Paper Citation Record · LEDGER

Cartan Networks: Group theoretical Hyperbolic Deep Learning

As of 8 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 4 inbound Pith citation observations for arXiv:2505.24353.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2505.24353 v1

Coverage vector

measured 55 of 55 reference resolution

Typed states for the displayed outbound observations.

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measured 59 of 59 standing notices

One-hop event checks from named stored sources.

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measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:22:45.739186Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-03T02:37:34.195980Z

Reference resolution

55 of 55 outbound references displayed

verified exact2
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 70a9cfb1-4ccb-44b0-86fc-4b16700ef8a4 · outbound

This paper cites Pattern Recognition and Machine Learning.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Pattern Recognition and Machine Learning

Reference 1

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Observation fc2f2664-698c-4fcf-9962-f4402040906e · outbound

This paper cites Poincaré embeddings for learning hierarchical represen- tations.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Poincaré embeddings for learning hierarchical represen- tations

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:33:54.200682Z

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Observation 4ea5bb02-758e-4de1-a345-d56d4d8367b9 · outbound

This paper cites Hyperbolic Neural Networks.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Hyperbolic Neural Networks

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:33:54.003447Z

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Observation 738a10be-d8b2-4ed4-9c73-ef7870b9eb60 · outbound

This paper cites Hyperbolic neural networks++.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Hyperbolic neural networks++

Reference 4

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Observation 85f7be8b-f835-4f6b-8578-b7f1f8ccb0ae · outbound

This paper cites Fully hyperbolic neural networks.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Fully hyperbolic neural networks

Reference 5

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Observation 8e2b62f2-23b2-4102-b3fd-2de487a65386 · outbound

This paper cites Fully hyperbolic convolutional neural networks for computer vision.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Fully hyperbolic convolutional neural networks for computer vision

Reference 6

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Observation 54a6097c-755b-4c9b-964a-588b2dd7fc13 · outbound

This paper cites Hyperbolic Graph Convolutional Neural Networks.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Hyperbolic Graph Convolutional Neural Networks

Reference 7

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Observation b0559d70-14a8-4ebc-aafb-4580b0f35836 · outbound

This paper cites Hyperbolic attention networks.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Hyperbolic attention networks

Reference 8

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Observation 68baa510-5260-4653-a4b0-eb654c15e9f4 · outbound

This paper cites Hyperbolic Deep Neural Networks: A Survey.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Hyperbolic Deep Neural Networks: A Survey

Reference 9

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Observation 2dc94106-718b-4629-a649-7a4612653922 · outbound

This paper cites Poincaré embedding reveals edge-based func- tional networks of the brain.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Poincaré embedding reveals edge-based func- tional networks of the brain

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:33:52.507844Z

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Observation 8f63f683-819b-4218-afb9-ffef98b5ab71 · outbound

This paper cites Poincaré maps for analyzing complex hierarchies in single-cell data.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Poincaré maps for analyzing complex hierarchies in single-cell data

Reference 11

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Observation 64f32e6c-e0e9-41b4-a415-c47fd80cf319 · outbound

This paper cites Scalable Hyperbolic Recommender Systems.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Scalable Hyperbolic Recommender Systems

Reference 12

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Observation 6c1d2fff-db88-46ca-8a4e-b08eb57ede77 · outbound

This paper cites Sur une classe remarquable d’espaces de Riemann.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Sur une classe remarquable d’espaces de Riemann

Reference 13

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Observation c3e6273c-93a5-4ecf-a0da-c67104c5e699 · outbound

This paper cites Differential geometry and symmetric spaces.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Differential geometry and symmetric spaces

Reference 14

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Observation 4788d0c0-bade-4b0f-ae93-4a5975c5f992 · outbound

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Cartan Networks: Group theoretical Hyperbolic Deep Learning Unresolved cited work

Reference 15

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Observation d986e8c1-2215-492f-8f56-bbfffadd8980 · outbound

This paper cites An introduction to symmetric spaces.

Cartan Networks: Group theoretical Hyperbolic Deep Learning An introduction to symmetric spaces

Reference 16

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Observation 5dbf7eaa-4b76-45a0-b7e8-ae9705e539fb · outbound

This paper cites Fré, and Mario Trigiante.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Fré, and Mario Trigiante

Reference 17

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Observation 5397833e-089a-4758-ab7e-e647f096fd3e · outbound

This paper cites Fré, Ruben Minasian, and Mario Trigiante.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Fré, Ruben Minasian, and Mario Trigiante

Reference 18

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Observation 9d053b2a-1b23-4c81-a972-22e0db131ff6 · outbound

This paper cites Fré, Floriana Gargiulo, Jan Rosseel, Ksenya Rulik, Mario Trigiante, and Antoine Van Proeyen.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Fré, Floriana Gargiulo, Jan Rosseel, Ksenya Rulik, Mario Trigiante, and Antoine Van Proeyen

Reference 19

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Observation 718d3e4e-a39c-49fd-9345-23c0f61b8c30 · outbound

This paper cites Alekseevsky.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Alekseevsky

