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Fully Hyperbolic Neural Networks

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arxiv 2105.14686 v3 pith:RXQVZE3G submitted 2021-05-31 cs.CL cs.LG

Weize Chen , Xu Han , Yankai Lin , Hexu Zhao , Zhiyuan Liu , Peng Li , Maosong Sun , Jie Zhou This is my paper · ORCID
classification cs.CLcs.LG
keywords hyperbolicnetworksexistinglorentzneuralspaceboostformalize
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Hyperbolic neural networks have shown great potential for modeling complex data. However, existing hyperbolic networks are not completely hyperbolic, as they encode features in a hyperbolic space yet formalize most of their operations in the tangent space (a Euclidean subspace) at the origin of the hyperbolic space. This hybrid method greatly limits the modeling ability of networks. In this paper, we propose a fully hyperbolic framework to build hyperbolic networks based on the Lorentz model by adapting the Lorentz transformations (including boost and rotation) to formalize essential operations of neural networks. Moreover, we also prove that linear transformation in tangent spaces used by existing hyperbolic networks is a relaxation of the Lorentz rotation and does not include the boost, implicitly limiting the capabilities of existing hyperbolic networks. The experimental results on four NLP tasks show that our method has better performance for building both shallow and deep networks. Our code will be released to facilitate follow-up research.

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Cited by 11 Pith papers

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

  1. 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...

  2. Advancing Multimodal Fusion on Heterogeneous Medical Data with Hybrid Geometry Attention

    cs.CV 2026-07 conditional novelty 6.0 of 10

    CURE, a cascaded fusion framework with hybrid hyperbolic/quantum attention, reports state-of-the-art accuracy and lower compute on 16 medical datasets.

  3. 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.

  4. HLFormer: Enhancing Partially Relevant Video Retrieval with Hyperbolic Learning

    cs.CV 2025-07 conditional novelty 6.0 of 10

    HLFormer adds hybrid Euclidean and Lorentz attention plus a partial-order cone loss to partially relevant video retrieval and reports the best total recall on ActivityNet Captions, Charades-STA, and TVR.

  5. Even Faster Hyperbolic Random Forests: A Beltrami-Klein Wrapper Approach

    cs.LG 2025-06 conditional novelty 6.0 of 10

    Fast-HyperDT reexpresses HyperDT as pre- and post-processing around standard Euclidean trees, making hyperbolic random forests practical.

  6. Hgformer: Hyperbolic Graph Transformer for Recommendation

    cs.IR 2024-12 reject novelty 6.0 of 10

    Hgformer is a hyperbolic graph transformer for collaborative filtering that reports improved recall and NDCG on six datasets, but its linear-attention approximation is not actually unbiased as claimed.

  7. Lorentzian Residual Neural Networks

    cs.LG 2024-12 conditional novelty 6.0 of 10

    LResNet performs hyperbolic residual connections with a normalized weighted sum (the Lorentzian centroid), avoiding tangent-space mappings and improving efficiency and accuracy in hyperbolic GNNs, graph transformers, ...

  8. Adversarial Attacks on Hyperbolic Networks

    cs.LG 2024-12 conditional novelty 5.0 of 10

    Hyperbolic versions of FGM and PGD attacks are proposed, and experiments show that Euclidean and hyperbolic ResNets have different, geometry-specific adversarial vulnerabilities.

  9. Multi-Order Hyperbolic Graph Convolution and Aggregated Attention for Social Event Detection

    cs.SI 2025-02 conditional novelty 4.0 of 10

    MOHGCAA, a multi-order hyperbolic graph convolution with aggregated attention, is reported to outperform prior Euclidean and hyperbolic baselines on four datasets in supervised and unsupervised settings.

  10. Revisiting the Necessity of Graph Learning and Common Graph Benchmarks

    cs.LG 2024-12 conditional novelty 4.0 of 10

    Tuned feature-only MLPs nearly match graph neural networks on five common graph benchmarks, suggesting those benchmarks measure feature quality more than graph learning.

  11. Hyperbolic Deep Learning for Foundation Models: A Survey

    cs.LG 2025-07 conditional novelty 1.0 of 10

    A structured survey of hyperbolic-geometry methods for foundation models, concluding the approach is promising but showing limited independent evidence at scale.

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