
Skipgram word embeddings in hyperbolic space
Embeddings of treelike graphs in hyperbolic space were recently shown t...
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HyperKG: Hyperbolic Knowledge Graph Embeddings for Knowledge Base Completion
Learning embeddings of entities and relations existing in knowledge base...
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Fully Hyperbolic Neural Networks
Hyperbolic neural networks have shown great potential for modeling compl...
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On the Schrödinger map for regular helical polygons in the hyperbolic space
The main purpose is to describe the evolution of = ∧_ , with (s,0) a re...
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Stable discretizations of elastic flow in Riemannian manifolds
The elastic flow, which is the L^2gradient flow of the elastic energy, ...
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Hyperbolic Image Embeddings
Computer vision tasks such as image classification, image retrieval and ...
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Estimation of spatially varying parameters with application to hyperbolic SPDEs
More often than not, we encounter problems with varying parameters as op...
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Stable Geodesic Update on Hyperbolic Space and its Application to Poincare Embeddings
A hyperbolic space has been shown to be more capable of modeling complex networks than a Euclidean space. This paper proposes an explicit update rule along geodesics in a hyperbolic space. The convergence of our algorithm is theoretically guaranteed, and the convergence rate is better than the conventional Euclidean gradient descent algorithm. Moreover, our algorithm avoids the "bias" problem of existing methods using the Riemannian gradient. Experimental results demonstrate the good performance of our algorithm in the embeddings of knowledge base data.
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