Paper Citation Record · LEDGER

Riemannian batch normalization for SPD neural networks

As of 17 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 2 inbound Pith citation observations for arXiv:1909.02414.

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

pith.paper-citation-record.v1
1909.02414 v2

Coverage vector

measured 44 of 44 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T05:21:44.981801Z

measured 46 of 46 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:02:50.153389Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-09T21:16:34.256122Z

Reference resolution

44 of 44 outbound references displayed

verified exact6
verified fuzzy21
unresolved17
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0c2dc1d1-9162-446d-9461-6948ff691c48 · outbound

This paper cites an unresolved cited work.

Riemannian batch normalization for SPD neural networks Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:21:46.369651Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 54b2e333-8bb2-4906-b94f-59a38b9f35b0 · outbound

This paper cites Arsigny, P.

Riemannian batch normalization for SPD neural networks Arsigny, P

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:46.346846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f29b8d23-7b8f-4aac-b98f-5d0134c82226 · outbound

This paper cites Atkinson and A.

Riemannian batch normalization for SPD neural networks Atkinson and A

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:46.324547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e4bc3b2a-6e7e-4d0a-b47e-32c655aad21d · outbound

This paper cites Barachant, S.

Riemannian batch normalization for SPD neural networks Barachant, S

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:46.298711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation eca27a80-b834-4316-b2b0-20b273fd1cf5 · outbound

This paper cites Barachant, S.

Riemannian batch normalization for SPD neural networks Barachant, S

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:46.276143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c3b95556-ec60-4290-b697-3dbba6562480 · outbound

This paper cites Barbaresco.

Riemannian batch normalization for SPD neural networks Barbaresco

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:46.248185Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 609133e0-afaf-4b33-bccd-a2f1ad0dbd09 · outbound

This paper cites an unresolved cited work.

Riemannian batch normalization for SPD neural networks Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:21:46.222932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation db9bf3f5-76a9-433a-9900-27c8c18eb166 · outbound

This paper cites Bonnabel and R.

Riemannian batch normalization for SPD neural networks Bonnabel and R

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:46.196952Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 02cf9873-095f-43fa-846b-a60b16bd3c42 · outbound

This paper cites Brodski˘ı, J.

Riemannian batch normalization for SPD neural networks Brodski˘ı, J

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:46.173637Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f7e336ac-ce4a-4d25-ad2f-2dbbb42fec1d · outbound

This paper cites an unresolved cited work.

Riemannian batch normalization for SPD neural networks Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:21:46.150297Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation bd36ff56-fc9d-494d-819c-0c2a76d08589 · outbound

This paper cites Cavazza, P.

Riemannian batch normalization for SPD neural networks Cavazza, P

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:46.119601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5d9b3e8b-2abd-4fc1-8e0e-0fa749b21e3f · outbound

This paper cites ManifoldNet: A Deep Network Framework for Manifold-valued Data.

Riemannian batch normalization for SPD neural networks ManifoldNet: A Deep Network Framework for Manifold-valued Data

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-14T05:21:44.553368Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 494ca7a0-964c-4666-9eab-38e650c56a77 · outbound

This paper cites Chakraborty, C.-H.

Riemannian batch normalization for SPD neural networks Chakraborty, C.-H

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:46.085877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b947a8f5-ae6f-48ae-8dea-5ff620836cda · outbound

This paper cites Charon and F.

Riemannian batch normalization for SPD neural networks Charon and F

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:46.057602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 53b58de2-5ba0-4a12-909e-84ff3590f175 · outbound

This paper cites an unresolved cited work.

Riemannian batch normalization for SPD neural networks Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:21:46.021994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 954fc817-568c-400a-a996-9de0e7aa382b · outbound

This paper cites Dhall, R.

Riemannian batch normalization for SPD neural networks Dhall, R

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:45.985371Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9f9384b2-b036-4a5d-a034-cfd1d00d22c6 · outbound

This paper cites an unresolved cited work.

Riemannian batch normalization for SPD neural networks Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:21:45.951176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7d03e57f-d1ea-447d-a737-50745887f677 · outbound

This paper cites Edelman, T.

Riemannian batch normalization for SPD neural networks Edelman, T

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:45.914127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8f4f7e04-384f-41f2-b751-82e20b537b88 · outbound

This paper cites DeepKSPD: Learning Kernel-matrix-based SPD Representation for Fine-grained Image Recognition.

Riemannian batch normalization for SPD neural networks DeepKSPD: Learning Kernel-matrix-based SPD Representation for Fine-grained Image Recognition

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:21:45.323728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 84a05e42-7fde-4a1b-b80a-9c8bebf62f96 · outbound

This paper cites an unresolved cited work.

Riemannian batch normalization for SPD neural networks Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:21:45.878206Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 61486dca-23aa-49f0-87c2-bc34c8ebf657 · outbound

This paper cites Learning a Robust Representation via a Deep Network on Symmetric Positive Definite Manifolds.

Riemannian batch normalization for SPD neural networks Learning a Robust Representation via a Deep Network on Symmetric Positive Definite Manifolds

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:21:45.294593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation aeab4f46-ef5d-4db2-9f8e-36c6063044d7 · outbound

This paper cites A Riemannian Network for SPD Matrix Learning.

