# Hyperbolic Busemann Learning with Ideal Prototypes

@inproceedings{Atigh2021HyperbolicBL, title={Hyperbolic Busemann Learning with Ideal Prototypes}, author={Mina Ghadimi Atigh and Martin Keller-Ressel and Pascal Mettes}, booktitle={Neural Information Processing Systems}, year={2021} }

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…

## 5 Citations

### Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projections

- Computer Science, MathematicsArXiv
- 2022

This work proposes to derive novel hyperbolic sliced-Wasserstein discrepancies based on constructions which use projections on the underlying geodesics either along horospheres or geodesICS, and studies and compares these constructions on different tasks wherehyperbolic representations are relevant.

### Few-shot Classification with Hypersphere Modeling of Prototypes

- Computer ScienceArXiv
- 2022

This work uses tensor ﬁelds (“areas”) to model classes from the geometrical perspective for few-shot learning and presents a simple and effective method, dubbed as hypersphere prototypes ( HyperProto), where class information is represented by hyperspheres with dynamic sizes with two sets of learnable parameters.

### Maximum Class Separation as Inductive Bias in One Matrix

- Computer ScienceArXiv
- 2022

This paper proposes a simple alternative to maximum separation as an inductive bias in the network by adding one matrix multiplication before computing the softmax activations, and illustrates that out-of-distribution and open-set recognition beneﬁt from an embedded maximum separation.

### Hyperbolic Image Segmentation

- Computer Science, Mathematics2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
- 2022

Hyperbolic Image Segmentation opens up new possibilities and practical benefits for segmentation, such as uncertainty estimation and boundary information for free, zero-label generalization, and increased performance in low-dimensional output embeddings.

### Hierarchical Explanations for Video Action Recognition

- Computer ScienceArXiv
- 2023

Hierarchical ProtoPNet is an interpretable network that explains its reasoning process by considering the hierarchical relationship between classes by dissecting the input video frames on multiple levels of the class hierarchy.

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