mlsanityData to 7 Oct 2026

Connecting Sphere Manifolds Hierarchically for Regularization

arXiv 2106.13549 ↗First posted 25 Jun 2021cs.CV cs.LGcited by 2

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Abstract (arXiv)

This paper considers classification problems with hierarchically organized classes. We force the classifier (hyperplane) of each class to belong to a sphere manifold, whose center is the classifier of its super-class. Then, individual sphere manifolds are connected based on their hierarchical relations. Our technique replaces the last layer of a neural network by combining a spherical fully-connected layer with a hierarchical layer. This regularization is shown to improve the performance of widely used deep neural network architectures (ResNet and DenseNet) on publicly available datasets (CIFAR100, CUB200, Stanford dogs, Stanford cars, and Tiny-ImageNet).

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 22 of its 45 references that are in the map. First posted on arXiv 25 Jun 2021.

Builds on

22 of 45 references.

References · 22

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2016Densely Connected Convolutional Networkscited by 6,691
  3. 2013Efficient Estimation of Word Representations in Vector Spacecited by 4,346
  4. 2013Distributed Representations of Words and Phrases and their Compositionalitycited by 3,462
  5. 2018Relational inductive biases, deep learning, and graph networkscited by 1,341
  6. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  7. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 674
  8. 2019Hyperbolic Graph Convolutional Neural Networkscited by 400
  9. 2018Hyperbolic Neural Networkscited by 393
  10. 2016Generative Visual Manipulation on the Natural Image Manifoldcited by 348
  11. 2016Large-Margin Softmax Loss for Convolutional Neural Networkscited by 296
  12. 2019Hyperbolic Graph Neural Networkscited by 244
10 more
  1. 2019Hyperbolic Image Embeddingscited by 219
  2. 2018Representation Tradeoffs for Hyperbolic Embeddingscited by 204
  3. 2018Riemannian Adaptive Optimization Methodscited by 187
  4. 2018Poincar'e GloVe: Hyperbolic Word Embeddingscited by 155
  5. 2015Order-Embeddings of Images and Languagecited by 112
  6. 2020Geoopt: Riemannian Optimization in PyTorchcited by 109
  7. 2019Constant Curvature Graph Convolutional Networkscited by 106
  8. 2019Mixed-curvature Variational Autoencoderscited by 85
  9. 2017Do Convolutional Neural Networks Learn Class Hierarchy?cited by 61
  10. 2016Nonparametric Spherical Topic Modeling with Word Embeddingscited by 16

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Cited by year

Citing papers per year: 2022: 1; 2023: 1.

2 papers.

  1. 2023Inducing Neural Collapse to a Fixed Hierarchy-Aware Frame for Reducing Mistake Severitycited by 13
  2. 2022Isometric Representations in Neural Networks Improve Robustnesscited by 1