Recently, there has been a surge of interest in representation learning in hyperbolic spaces, driven by their ability to represent hierarchical data with significantly fewer dimensions than standard Euclidean spaces. However, the viability and benefits of hyperbolic spaces for downstream machine learning tasks have received less attention. In this paper, we present, to our knowledge, the first theoretical guarantees for learning a classifier in hyperbolic rather than Euclidean space. Specifically, we consider the problem of learning a large-margin classifier for data possessing a hierarchical structure. We provide an algorithm to efficiently learn a large-margin hyperplane, relying on the careful injection of adversarial examples. Finally, we prove that for hierarchical data that embeds well into hyperbolic space, the low embedding dimension ensures superior guarantees when learning the classifier directly in hyperbolic space.
Enhancing Hyperbolic Graph Embeddings via Contrastive Learning
Harbin Institute of Technology(Shenzhen)（哈尔滨工业大学（深圳））；The Chinese University of Hong Kong（香港中文大学）；Huawei Technologies co.ltd（华为技术有限公司）；Shenzhen University（深圳大学）
Convex Relaxation for Solving Large-Margin Classifiers in Hyperbolic Space
John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Center for Brain Science, Harvard University（哈佛大学脑科学中心）；Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University（哈佛大学肯普ner自然与人工智能研究所）
A Robust Twin Parametric Margin Support Vector Machine for Multiclass Classification
School of Science and Technology, University of Camerino（科学与技术学院，坎皮诺大学）；Department of Management, Information and Production Engineering, University of Bergamo（管理、信息与生产工程系，贝拉姆多大学）
Hyperbolic Structured Classification for Robust Single Positive Multi-label Learning
School of Advanced Technology（高级技术学院）；Xi'an Jiaotong-Liverpool University（西安交通大学利物浦大学）；School of Data Science（数据科学学院）；Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Digital Innovation Research Center（数字创新研究中心）；Duke Kunshan University（杜克大学昆山分校）
ProME: Prototype-Margin Environments with Repair-Aware Selection for Group-Robust Learning
Shenzhen Key Laboratory of Safety and Security for Next Generation of Industrial Internet（深圳市下一代工业互联网安全重点实验室）；Department of Statistics and Data Science, Southern University of Science and Technology（南方科技大学统计与数据科学系）
Centre de Recherche en Informatique, Signal et Automatique de Lille（里尔计算机、信号与自动化研究中心）；Label4.ai；IMT Nord Europe, Institut Mines-Télécom（法国国立高等矿业电信学校北欧分校（ Mines-Telecom 学院））