Reference 20

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Observation aba471e3-123c-4a09-8419-4845ec106183 · outbound

This paper cites Alekseevskian spaces.Differential Geometry and its Applications, 6(2):129–168, 1996.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Alekseevskian spaces.Differential Geometry and its Applications, 6(2):129–168, 1996

Reference 21

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Observation d48637de-b400-48ca-9f15-23eab2903c38 · outbound

This paper cites Alekseevsky, Vicente Cortés, Chandrashekar Devchand, and Antoine Van Proeyen.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Alekseevsky, Vicente Cortés, Chandrashekar Devchand, and Antoine Van Proeyen

Reference 22

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Observation f12a20bc-7845-4d0e-b465-f690b004b3a3 · outbound

This paper cites The paint group Tits Satake theory of hyperbolic symmetric spaces: the distance function, paint invariants and discrete subgroups.

Cartan Networks: Group theoretical Hyperbolic Deep Learning The paint group Tits Satake theory of hyperbolic symmetric spaces: the distance function, paint invariants and discrete subgroups

Reference 23

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Observation 4259ca09-630f-47ed-9308-de93635836ba · outbound

This paper cites Navigation through Non Compact Symmetric Spaces, that is Cartan Neural Networks.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Navigation through Non Compact Symmetric Spaces, that is Cartan Neural Networks

Reference 24

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Observation dbdfd891-a007-4122-bc1c-6813c32cca02 · outbound

This paper cites A Gyrovector Space Approach to Hyperbolic Geometry.

Cartan Networks: Group theoretical Hyperbolic Deep Learning A Gyrovector Space Approach to Hyperbolic Geometry

Reference 25

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Observation 2fa4bba1-212b-4e28-a3b4-584e7f0daca4 · outbound

This paper cites Hyperbolic Convolutional Neural Networks.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Hyperbolic Convolutional Neural Networks

Reference 26

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Observation 78fc9447-c31c-4592-a732-f6f5b678ecb6 · outbound

This paper cites On the Universal Statistical Consistency of Expansive Hyperbolic Deep Convolutional Neural Networks.

Cartan Networks: Group theoretical Hyperbolic Deep Learning On the Universal Statistical Consistency of Expansive Hyperbolic Deep Convolutional Neural Networks

Reference 27

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This paper cites Cohen, Mario Geiger, and Maurice Weiler.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Cohen, Mario Geiger, and Maurice Weiler

Reference 28

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Cartan Networks: Group theoretical Hyperbolic Deep Learning Unresolved cited work

Reference 29

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Observation 38978b12-e068-4bfb-a8d4-e884e8eb0c09 · outbound

This paper cites A Unified Framework to Enforce, Discover, and Promote Symmetry in Machine Learning.

Cartan Networks: Group theoretical Hyperbolic Deep Learning A Unified Framework to Enforce, Discover, and Promote Symmetry in Machine Learning

Reference 30

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This paper cites Lie neurons: Adjoint-equivariant neural networks for semisimple lie algebras.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Lie neurons: Adjoint-equivariant neural networks for semisimple lie algebras

Reference 31

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This paper cites A group-theoretic framework for machine learning in hyperbolic spaces.

Cartan Networks: Group theoretical Hyperbolic Deep Learning A group-theoretic framework for machine learning in hyperbolic spaces

Reference 32

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This paper cites Humphreys.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Humphreys

Reference 33

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Observation c77a7402-ba8c-484f-9f3c-6402a24810ff · outbound

This paper cites The Numerical Stability of Hyperbolic Representation Learning.

Cartan Networks: Group theoretical Hyperbolic Deep Learning The Numerical Stability of Hyperbolic Representation Learning

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:33:49.143379Z

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Observation 71fe5345-349e-4155-a888-7e95d850a3cd · outbound

This paper cites Clustering in hyperbolic balls.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Clustering in hyperbolic balls

Reference 35

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Observation 3e07debb-8b81-4f27-a3ab-bdbeeb78c442 · outbound

This paper cites Compact manifolds of nonpositive curvature.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Compact manifolds of nonpositive curvature

Reference 36

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Observation 278d249f-1743-4e9d-8883-a235ecbe045f · outbound

This paper cites Nguyen, and Christopher Re.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Nguyen, and Christopher Re

Reference 37

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This paper cites Stochastic gradient descent on riemannian manifolds.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Stochastic gradient descent on riemannian manifolds

Reference 38

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Observation e8c4d023-ebf0-4d4e-81b4-2c45fe7e897a · outbound

This paper cites Riemannian adaptive optimization methods.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Riemannian adaptive optimization methods

Reference 39

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Observation 00ab652a-c557-448e-9fb1-3f338b82e5ae · outbound

This paper cites Fast and accurate deep net- work learning by exponential linear units (elus).

Cartan Networks: Group theoretical Hyperbolic Deep Learning Fast and accurate deep net- work learning by exponential linear units (elus)

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:33:48.350382Z

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Observation 83f6646e-2630-4465-85ed-24d5321b36fa · outbound

This paper cites PyTorch: An Imperative Style, High-Performance Deep Learning Library.

