Paper Citation Record · LEDGER

Probing Equivariance and Symmetry Breaking in Convolutional Networks

As of 20 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 8 inbound Pith citation observations for arXiv:2501.01999.

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

pith.paper-citation-record.v1
2501.01999 v3

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T22:48:24.886018Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 8 of 8 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:30:56.597601Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-06-29T19:23:53.861003Z

Reference resolution

18 of 18 outbound references displayed

verified exact0
verified fuzzy9
unresolved8
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1bcde8be-4bc8-4dfc-a8f8-3a9b5fed8a8f · outbound

This paper cites This is because the action of g ∈ SE(3) permutes these values on the fiber or spatially, but the activation acts on each scalar value independently.

Probing Equivariance and Symmetry Breaking in Convolutional Networks This is because the action of g ∈ SE(3) permutes these values on the fiber or spatially, but the activation acts on each scalar value independently

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:48:25.956083Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 4639ec48-e484-4f96-a71f-8a9bc5531a72 · outbound

This paper cites Bekkers et al., 2024, Appx.

Probing Equivariance and Symmetry Breaking in Convolutional Networks Bekkers et al., 2024, Appx

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:48:25.945199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 931593ce-4618-49b5-a719-f2dd12ca1977 · outbound

This paper cites channel mixing.

Probing Equivariance and Symmetry Breaking in Convolutional Networks channel mixing

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:48:25.923405Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3d86f210-9df3-4bc1-bea4-bff49798b705 · outbound

This paper cites On genuine invariance learning without weight-tying.

Probing Equivariance and Symmetry Breaking in Convolutional Networks On genuine invariance learning without weight-tying

Reference 4

Resolution: metadata mismatch; local_arxiv, observed 2026-08-10T22:48:25.115492Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2b752daa-b3f5-4d9a-abf6-bbda60d0b636 · outbound

This paper cites PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation.

Probing Equivariance and Symmetry Breaking in Convolutional Networks PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-10T22:48:24.601472Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0905f5be-2bf5-4fec-a28f-9842062637ac · outbound

This paper cites Clifford Group Equivariant Neural Networks.

Probing Equivariance and Symmetry Breaking in Convolutional Networks Clifford Group Equivariant Neural Networks

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-10T22:48:24.605932Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78a972fc-0013-4cbc-b35e-cdaaaa227566 · outbound

This paper cites Specifically, f (X, Z) = f (X, Id) for any Z ∈ SO(3), where Id is the identity element in SO(3).

Probing Equivariance and Symmetry Breaking in Convolutional Networks Specifically, f (X, Z) = f (X, Id) for any Z ∈ SO(3), where Id is the identity element in SO(3)

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:48:25.834748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e035c693-396e-4850-859d-52461f384a5c · outbound

This paper cites The model cannot utilize any specific orientation information conveyed by Z.

Probing Equivariance and Symmetry Breaking in Convolutional Networks The model cannot utilize any specific orientation information conveyed by Z

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:48:25.812531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 0f05ca3a-5193-41df-b372-1771df1f1c99 · outbound

This paper cites an unresolved cited work.

Probing Equivariance and Symmetry Breaking in Convolutional Networks Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:48:25.789114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e853b317-7903-40aa-bb8f-21ec4c53537d · outbound

This paper cites That is, f (gX, Id) = f (X, Id) for all g ∈ SO(3).

Probing Equivariance and Symmetry Breaking in Convolutional Networks That is, f (gX, Id) = f (X, Id) for all g ∈ SO(3)

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:48:25.715583Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 4bbc0025-05d6-4cdf-a6bb-a27c7153550a · outbound

This paper cites an unresolved cited work.

Probing Equivariance and Symmetry Breaking in Convolutional Networks Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:48:25.607551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 91c7e14d-5070-403c-8217-6c5b015ebaa3 · outbound

This paper cites This establishes that f (X, Z) is independent of Z.

Probing Equivariance and Symmetry Breaking in Convolutional Networks This establishes that f (X, Z) is independent of Z

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:48:25.524142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 6c52f336-85d8-494a-8129-ea06a5fa5cce · outbound

This paper cites an unresolved cited work.

