HoroPCA:HyperbolicDimensionalityReductionviaHorosphericalProjectionsInesChami1AlbertGu1DatNguyen1ChristopherRe´1Abstractneighborsearch(Krauthgamer&Lee,2006;Wu&Charikar,2020),hierarchicalclustering...
GeneralizationErrorBoundforHyperbolicOrdinalEmbeddingAtsushiSuzuki1AtsushiNitanda2JingWang1LinchuanXu3MarcCavazza1KenjiYamanishi4Abstracttheyareasconsistentaspossiblewithgivenordinaldataintheformof...
LatentVariableModellingwithHyperbolicNormalizingFlowsAvishekJoeyBose12AriellaSmofsky12RenjieLiao34PrakashPanangaden12WilliamL.Hamilton12Abstractℝ2ℍ2KThechoiceofapproximateposteriordistributionsℝ...
LorentzianDistanceLearningforHyperbolicRepresentationsMarcT.Law123RenjieLiao12JakeSnell12RichardS.Zemel12AbstractAcommonandnaturalnon-Euclideanrepresentationspaceisthesphericalmodel(e.g.(Wangetal.,...
HyperbolicDiskEmbeddingsforDirectedAcyclicGraphsRyotaSuzuki1RyusukeTakahama1ShunOnoda1Abstractembeddingsformodelinitializationleadstoimprovementsinvariousoftasks(Kim,2014).Inthesemethods,sym-Obtain...
AWrappedNormalDistributiononHyperbolicSpaceforGradient-BasedLearningYoshihiroNagano1ShoichiroYamaguchi2YasuhiroFujita2MasanoriKoyama2Abstract(a)AtreerepresentationofthetrainingdatasetHyperbolicspac...
RepresentationTradeoffsforHyperbolicEmbeddingsFredericSala1ChristopherDeSa2AlbertGu1ChristopherRe´1Abstractfortrees—evenusinganunboundednumberofdimensions.Hyperbolicembeddingsofferexcellentqualit...
HyperbolicEntailmentConesforLearningHierarchicalEmbeddingsOctavian-EugenGanea1GaryBe´cigneul1ThomasHofmann1AbstractPopularmethodstypicallyembedsymbolicobjectsinlowdimensionalEuclideanvectorspacesu...