4,851 research outputs found
Laplacian Features for Learning with Hyperbolic Space
Due to its geometric properties, hyperbolic space can support high-fidelity
embeddings of tree- and graph-structured data. As a result, various hyperbolic
networks have been developed which outperform Euclidean networks on many tasks:
e.g. hyperbolic graph convolutional networks (GCN) can outperform vanilla GCN
on some graph learning tasks. However, most existing hyperbolic networks are
complicated, computationally expensive, and numerically unstable -- and they
cannot scale to large graphs due to these shortcomings. With more and more
hyperbolic networks proposed, it is becoming less and less clear what key
component is necessary to make the model behave. In this paper, we propose
HyLa, a simple and minimal approach to using hyperbolic space in networks: HyLa
maps once from a hyperbolic-space embedding to Euclidean space via the
eigenfunctions of the Laplacian operator in the hyperbolic space. We evaluate
HyLa on graph learning tasks including node classification and text
classification, where HyLa can be used together with any graph neural networks.
When used with a linear model, HyLa shows significant improvements over
hyperbolic networks and other baselines
Hyperbolic Interaction Model For Hierarchical Multi-Label Classification
Different from the traditional classification tasks which assume mutual
exclusion of labels, hierarchical multi-label classification (HMLC) aims to
assign multiple labels to every instance with the labels organized under
hierarchical relations. Besides the labels, since linguistic ontologies are
intrinsic hierarchies, the conceptual relations between words can also form
hierarchical structures. Thus it can be a challenge to learn mappings from word
hierarchies to label hierarchies. We propose to model the word and label
hierarchies by embedding them jointly in the hyperbolic space. The main reason
is that the tree-likeness of the hyperbolic space matches the complexity of
symbolic data with hierarchical structures. A new Hyperbolic Interaction Model
(HyperIM) is designed to learn the label-aware document representations and
make predictions for HMLC. Extensive experiments are conducted on three
benchmark datasets. The results have demonstrated that the new model can
realistically capture the complex data structures and further improve the
performance for HMLC comparing with the state-of-the-art methods. To facilitate
future research, our code is publicly available
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