SURVEY ON LEARNING IN THE HYPERBOLIC SPACE

PhD Qualifying Examination


Title: "SURVEY ON LEARNING IN THE HYPERBOLIC SPACE"

by

Miss Huiru XIAO


Abstract:

Hyperbolic space has gained more and more attention in machine learning field 
in recent years because of its tree-like properties such as exponential volume 
growth. These properties make hyperbolic space highly suitable to represent 
hierarchical structures. In consequence, embedding the data with a hierarchical 
structure in hyperbolic space achieves better results than traditional 
Euclidean embeddings. Inspired by representation learning in hyperbolic space, 
the derivation of basic operations and units of deep neural networks in 
hyperbolic space is also under development. The hyperbolic neural network 
frameworks in turn help the utilization of hyperbolic embeddings. In this 
survey, we introduce the research works on learning in the hyperbolic space, 
including hyperbolic representation learning, hyperbolic neural networks and 
their applications. For representation learning, we present hyperbolic graph 
embeddings and hyperbolic word embeddings, most of which choose Poincar?? ball 
model or the hyperboloid model as the embedding space. The two models have 
relatively simple distance functions and metric tensors, thus easier to adapt 
Riemannian optimization. We then introduce hyperbolic neural networks, mainly 
focusing on recurrent neural networks, autoencoders and attention networks 
redefined in hyperbolic space. Finally, we summarize the applications of 
hyperbolic learning, including link prediction, hypernymy detection, 
recommender systems and so on.


Date:			Monday, 17 June 2019

Time:                  	3:00pm - 5:00pm

Venue:                  Room 3494
                         Lifts 25/26

Committee Members:	Dr. Yangqiu Song (Supervisor)
 			Prof. Nevin Zhang (Chairperson)
 			Dr. Raymond Wong
 			Prof. Dit-Yan Yeung


**** ALL are Welcome ****