Cartan Networks: Group theoretical Hyperbolic Deep Learning PyTorch: An Imperative Style, High-Performance Deep Learning Library

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:33:48.172978Z

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This paper cites Lie groups, Lie algebras, and some of their applications.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Lie groups, Lie algebras, and some of their applications

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:33:47.915129Z

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Cartan Networks: Group theoretical Hyperbolic Deep Learning Unresolved cited work

Reference 43

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Cartan Networks: Group theoretical Hyperbolic Deep Learning do Carmo

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:33:47.395903Z

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Observation b4b15a55-bd1e-4f93-8775-6c1822dc4df9 · outbound

This paper cites Fré, Floriana Gargiulo, and Ksenya Rulik.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Fré, Floriana Gargiulo, and Ksenya Rulik

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:33:47.155024Z

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Observation ebe76caa-eadd-4958-abca-887750e45fed · outbound

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Cartan Networks: Group theoretical Hyperbolic Deep Learning Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:33:46.824590Z

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Observation d6ce4830-f024-4618-ace8-abe1dd17e441 · outbound

This paper cites Foundations of Differential Geometry, volume 2.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Foundations of Differential Geometry, volume 2

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:33:46.432736Z

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Observation 26a8c247-a476-4ac2-a517-405a3a2ca7a4 · outbound

This paper cites Geoopt: Riemannian Optimization in PyTorch.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Geoopt: Riemannian Optimization in PyTorch

Reference 48

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Observation adf9239e-2413-48c7-9f85-5c13f046ec96 · outbound

This paper cites The merged-staircase prop- erty: a necessary and nearly sufficient condition for sgd learning of sparse functions on two-layer neural networks.

Cartan Networks: Group theoretical Hyperbolic Deep Learning The merged-staircase prop- erty: a necessary and nearly sufficient condition for sgd learning of sparse functions on two-layer neural networks

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:33:46.254198Z

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Observation 16d94bee-8073-471b-8037-bed35de8ed0e · outbound

This paper cites Gradient-based learning applied to document recognition.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Gradient-based learning applied to document recognition

Reference 50

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Observation a49e5085-2a3a-44f5-b078-0dc5d767e545 · outbound

This paper cites Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-07T12:33:44.474942Z

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Observation 2bc9146c-4a96-4031-b5d4-7ae8c3bcc360 · outbound

This paper cites Deep Learning for Classical Japanese Literature.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Deep Learning for Classical Japanese Literature

Reference 52

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Source-reported events for the cited work

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Observation a3839ec1-a19b-4bff-b5cd-0b83753c4fd0 · outbound

This paper cites Learning multiple layers of features from tiny images.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Learning multiple layers of features from tiny images

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:33:46.041768Z

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Observation 23173c7d-0c2a-422a-80fd-e208576ae23d · outbound

This paper cites an unresolved cited work.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Unresolved cited work

Reference 54

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:33:45.928473Z

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Observation e9be5bb9-4289-4222-8db9-8611b30e396e · outbound

This paper cites an unresolved cited work.

Cartan Networks: Group theoretical Hyperbolic Deep Learning Unresolved cited work

Reference 55

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:33:45.710124Z

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Pith citing papers

Observation 33322580-522a-401f-9f70-3ba39c535fc4 · inbound

Navigation through Non-Compact Symmetric Spaces: a mathematical perspective on Cartan Neural Networks cites this paper.

Navigation through Non-Compact Symmetric Spaces: a mathematical perspective on Cartan Neural Networks Cartan Networks: Group theoretical Hyperbolic Deep Learning

Reference 11

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Observation f091665a-4ade-44ef-b8f8-e12a1b9e4db4 · inbound

Thermodynamics a la Souriau on K\"ahler Non Compact Symmetric Spaces for Cartan Neural Networks cites this paper.

Thermodynamics a la Souriau on K\"ahler Non Compact Symmetric Spaces for Cartan Neural Networks Cartan Networks: Group theoretical Hyperbolic Deep Learning

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T15:35:34.827480Z

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Observation 6d9ffe3d-54dc-47bd-8e2b-ecfb3e4a0f28 · inbound

The macroscopic Kaehler metric of Geometric Thermodynamics versus the microscopic one on the Event Manifold: Exact Partition Functions on CV manifolds. Extended Souriau temperatures and spontaneous magnetizations cites this paper.

The macroscopic Kaehler metric of Geometric Thermodynamics versus the microscopic one on the Event Manifold: Exact Partition Functions on CV manifolds. Extended Souriau temperatures and spontaneous magnetizations Cartan Networks: Group theoretical Hyperbolic Deep Learning

Reference 18

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Observation 99f4d2c7-804b-4bf3-b103-b4d5b9116626 · inbound

General Properties of the Thermo-Metric for CV event manifolds and the magnetization combinatorial scheme cites this paper.

General Properties of the Thermo-Metric for CV event manifolds and the magnetization combinatorial scheme Cartan Networks: Group theoretical Hyperbolic Deep Learning

Reference 3

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