Paper Citation Record · LEDGER

Asymptotic Signal Subspace Recovery in Softmax Attention Models

As of 13 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2606.22406.

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

pith.paper-citation-record.v1
2606.22406 v2

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-26T11:06:00.666399Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

29 of 29 outbound references displayed

verified exact2
verified fuzzy0
unresolved26
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 63b38643-710a-4a5a-83b2-0bae411520f1 · outbound

This paper cites Kakade, and Matus Telgarsky.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Kakade, and Matus Telgarsky

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0091188-39ff-442a-85ee-717af5fd131d · outbound

This paper cites Neural machine translation by jointly learning to align and translate.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Neural machine translation by jointly learning to align and translate

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation acc5e70f-f790-4a26-8a2b-bc562a1fe4c2 · outbound

This paper cites Inferential theory for factor models of large dimensions.Econometrica, 71(1):135–171, 2003.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Inferential theory for factor models of large dimensions.Econometrica, 71(1):135–171, 2003

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 72a78eed-e0c6-451d-9f4b-d180e6d1f2d6 · outbound

This paper cites an unresolved cited work.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Unresolved cited work

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-07-04T08:49:41.510418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1445abd7-40ff-48c9-b324-8a0c562f74e3 · outbound

This paper cites A dynamical system approach to stochastic approximations.SIAM Journal on Control and Optimization, 34(2):437–472, 1996.

Asymptotic Signal Subspace Recovery in Softmax Attention Models A dynamical system approach to stochastic approximations.SIAM Journal on Control and Optimization, 34(2):437–472, 1996

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 290af593-58ea-476d-9d83-cf7ea118e8b7 · outbound

This paper cites Dynamics of stochastic approximation algorithms.Séminaire de Probabilités XXXIII, 1709:1–68, 1999.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Dynamics of stochastic approximation algorithms.Séminaire de Probabilités XXXIII, 1709:1–68, 1999

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11a4f1f5-2485-491f-a29d-9365ce8a83eb · outbound

This paper cites Stochastic approximations and differential inclusions.SIAM Journal on Control and Optimization, 44(1):328–348, 2005.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Stochastic approximations and differential inclusions.SIAM Journal on Control and Optimization, 44(1):328–348, 2005

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 87a23d72-e888-4716-9b62-c26e526f1eca · outbound

This paper cites Billingsley.Probability and Measure.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Billingsley.Probability and Measure

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a2adc60e-6279-42ea-98d5-3a978eec643a · outbound

This paper cites Borkar.Stochastic Approximation: A Dynamical Systems Viewpoint.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Borkar.Stochastic Approximation: A Dynamical Systems Viewpoint

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47e8c12a-383f-4dd3-81d7-6fbe5a769ed1 · outbound

This paper cites an unresolved cited work.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Unresolved cited work

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-07-04T08:49:41.510853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 49b2116b-db80-4eb9-a274-d53c8e06d86d · outbound

This paper cites Durrett.Probability: Theory and Examples.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Durrett.Probability: Theory and Examples

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 54d49c5a-8845-42ab-a14a-cd762e32e0fb · outbound

This paper cites What can transformers learn in-context? a case study of simple function classes.

Asymptotic Signal Subspace Recovery in Softmax Attention Models What can transformers learn in-context? a case study of simple function classes

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bf109880-d1b0-4c16-8c94-daae27194ae9 · outbound

This paper cites Hirsch, Stephen Smale, and Robert L.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Hirsch, Stephen Smale, and Robert L

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c04794ca-84e7-4f39-9383-68f57f8605a3 · outbound

This paper cites Johnstone.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Johnstone

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8ad2a363-4ad6-48f1-8aa4-5826cb4296a4 · outbound

This paper cites Jolliffe.Principal Component Analysis.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Jolliffe.Principal Component Analysis

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a871b8ce-aa14-45f4-b67f-c2cd02ebda17 · outbound

This paper cites Kolda and Brett W.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Kolda and Brett W

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e1258749-5e96-42d8-a18b-a4c387a4d6a2 · outbound

This paper cites Kushner and Dean S.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Kushner and Dean S

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3e53c6a7-4765-473e-b41f-479b8e8fe336 · outbound

This paper cites Kushner and G.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Kushner and G

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 289540c4-770c-4d30-a797-83d8e42e26f4 · outbound

This paper cites Lee.Introduction to Smooth Manifolds.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Lee.Introduction to Smooth Manifolds

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9652df84-9362-456d-9480-dbe4f3e13098 · outbound

This paper cites On the expressive flexibility of self-attention matrices.

Asymptotic Signal Subspace Recovery in Softmax Attention Models On the expressive flexibility of self-attention matrices

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 49e0f2ce-cf87-44dc-93d3-2cf9c9a83277 · outbound

This paper cites Analysis of recursive stochastic algorithms.IEEE Transactions on Automatic Control, 22(4):551–575, 1977.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Analysis of recursive stochastic algorithms.IEEE Transactions on Automatic Control, 22(4):551–575, 1977

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c3b596ed-c223-4253-a0dc-e77d6efd66be · outbound

This paper cites On the turing completeness of modern neural network architectures.

Asymptotic Signal Subspace Recovery in Softmax Attention Models On the turing completeness of modern neural network architectures

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ae99b6f-5173-422b-ad0f-77820d22b432 · outbound

This paper cites Hopfield Networks is All You Need.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Hopfield Networks is All You Need

Reference 23

Resolution: metadata mismatch; local_arxiv, observed 2026-07-04T08:49:41.512822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 838a0c35-efe6-465b-84e0-072bb9855908 · outbound

This paper cites A stochastic approximation method.The Annals of Mathematical Statistics, 22(3):400–407, 1951.

Asymptotic Signal Subspace Recovery in Softmax Attention Models A stochastic approximation method.The Annals of Mathematical Statistics, 22(3):400–407, 1951

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 73d83f85-454a-437f-967a-aa78ca9ef3c1 · outbound

This paper cites Royden and P.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Royden and P

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1d604452-c7e0-4d97-97e9-7a7fb6b6bad6 · outbound

This paper cites Generalized low rank models.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Generalized low rank models

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee7d01be-5956-48e4-bd93-109427e1b9fa · outbound

This paper cites Gomez, Lukasz Kaiser, and Illia Polosukhin.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Gomez, Lukasz Kaiser, and Illia Polosukhin

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c0e75b4f-92e6-45c2-946c-26d70fcb8a35 · outbound

This paper cites Randazzo, João Sacramento, Alexander Mordv- intsev, Andrey Zhmoginov, and Max Vladymyrov.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Randazzo, João Sacramento, Alexander Mordv- intsev, Andrey Zhmoginov, and Max Vladymyrov

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b11aa385-2908-4a9a-89ab-e1956bb2bff6 · outbound

This paper cites Are transformers universal approximators of sequence-to-sequence functions? InInternational Conference on Learning Representations (ICLR), 2020.

Asymptotic Signal Subspace Recovery in Softmax Attention Models Are transformers universal approximators of sequence-to-sequence functions? InInternational Conference on Learning Representations (ICLR), 2020

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-26T11:06:00.666399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.