Paper Citation Record · LEDGER

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention

As of 5 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 1 inbound Pith citation observation for arXiv:2605.04279.

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

pith.paper-citation-record.v1
2605.04279 v2

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-11T00:57:06.133474Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-04T06:34:03.388597+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-31T13:07:58.361038Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

21 of 21 outbound references displayed

verified exact11
verified fuzzy7
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d93afde8-c092-4db3-8f50-8a4e40c9a545 · outbound

This paper cites Ambrosio, N.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Ambrosio, N

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-16T00:47:01.269840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation b7065e62-b902-4018-ab33-742068e55bcd · outbound

This paper cites Layer Normalization.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Layer Normalization

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-05-11T04:56:00.593630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 52b914a4-29ba-4c99-81cc-8fca5f91eefd · outbound

This paper cites Bruno, F.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Bruno, F

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-16T00:47:01.299485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 59cd1dc0-6272-40d6-a136-2a0f1766818c · outbound

This paper cites Quantitative Clustering in Mean-Field Transformer Models.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Quantitative Clustering in Mean-Field Transformer Models

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-05-12T01:43:41.789380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation e8441e13-58a0-4289-99ab-94d4a1eb64e5 · outbound

This paper cites an unresolved cited work.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-05-16T00:47:01.288224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation b50ee53a-bd03-4a1c-b658-c8bac891dbc2 · outbound

This paper cites an unresolved cited work.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-05-16T00:47:01.276521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 3c0a8cf4-e997-4a40-b731-80530500916d · outbound

This paper cites Synchronization on circles and spheres with nonlinear interactions.arXiv preprint arXiv:2405.18273.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Synchronization on circles and spheres with nonlinear interactions.arXiv preprint arXiv:2405.18273

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-11T04:56:00.616012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 051487e6-bd6b-4a64-b3aa-30cee5a45cf4 · outbound

This paper cites Dynamic metastability in the self-attention model.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Dynamic metastability in the self-attention model

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-05-11T04:56:00.661907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 9a6b309f-af9a-47bc-b381-af8b74d6aac8 · outbound

This paper cites The emergence of clusters in self-attention dynamics.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention The emergence of clusters in self-attention dynamics

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-07-28T01:23:22.248437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 64bd72f5-9074-4754-a054-ae106b13cdfd · outbound

This paper cites A mathematical perspective on Transformers.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention A mathematical perspective on Transformers

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-11T04:56:00.577365Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 4bf36d86-cde8-4aed-b373-3a5a920d0251 · outbound

This paper cites Entropy-Guided Attention for Private LLMs.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Entropy-Guided Attention for Private LLMs

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-11T04:56:00.587367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 8cf23d5e-61b4-4a5a-881d-fda06e19266e · outbound

This paper cites Karagodin, S.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Karagodin, S

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-16T00:47:01.295633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 77121e11-0367-45a3-ab81-fa7fe59c7fc0 · outbound

This paper cites Karagodin, Y.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Karagodin, Y

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-16T00:47:01.303060Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 0f9d53fa-88c4-47d2-8984-d13984184696 · outbound

This paper cites Kuramoto.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Kuramoto

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-16T00:47:01.284078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation f6f7aad7-0e21-4d32-aa1b-1ffa11d8b446 · outbound

This paper cites Synchronization of mean-field models on the circle.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Synchronization of mean-field models on the circle

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-11T04:56:00.620927Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 40248520-70b9-4616-b933-3f69e89253c6 · outbound

This paper cites arXiv, ://arxiv.org/abs/2512.01868, arXiv:2512.01868 [cs], doi:10.48550/arXiv.2512.01868.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention arXiv, ://arxiv.org/abs/2512.01868, arXiv:2512.01868 [cs], doi:10.48550/arXiv.2512.01868

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-11T04:56:00.606667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation f6b15455-ec76-4ef8-9fb3-c98cc4aa090b · outbound

This paper cites A Study on ReLU and Softmax in Transformer.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention A Study on ReLU and Softmax in Transformer

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-11T04:56:00.630980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 863f3136-1bfb-4fd7-bd6b-d2033737b681 · outbound

This paper cites Tomihari and R.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Tomihari and R

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-16T00:47:01.280274Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 9b273a55-e2b5-4808-a9a1-b85b2fa737e0 · outbound

This paper cites Vaswani, N.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Vaswani, N

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-16T00:47:01.273536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation aa7f221f-e686-44fc-adaa-1c52b9fecab6 · outbound

This paper cites Replacing softmax with ReLU in Vision Transformers.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Replacing softmax with ReLU in Vision Transformers

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-11T04:56:00.643122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 819bebeb-bc19-4c21-97eb-f82d1aafbbc4 · outbound

This paper cites an unresolved cited work.

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-05-16T00:47:01.292143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Pith citing papers

Observation f710e1bd-606f-496d-97fa-f0c62d4b95fe · inbound

Self-Attention Dynamics with Rotary Position Embeddings: Twisted States and Explicit Consensus Rates on the Sphere cites this paper.

Self-Attention Dynamics with Rotary Position Embeddings: Twisted States and Explicit Consensus Rates on the Sphere Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-31T13:07:58.361038Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.