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Paper Citation Record · LEDGER

Minimax Optimal Rates for Regression on Manifolds and Distributions

As of 7 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 1 inbound Pith citation observation for arXiv:2506.07504.

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

pith.paper-citation-record.v1
2506.07504 v1

Coverage vector

measured 51 of 51 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-07T05:45:58.257921Z

measured 52 of 52 standing notices

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measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T20:21:45.303967Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

51 of 51 outbound references displayed

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External citation measurements

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Outbound references

Observation e1992c7b-28ef-458e-b0bf-902a31e626c4 · outbound

This paper cites an unresolved cited work.

Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

Reference 1

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Observation 89107439-0ada-4feb-939f-66f0202a79c4 · outbound

This paper cites an unresolved cited work.

Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

Reference 2

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Observation 8baf70ef-2905-4f28-8b16-dfe353f7b5f9 · outbound

This paper cites Using the partition of unity, one can glue constructions in the local charts to form a global construc- tion on the manifold.

Minimax Optimal Rates for Regression on Manifolds and Distributions Using the partition of unity, one can glue constructions in the local charts to form a global construc- tion on the manifold

Reference 3

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Observation 389b5276-2a9e-4154-9f46-3f710d3db668 · outbound

This paper cites The proof of Lemma 7 is provided in Appendix E.1.

Minimax Optimal Rates for Regression on Manifolds and Distributions The proof of Lemma 7 is provided in Appendix E.1

Reference 4

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Observation 200426a8-8d25-4273-bd88-bfa9d0abe5e7 · outbound

This paper cites 35 A.2 Smooth submanifold family and smooth conditional distributions Firstly we recall the definition of(β Y , βX )-smooth manifold family defined in Definition 4 of the main text.

Minimax Optimal Rates for Regression on Manifolds and Distributions 35 A.2 Smooth submanifold family and smooth conditional distributions Firstly we recall the definition of(β Y , βX )-smooth manifold family defined in Definition 4 of the main text

Reference 8

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Observation d641b07e-aae7-4a47-b5c7-0797a88637bd · outbound

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

Reference 9

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Observation 545f720f-4371-4c75-87ab-d2e7093c25a4 · outbound

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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Observation b072e901-28c9-4e38-af80-34ddbb25875e · outbound

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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Observation 63aa5de2-a233-4f98-aa65-29892cd59bb4 · outbound

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

Reference 12

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Observation a83f2e52-ef1c-4d31-8fb1-f9eac1b23dc3 · outbound

This paper cites Then there existsL′ so that{µ ∗ Y|x }x∈MX ∈C βY ,βX ,αY ,αX τ,τ1,L′ (dY , DY ,M X ).

Minimax Optimal Rates for Regression on Manifolds and Distributions Then there existsL′ so that{µ ∗ Y|x }x∈MX ∈C βY ,βX ,αY ,αX τ,τ1,L′ (dY , DY ,M X )

Reference 13

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Observation 0291a98f-708a-435c-8557-751165a03ae1 · outbound

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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Observation 34456ac7-e6b6-4ddd-ab6d-2455b82a905b · outbound

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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Observation 7f9d9652-f933-42b1-b4f0-057411e7b56c · outbound

This paper cites 38 (d) for anyj≥1andx∈R d, {ψ∈ Ψ d j :I ψ ∩B Rd(x,2 −(j−1))̸=∅} ≤C ‡ L.

Minimax Optimal Rates for Regression on Manifolds and Distributions 38 (d) for anyj≥1andx∈R d, {ψ∈ Ψ d j :I ψ ∩B Rd(x,2 −(j−1))̸=∅} ≤C ‡ L

Reference 16

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Observation 717d9667-f1a1-4ccc-9251-ac7870b9ef0f · outbound

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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Observation 9b8ca4a9-dd40-479f-a60a-4ee11bb89b97 · outbound

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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Observation 440c811e-d610-43f5-bd0e-ef67bf09f681 · outbound

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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Observation 7ce7f15c-0d06-4eaf-ba9e-70b1c252f8ea · outbound

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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Observation ca70f7cc-bda5-4328-87d9-89481e950f43 · outbound

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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Observation 40d58c41-7668-4657-8fda-036801a5a5c2 · outbound

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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This paper cites Moreover, since for anyk∈[K]\ bK, it holds that 1 n X i∈I1 ρ[k](Xi, Yi)≤ 1 n X i∈I1 1(∥(Xi, Yi)−(x k, yk)∥ ≤ √ 2τ2) = 0.