Probing Equivariance and Symmetry Breaking in Convolutional Networks Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:48:25.279990Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c06ba5d9-4e9d-47aa-abb3-020c3866cb0e · outbound

This paper cites top" from.

Probing Equivariance and Symmetry Breaking in Convolutional Networks top" from

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:48:25.171967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 21a91926-46b1-49f6-b66a-e0c311442de0 · outbound

This paper cites SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks.

Probing Equivariance and Symmetry Breaking in Convolutional Networks SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-10T22:48:24.592560Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 625a10cc-f7d6-4e26-ac60-9514e368505b · outbound

This paper cites See Figure 7 to see instance of the dataset.

Probing Equivariance and Symmetry Breaking in Convolutional Networks See Figure 7 to see instance of the dataset

Reference 2022

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:48:25.159372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 13df1c82-244b-4191-8cf3-9aa804e14e45 · outbound

This paper cites Geometric Algebra Transformer.

Probing Equivariance and Symmetry Breaking in Convolutional Networks Geometric Algebra Transformer

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-10T22:48:24.558268Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f48a1122-e8ec-4f03-bf26-2b9135b7b2ef · outbound

This paper cites Does equivariance matter at scale?.

Probing Equivariance and Symmetry Breaking in Convolutional Networks Does equivariance matter at scale?

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-10T22:48:24.587722Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 905aba6d-5da2-46fc-b8cd-517097a6abd2 · inbound

AdS-GNN -- a Conformally Equivariant Graph Neural Network cites this paper.

AdS-GNN -- a Conformally Equivariant Graph Neural Network Probing Equivariance and Symmetry Breaking in Convolutional Networks

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T20:30:56.597601Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2080a968-4a48-4648-b484-eca3e9e4bed6 · inbound

Quick ViTs: Speeding up Vision Transformers through Equivariance cites this paper.

Quick ViTs: Speeding up Vision Transformers through Equivariance Probing Equivariance and Symmetry Breaking in Convolutional Networks

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-07T15:25:00.088220Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1f721928-f412-4ef9-ac94-d3c8a5bd676b · inbound

CP$^2$: Leveraging Geometry for Conformal Prediction via Canonicalization cites this paper.

CP$^2$: Leveraging Geometry for Conformal Prediction via Canonicalization Probing Equivariance and Symmetry Breaking in Convolutional Networks

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-06T23:48:27.282258Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c0fad21-4b9e-4ce8-83e3-f240ce44c025 · inbound

On Equivariant Model Selection through the Lens of Uncertainty cites this paper.

On Equivariant Model Selection through the Lens of Uncertainty Probing Equivariance and Symmetry Breaking in Convolutional Networks

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-15T18:49:05.200926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 32506c17-ef40-441a-8cd4-406528ab8182 · inbound

Platonic Transformers: A Solid Choice For Equivariance cites this paper.

Platonic Transformers: A Solid Choice For Equivariance Probing Equivariance and Symmetry Breaking in Convolutional Networks

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-04T12:27:30.797057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a9c86a46-b13c-4dd3-b683-4fc91a663cc4 · inbound

Discretizing Group-Convolutional Neural Networks for 3D Geometry in Feature Space cites this paper.

Discretizing Group-Convolutional Neural Networks for 3D Geometry in Feature Space Probing Equivariance and Symmetry Breaking in Convolutional Networks

Reference 57

Resolution: verified exact; arxiv_id, observed 2026-05-19T15:57:49.373076Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 68cfec4e-3fb0-4943-ab15-d87f196885dd · inbound

Symmetry in the Wild: The Role of Equivariance in Neural Fluid Surrogates cites this paper.

Symmetry in the Wild: The Role of Equivariance in Neural Fluid Surrogates Probing Equivariance and Symmetry Breaking in Convolutional Networks

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-20T23:03:50.465277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1ccd86b8-61c3-4f3a-ae6c-97744aeb5c56 · inbound

Recursive Flow Matching cites this paper.

Recursive Flow Matching Probing Equivariance and Symmetry Breaking in Convolutional Networks

Reference 41

Resolution: metadata mismatch; arxiv_id, observed 2026-06-29T19:23:53.862435Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.