Poincaré, Hyperbolic, Curvilinear

:+1: means being highly related to my personal research interest.

NeurIPS 2019-Multi-relational Poincaré Graph Embeddings

NOTE: Hyperbolic embeddings have recently gained attention in machine learning due to their ability to represent hierarchical data more accurately and succinctly than their Euclidean analogues. However, multi-relational knowledge graphs often exhibit multiple simultaneous hierarchies, which current hyperbolic models do not capture. To address this, we propose a model that embeds multi-relational graph data in the Poincaré ball model of hyperbolic space. Our Multi-Relational Poincaré model (MuRP) learns relation-specific parameters to transform entity embeddings by Möbius matrix-vector multiplication and Möbius addition. Experiments on the hierarchical WN18RR knowledge graph show that our multi-relational Poincaré embeddings outperform their Euclidean counterpart and existing embedding methods on the link prediction task, particularly at lower dimensionality.

NeurIPS 2019-Numerically Accurate Hyperbolic Embeddings Using Tiling-Based Models

NOTE: Not available yet.
Related work:
    HyperE: Hyperbolic Embeddings for Entities.

NeurIPS 2019-Curvilinear Distance Metric Learning

NOTE: Not available yet.

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