{"id":44469,"date":"2021-09-24T16:57:44","date_gmt":"2021-09-24T14:57:44","guid":{"rendered":"https:\/\/www.h-its.org\/de\/?post_type=hits-project&p=44469"},"modified":"2026-03-31T12:00:29","modified_gmt":"2026-03-31T10:00:29","slug":"geometry-and-representation-learning","status":"publish","type":"hits-project","link":"https:\/\/www.h-its.org\/de\/projects\/geometry-and-representation-learning\/","title":{"rendered":"Geometry and Representation Learning"},"content":{"rendered":"
\n
\"\"<\/a>
Analyse der Struktur von Graphen f\u00fcr reale Datens\u00e4tze, BIO-DISEASOME (links), CSPHD (Mitte) und FACEBOOK (rechts). Unsere Methode unterscheidet dichter verbundene Teile der Graphen (blau\/gr\u00fcn in BIO-DISEASOME und FACEBOOK) von weniger verbundenen, baumstruktur\u00e4hnlichen Teilen (gelb in CSPHD).<\/figcaption><\/figure>\n<\/div>\n\n\n

In den letzten Jahren ist das Interesse an der hyperbolischen Geometrie in der Datenanalyse und im maschinellen Lernen f\u00fcr das \u201eRepresentation learning\u201c, also das Lernen von Darstellungen mittels Einbettungen von Graphen, und f\u00fcr die Konstruktion sogenannter hyperbolischer neuronaler Netze gewachsen.
<\/p>\n\n\n\n

Das Erlernen von Graphenrepr\u00e4sentationen mit niedrigdimensionalen Einbettungen ist ein wichtiges Problem beim maschinellen Lernen, da in vielen Situationen (z. B. in der Linguistik, Evolutionsbiologie, in Computernetzwerken usw.) Daten einer (teilweise hierarchischen) Graphenstruktur vorliegen. Hyperbolische R\u00e4ume bieten oftmals bessere Umgebungsr\u00e4ume f\u00fcr die Einbettung von Graphen als euklidische R\u00e4ume, da letztere nicht so viel Platz f\u00fcr das exponentielle Wachstum vieler Graphen und B\u00e4ume bieten.
<\/p>\n\n\n\n

Im Jahr 2020 begann die beiden Gruppen GRG und NLP, gemeinsam die komplizierteren nicht-euklidischen Geometrien zu erforschen, die sich aus symmetrischen R\u00e4umen ergeben. Eine erste Arbeit, in der wir einen systematischen Rahmen und Metriken f\u00fcr das Lernen von Grapheneinbettungen in symmetrischen R\u00e4umen vorschlagen, wurde im Juni 2021auf der International Conference on Machine Learning<\/a> (ICML 2021) ver\u00f6ffentlicht.<\/p>\n\n\n\n

Beteiligte:<\/strong><\/p>\n\n\n\n

Michael Strube <\/a>(NLP)
Anna Wienhard<\/a> (GRG)<\/p>\n\n\n\n


<\/p>\n\n\n\n

Publikationen:<\/strong>
„Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach“ (accepted to ICML 2021 Conference) https:\/\/arxiv.org\/abs\/2106.04941<\/a>
„Hermitian Symmetric Spaces for Graph Embeddings“, presentation in the NeurIPS 2020 workshop on Differential Geometry meets Deep Learning, arXiv:2105.05275<\/a>
„Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matrices“ (accepted for a spotlight presentation at NeurIPS2021) https:\/\/arxiv.org\/abs\/2110.13475<\/a><\/p>\n\n\n\n

Kooperationspartner:<\/strong>
Maria Beatrice Pozzetti (Universit\u00e4t Heidelberg)
Steve Trettel<\/a> (Stanford University)<\/p>\n","protected":false},"author":58,"featured_media":44472,"template":"","hits-research-group":[1293,1302,1418],"hits-project-category":[1396],"class_list":["post-44469","hits-project","type-hits-project","status-publish","has-post-thumbnail","hentry","hits-research-group-grg-de","hits-research-group-nlp-de","hits-research-group-hits-lab","hits-project-category-previous-projects-de"],"acf":[],"yoast_head":"\nGeometry and Representation Learning - HITS gGmbH<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.h-its.org\/de\/projects\/geometry-and-representation-learning\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Geometry and Representation Learning - HITS gGmbH\" \/>\n<meta property=\"og:description\" content=\"In den letzten Jahren ist das Interesse an der hyperbolischen Geometrie in der Datenanalyse und im maschinellen Lernen f\u00fcr das \u201e...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.h-its.org\/de\/projects\/geometry-and-representation-learning\/\" \/>\n<meta property=\"og:site_name\" content=\"HITS gGmbH\" \/>\n<meta property=\"article:modified_time\" content=\"2026-03-31T10:00:29+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.h-its.org\/de\/wp-content\/uploads\/sites\/2\/2021\/09\/TeaserBild_Fig_1_Geometry_RepLearning.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"580\" \/>\n\t<meta property=\"og:image:height\" content=\"467\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Gesch\u00e4tzte Lesezeit\" \/>\n\t<meta name=\"twitter:data1\" content=\"2\u00a0Minuten\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.h-its.org\\\/de\\\/projects\\\/geometry-and-representation-learning\\\/\",\"url\":\"https:\\\/\\\/www.h-its.org\\\/de\\\/projects\\\/geometry-and-representation-learning\\\/\",\"name\":\"Geometry and Representation Learning - 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