Riemannian batch normalization for SPD neural networks A Riemannian Network for SPD Matrix Learning

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-14T05:21:44.627597Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c8d026bf-c407-4753-a656-980e9c786cf1 · outbound

This paper cites Deep Learning on Lie Groups for Skeleton-based Action Recognition.

Riemannian batch normalization for SPD neural networks Deep Learning on Lie Groups for Skeleton-based Action Recognition

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:21:45.225973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 42f8ff75-b362-4f37-ba61-658511d610d6 · outbound

This paper cites Building Deep Networks on Grassmann Manifolds.

Riemannian batch normalization for SPD neural networks Building Deep Networks on Grassmann Manifolds

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:21:45.189459Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8fafc401-f8bf-4a3c-a56d-d628e548b6f1 · outbound

This paper cites Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift.

Riemannian batch normalization for SPD neural networks Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-14T05:21:44.648402Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7cd00cf2-32dc-4c2b-b59f-efb79465d77b · outbound

This paper cites Ionescu, O.

Riemannian batch normalization for SPD neural networks Ionescu, O

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:45.839154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d13ce670-d92f-4860-94dd-cc860a895fce · outbound

This paper cites Jaquier and S.

Riemannian batch normalization for SPD neural networks Jaquier and S

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:45.799148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6cf56292-70c9-475e-821a-d3fe3c8c48f3 · outbound

This paper cites an unresolved cited work.

Riemannian batch normalization for SPD neural networks Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:21:45.757486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation afc50aa9-0e48-4479-83df-fe0b2dab3a72 · outbound

This paper cites Lecun, L.

Riemannian batch normalization for SPD neural networks Lecun, L

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:45.729608Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 657af0e4-0a92-4bb1-88c4-01800ee95208 · outbound

This paper cites an unresolved cited work.

Riemannian batch normalization for SPD neural networks Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:21:45.699004Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d0258808-40f6-49fd-ad25-43df1b2a58c0 · outbound

This paper cites an unresolved cited work.

Riemannian batch normalization for SPD neural networks Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:21:45.671723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation dd057da4-8d0d-4745-872b-b8562f4197f1 · outbound

This paper cites Marceau-Caron and Y.

Riemannian batch normalization for SPD neural networks Marceau-Caron and Y

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:45.647936Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e074d7aa-2137-4a3f-8f4c-ffc6d92c6e92 · outbound

This paper cites Müller, T.

Riemannian batch normalization for SPD neural networks Müller, T

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:45.615743Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 31985102-d0da-4cfb-b1ec-2a23a4acb04e · outbound

This paper cites Paszke, S.

Riemannian batch normalization for SPD neural networks Paszke, S

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:45.589641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1aa41c98-3fc4-4d58-ad56-698f44655996 · outbound

This paper cites Pennec, P.

Riemannian batch normalization for SPD neural networks Pennec, P

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:45.562710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c98c7b90-cd40-4110-89d1-0f32e1553f4c · outbound

This paper cites an unresolved cited work.

Riemannian batch normalization for SPD neural networks Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:21:45.538367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0f0345d5-2baf-41ce-8e2a-b0ac1e116d04 · outbound

This paper cites Riemannian Gaussian Distributions on the Space of Symmetric Positive Definite Matrices.

Riemannian batch normalization for SPD neural networks Riemannian Gaussian Distributions on the Space of Symmetric Positive Definite Matrices

Reference 37

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:21:45.109297Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e4e74275-236d-4032-9b5d-0ec4c758c739 · outbound

This paper cites Tuzel, F.

Riemannian batch normalization for SPD neural networks Tuzel, F

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:45.503258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8d9b1098-51c9-4144-946c-f3236f204aa9 · outbound

This paper cites an unresolved cited work.

Riemannian batch normalization for SPD neural networks Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:21:45.475171Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 102e6e18-f651-4ffb-969f-b16ae4375c85 · outbound

This paper cites an unresolved cited work.

Riemannian batch normalization for SPD neural networks Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:21:45.450867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 37f08fae-1a0e-414b-8a12-261b573bf3fe · outbound

This paper cites an unresolved cited work.

Riemannian batch normalization for SPD neural networks Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:21:45.417844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d5081b96-7938-4f13-b90f-7a705abec10e · outbound

This paper cites an unresolved cited work.

Riemannian batch normalization for SPD neural networks Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:21:45.393798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 85b5acb5-bd6d-4ffb-9319-8ef18cae3f4a · outbound

This paper cites Supervised LogEuclidean Metric Learning for Symmetric Positive Definite Matrices.

Riemannian batch normalization for SPD neural networks Supervised LogEuclidean Metric Learning for Symmetric Positive Definite Matrices

Reference 43

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:21:45.069326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation bf0b253d-4db1-4d32-a196-0cee22b30750 · outbound

This paper cites Zhang, W.

Riemannian batch normalization for SPD neural networks Zhang, W

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:21:45.372696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

Observation 2893690b-bdc0-4215-9449-284395a144b3 · inbound

Constitutive Manifold Neural Networks cites this paper.

Constitutive Manifold Neural Networks Riemannian batch normalization for SPD neural networks

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T20:02:50.153389Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ef12b601-9f49-4a2e-a501-ee854253f2d4 · inbound

Riemannian Geometry for Pre-trained Language Model Embeddings cites this paper.

Riemannian Geometry for Pre-trained Language Model Embeddings Riemannian batch normalization for SPD neural networks

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-07-09T21:16:34.257362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.