning tools: multinomial logistic regression, feed-forward and recurrent neural networks. This allows to embed sequential data and perform classification in the hyperbolic space. Empirically, we show that, even if hyperbolic optimization tools are limited, hyperbolic sentence embeddings either outperform or are on par with their Euclidean variants on textual entailment and noisy-prefix recognition tasks.

Keywords:  
Hyperbolic Neural Networks
Machine Learning
Deep Learning

Author(s) Name:  Octavian Ganea, Gary Becigneul, Thomas Hofmann

Journal name:  NeurIPS Proceeding

Conferrence name:  

Publisher name:  arxiv

DOI:  10.48550/arXiv.1805.09112

Volume Information:  Volume 2018