Hyperbolic Busemann Learning with Ideal Prototypes release_r5poy2x6pjdmpbwjwtkq2keio4

by Mina Ghadimi Atigh, Martin Keller-Ressel, Pascal Mettes

Released as a article .

2021  

Abstract

Hyperbolic space has become a popular choice of manifold for representation learning of arbitrary data, from tree-like structures and text to graphs. Building on the success of deep learning with prototypes in Euclidean and hyperspherical spaces, a few recent works have proposed hyperbolic prototypes for classification. Such approaches enable effective learning in low-dimensional output spaces and can exploit hierarchical relations amongst classes, but require privileged information about class labels to position the hyperbolic prototypes. In this work, we propose Hyperbolic Busemann Learning. The main idea behind our approach is to position prototypes on the ideal boundary of the Poincare ball, which does not require prior label knowledge. To be able to compute proximities to ideal prototypes, we introduce the penalised Busemann loss. We provide theory supporting the use of ideal prototypes and the proposed loss by proving its equivalence to logistic regression in the one-dimensional case. Empirically, we show that our approach provides a natural interpretation of classification confidence, while outperforming recent hyperspherical and hyperbolic prototype approaches.
In text/plain format

Archived Files and Locations

application/pdf  865.8 kB
file_f7m2bkuqprg23ix3w2igyxzk7q
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2021-06-28
Version   v1
Language   en ?
arXiv  2106.14472v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: b556429f-8fb4-4a68-b829-7a0affc82188
API URL: JSON