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Hyperbolic Neural Networks++

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arxiv 2006.08210 v3 pith:FM2KN366 submitted 2020-06-15 cs.LG stat.ML

Ryohei Shimizu , Yusuke Mukuta , Tatsuya Harada This is my paper
classification cs.LGstat.ML
keywords hyperboliccomponentslayersmodelnetworksneuralwithoutapplied
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Hyperbolic spaces, which have the capacity to embed tree structures without distortion owing to their exponential volume growth, have recently been applied to machine learning to better capture the hierarchical nature of data. In this study, we generalize the fundamental components of neural networks in a single hyperbolic geometry model, namely, the Poincar\'e ball model. This novel methodology constructs a multinomial logistic regression, fully-connected layers, convolutional layers, and attention mechanisms under a unified mathematical interpretation, without increasing the parameters. Experiments show the superior parameter efficiency of our methods compared to conventional hyperbolic components, and stability and outperformance over their Euclidean counterparts.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. LieBN: Batch Normalization over Lie Groups

    cs.LG 2026-06 conditional novelty 7.0 of 10

    LieBN normalizes both Fréchet mean and variance on any Lie group under its natural invariant metrics, with concrete realisations on four SPD geometries (including a new right-invariant metric), SO(n) and four correlat...

  2. New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures

    quant-ph 2026-04 unverdicted novelty 7.0 of 10

    On 100-site Heisenberg J1-J2 and J1-J2-J3 chains, hyperbolic Poincaré/Lorentz RNN and GRU neural quantum states mostly beat Euclidean counterparts; Lorentz RNN wins four of eight settings despite about three times few...

  3. Learning Taxonomic Trees with Hierarchical Representation Regularization for Large Multimodal Models

    cs.CV 2026-07 conditional novelty 6.0 of 10

    HiR² extracts coarse-to-fine visual features from LMM layers and regularizes them with Lorentz entailment cones and unit-sphere dispersive loss, improving hierarchical consistency across models and fine-tuning methods.

  4. HyPCV-Former: Hyperbolic Spatio-Temporal Transformer for 3D Point Cloud Video Anomaly Detection

    cs.CV 2025-08 unverdicted novelty 6.0 of 10

    HyPCV-Former embeds point cloud video features in Lorentzian hyperbolic space and uses hyperbolic attention to improve video anomaly detection on two benchmarks.

  5. A Set-to-Set Distance Measure in Hyperbolic Space

    cs.CV 2025-06 reject novelty 6.0 of 10

    A hyperbolic set-to-set distance that blends Einstein-midpoint geodesic distance with a Thue-Morse graph-topology term is proposed and reported to improve entity matching and few-shot classification.

  6. Continual Hyperbolic Learning of Instances and Classes

    cs.CV 2025-06 conditional novelty 6.0 of 10

    HyperCLIC embeds the instance-class hierarchy in hyperbolic space and uses hyperbolic classification and distillation losses to continuously learn both fine-grained instances and coarse-grained classes on EgoObjects, ...

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