Paper Citation Record · LEDGER

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models

As of 8 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2505.21475.

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

pith.paper-citation-record.v1
2505.21475 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:35:57.167828Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

38 of 38 outbound references displayed

verified exact0
verified fuzzy12
unresolved26
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External citation measurements

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Outbound references

Observation 56a71cf8-cd63-4f4e-93c0-72b6385175d6 · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:15.752201Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6129e029-113f-42da-ad93-78cba584f776 · outbound

This paper cites We next give the generalization of Deﬁnition 3.2.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models We next give the generalization of Deﬁnition 3.2

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:15.631369Z

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Observation 76dba6c9-d9f2-4de2-bc74-e00da669626a · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:15.443939Z

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Observation c1ab39c6-7a8e-49d4-a5a6-2474745c3839 · outbound

This paper cites null hypothesis.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models null hypothesis

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:15.276958Z

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This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:15.123871Z

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Observation c13cbd29-6560-4631-b36a-c12f7a4dc7f8 · outbound

This paper cites sufﬁcien tly close.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models sufﬁcien tly close

Reference 6

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Source-reported events for the cited work

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Observation 9de61848-0f01-441e-8164-abca1c656841 · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:14.871358Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0ef87cf5-3bdd-48a4-93e2-5c4c8cbafdcb · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:14.725859Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 9

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Observation f8281a6c-6c01-41df-99d5-ec74f38221dc · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:36:03.623946Z

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Observation 4ca0d7dd-ef29-4b7c-a326-b856925a1967 · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:36:03.400766Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5c22144c-34c1-4132-b002-e687f5542c46 · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:36:03.206490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e4c6b63c-507e-4d6d-bcee-b15b142e32b6 · outbound

This paper cites The direction that Condition 2 implies Condition 1 is immedi ate.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models The direction that Condition 2 implies Condition 1 is immedi ate

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:36:02.956823Z

Source-reported events for the cited work

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Observation 1da76046-f2db-42d6-8730-3b8ad8a9ce03 · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:36:02.821560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8c257ae8-cc9f-47d0-8848-9851b36ca6af · outbound

This paper cites Let u = wV ⊥/‖wV ⊥‖2 and w′ = uW /‖uW‖2.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Let u = wV ⊥/‖wV ⊥‖2 and w′ = uW /‖uW‖2

Reference 15

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7a210ef9-ee2a-4547-a3f1-d5e95e94787b · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 16

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Observation cb5c7ae3-fddc-4b11-8a9b-0dd6d6c5f21a · outbound

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Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 17

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Source-reported events for the cited work

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Observation a317b4fd-e2f7-43c3-b2a0-0247324b687a · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 18

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f08373e2-903f-4dbf-a9a6-b37f6f283a40 · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 19

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Observation 9b071327-e7b5-4f03-af97-e9b486604ec2 · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 20

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Observation dff0a582-27eb-4c6b-8a41-6f396c084363 · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:36:01.055715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation cf19c250-ed7f-450e-ab59-2842face14c0 · outbound

This paper cites , T (a) Draw a set St of N i.i.d.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models , T (a) Draw a set St of N i.i.d

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:36:00.743894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b9a0859c-e130-4c13-aab2-5048488b823a · outbound

This paper cites Algorithm 3: Robustly Learning Well-Behaved MIMs FindDirection: Estimating a relevant direction Input: η, ǫ1, ǫ2, B, λ>0, a subspace V⊆ Rd, samples{(x(i), yi)}N i=1 from a distr.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Algorithm 3: Robustly Learning Well-Behaved MIMs FindDirection: Estimating a relevant direction Input: η, ǫ1, ǫ2, B, λ>0, a subspace V⊆ Rd, samples{(x(i), yi)}N i=1 from a distr

Reference 25

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 83b0c87e-329d-4f4e-a4dd-45a6cbb9a2f7 · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:35:59.918359Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4c36ebd3-6242-4680-811c-d383645615de · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:35:59.643033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 842256f6-61eb-4bb2-b38f-7dfc2f1e21b4 · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:35:59.359257Z

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Observation 74f0dd86-2b3c-463d-84e6-0343cc4b334b · outbound

This paper cites Algorithm 4: Estimating a relevant direction Lemma D.6 (Piecewise constant approximation sufﬁces).

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Algorithm 4: Estimating a relevant direction Lemma D.6 (Piecewise constant approximation sufﬁces)

Reference 29

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Observation 97a58bb3-02f2-40b3-a28c-0fa50051fb1b · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:35:58.956527Z

Source-reported events for the cited work

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Observation 4dc74bbe-e8af-4b52-9ca2-827a92d7c902 · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 31

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Source-reported events for the cited work

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Observation 5c82f7b5-a9d6-4fc6-85bf-838afb91de34 · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:35:58.716532Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 476159c8-317d-404c-9e51-0d29f2a02a5f · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:35:58.609144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5a41c373-5738-45a7-a4a4-b6005884f231 · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:35:58.330590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6dac7c4f-49c8-4c6f-891b-909ae2779e03 · outbound

This paper cites , T (a) Draw a set St of N i.i.d.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models , T (a) Draw a set St of N i.i.d

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:35:58.137857Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 22db305a-1070-4dc9-920f-9930f18bb91f · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:36:00.517581Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6dfa71cf-6e8e-46cf-b02c-735ee0c62ef4 · outbound

This paper cites samples from D and construct the piecewise constant function hS as follows: For each S∈S , assign the median of O(log(1/δ)) means of the labels from the samples falling in S.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models samples from D and construct the piecewise constant function hS as follows: For each S∈S , assign the median of O(log(1/δ)) means of the labels from the samples falling in S

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:36:00.331778Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a04e5a6e-76a7-47ec-bdf5-a59f9a55b9c5 · outbound

This paper cites Algorithm 5: Learning Well-Behaved MIM distributions.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Algorithm 5: Learning Well-Behaved MIM distributions

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:35:57.923226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5572fe35-fb88-47ef-afd0-0eaa076b2abd · outbound

This paper cites an unresolved cited work.

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:35:57.685986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation af0cc191-94ed-44a4-8de7-937ca0f3080a · outbound

This paper cites Fact E.3 (Gaussian Annulus Theorem see e.g., [V er18]).

Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models Fact E.3 (Gaussian Annulus Theorem see e.g., [V er18])

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:35:57.493614Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

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