Minimax Optimal Rates for Regression on Manifolds and Distributions Moreover, since for anyk∈[K]\ bK, it holds that 1 n X i∈I1 ρ[k](Xi, Yi)≤ 1 n X i∈I1 1(∥(Xi, Yi)−(x k, yk)∥ ≤ √ 2τ2) = 0

Reference 29

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Observation 1c7468e3-9d28-4f3c-84d9-19eab2f301a5 · outbound

This paper cites For eachω∈ {0,1}mdY 1 ×mdX 2 , define¯ω= 1−ωin the element-wise manner.

Minimax Optimal Rates for Regression on Manifolds and Distributions For eachω∈ {0,1}mdY 1 ×mdX 2 , define¯ω= 1−ωin the element-wise manner

Reference 30

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Observation cdfddbd8-deab-4539-88e5-531abc5e2d0b · outbound

This paper cites Consequently, we have for anyx∈ M X, 1 c4 f(·, x)∈ Hγ 1 (RD Y )(recall that we only considerγ <1).

Minimax Optimal Rates for Regression on Manifolds and Distributions Consequently, we have for anyx∈ M X, 1 c4 f(·, x)∈ Hγ 1 (RD Y )(recall that we only considerγ <1)

Reference 31

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Observation a309d367-039e-459f-9003-dba4da66a4f4 · outbound

This paper cites Consider anyγ 1 ∈(0,1]and denoteN(G, d γ1 ∞, ε)as theε-covering number of Gwith respect to thed γ1 ∞ distance, whered γ1 ∞(G1, G2) = sup z∈RdY ,x∈RDX ∥G1(z, x)−G2(z, x)∥γ1.

Minimax Optimal Rates for Regression on Manifolds and Distributions Consider anyγ 1 ∈(0,1]and denoteN(G, d γ1 ∞, ε)as theε-covering number of Gwith respect to thed γ1 ∞ distance, whered γ1 ∞(G1, G2) = sup z∈RdY ,x∈RDX ∥G1(z, x)−G2(z, x)∥γ1

Reference 32

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Observation f983690f-5ecc-4448-b97b-0f0a3d304b92 · outbound

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

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Observation 4b005d91-4fd3-4e37-97b8-e29e68ec5b9d · outbound

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

Reference 34

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Observation 9716a5b1-9534-42ab-86ce-2d1be350951e · outbound

This paper cites LetN z c2 −j be ac2 −j-covering set ofB RdY (0, τ1), contained withinB RdY (0, τ1), wherecis a small enough positive constant.

Minimax Optimal Rates for Regression on Manifolds and Distributions LetN z c2 −j be ac2 −j-covering set ofB RdY (0, τ1), contained withinB RdY (0, τ1), wherecis a small enough positive constant

Reference 35

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Observation 5f6266e1-2ee1-4c4b-9005-1c0e2e19adb4 · outbound

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Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

Reference 36

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Observation cae4e089-57e2-444e-b250-58bc09e07a49 · outbound

This paper cites The proof of Lemma 19 is provided in Appendix D.14.

Minimax Optimal Rates for Regression on Manifolds and Distributions The proof of Lemma 19 is provided in Appendix D.14

Reference 37

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verified fuzzy
raw_fallback, observed 2026-08-07T05:45:58.594829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.184995Z digest=sha256:57b0e7e221b1d30156bf6afbb57159478bda0e709eaa7b85a6571b581db353a5

Observation caad69de-15ec-4dad-b78e-63148304bce8 · outbound

This paper cites Hencesup x∈Rd P ψ∈Ψd j 1(x∈I ψ)≤C ′ L.

Minimax Optimal Rates for Regression on Manifolds and Distributions Hencesup x∈Rd P ψ∈Ψd j 1(x∈I ψ)≤C ′ L

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:45:58.576151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.191061Z digest=sha256:f065a91e7ab31b247b6c2501e76968234a5cd28a439fd39ae9c6c56e920f6b41

Observation a733031d-ee5b-42f1-9fb8-bb047ffccd5c · outbound

This paper cites an unresolved cited work.

Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:45:58.560808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.196185Z digest=sha256:ad17674a611dc6ac612e99d668ade2b03bdee30aa44970a8b8ca2b73542c6b88

Observation 94447610-2f27-4172-9190-df92beda1754 · outbound

This paper cites 116 For the last statement.

Minimax Optimal Rates for Regression on Manifolds and Distributions 116 For the last statement

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:45:58.544279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.200996Z digest=sha256:6f53cfc80fbf62fbd907634201482c3ce94b1ee287be0154ec97f26c2a7f56d4

Observation aabc45be-6132-47c7-9620-ebb2141586fe · outbound

This paper cites an unresolved cited work.

Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:45:58.528994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.206082Z digest=sha256:acf39752db6508a5bb71bcc36f352bfd2131735fc7f3129759c641c33d5c7389

Observation 3717858e-0d14-4d4d-a356-255de293c18e · outbound

This paper cites an unresolved cited work.

Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

Reference 42

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:45:58.512268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.210829Z digest=sha256:ceebaded35510960540e7865809c58b87d8f23aeb220a083eb026b4fba8bf7fe

Observation 214a88ca-0441-49e9-b89f-5f000d0b1a3d · outbound

This paper cites an unresolved cited work.

Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

Reference 43

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:45:58.496527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.215953Z digest=sha256:007dff6211a65e894c2d1d4b398bfff439023316ecfaa4b4d366ed9aab4da495

Observation ee220c95-05dd-4446-a168-9662bd27d042 · outbound

This paper cites an unresolved cited work.

Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:45:58.479877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.220916Z digest=sha256:a08334054e9f70f621f7e0ac41c6724ac1111e48cfcbf8d1e2b313bd86f1827f

Observation 1b90515d-1474-4d28-ba1d-db19c56f0023 · outbound

This paper cites an unresolved cited work.

Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:45:58.463277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.226171Z digest=sha256:3937cc4d044faff121d942ddc9ae5e77fc5cdee7d67313f0b41e6e6cda218fcb

Observation 2ea0a67a-91fb-446f-99b7-c10a51e7cada · outbound

This paper cites an unresolved cited work.

Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

Reference 46

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:45:58.446170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.231086Z digest=sha256:30baeb22c9def56ea2fe832534575572f61be6fd8e7f1b50c430b503342c2439

Observation 3348066f-09cd-4382-94cd-d862e7917846 · outbound

This paper cites an unresolved cited work.

Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

Reference 47

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:45:58.428209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.236314Z digest=sha256:940d27606ea0cc05fdc3c65c9799458bb126a3a96c22c88152f68bfeea37451a

Observation 0cb82a27-3dc7-4121-aab2-98990acd6a0f · outbound

This paper cites • if∥z−z 0∥<1, then |G(ej +j1,j2) [k] (z, x)−G(ej +j1,j2) [k] (z0, x)| ≤ p dY L∥z−z 0∥ ≤ p dY L∥z−z 0∥αY −|j1|− αY αX |j2|.

Minimax Optimal Rates for Regression on Manifolds and Distributions • if∥z−z 0∥<1, then |G(ej +j1,j2) [k] (z, x)−G(ej +j1,j2) [k] (z0, x)| ≤ p dY L∥z−z 0∥ ≤ p dY L∥z−z 0∥αY −|j1|− αY αX |j2|

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:45:58.409738Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.242036Z digest=sha256:ef74790285190b1145b342c23032206cbbe231ab2f16470c79b932e5375a81e8

Observation 50524221-e1f6-4159-977c-95061cac46e1 · outbound

This paper cites • if∥z−z 0∥<1, then |G(ej +j1,j2) [k] (z, x)−G(ej +j1,j2) [k] (z0, x)| ≤L∥z−z0∥βY −|j1|−1− βY βX |j2| ≤L∥z−z 0∥αY −|j1|− αY αX |j2|.

Minimax Optimal Rates for Regression on Manifolds and Distributions • if∥z−z 0∥<1, then |G(ej +j1,j2) [k] (z, x)−G(ej +j1,j2) [k] (z0, x)| ≤L∥z−z0∥βY −|j1|−1− βY βX |j2| ≤L∥z−z 0∥αY −|j1|− αY αX |j2|

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:45:58.393007Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.247068Z digest=sha256:8a1dc50468c54984593065610acb075a02dfa483dc77eb4ecdf34dce041823e9

Observation 9ad7a178-f59a-461e-9169-1ade79081841 · outbound

This paper cites an unresolved cited work.

Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work

Reference 50

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:45:58.376083Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.252740Z digest=sha256:e35c974649b5519a18ec6d56af366c76700e8d93024618090ea8af40544ed6cb

Observation aacec020-7d7a-448f-9f08-e8980663ed0e · outbound

This paper cites Z rn 0 r Wn log 4Tnρ ε2 dε # = C4√n Eµ∗,⊗n.

Minimax Optimal Rates for Regression on Manifolds and Distributions Z rn 0 r Wn log 4Tnρ ε2 dε # = C4√n Eµ∗,⊗n

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:45:58.358235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.257921Z digest=sha256:575a2acee759fa4f4df577d066859c1975f1885a883780c9eeabaed31e289f5b

Observation 7a77737c-a993-49b5-bee0-4e863394a0f3 · outbound

This paper cites Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory.

Minimax Optimal Rates for Regression on Manifolds and Distributions Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory

Reference 2013

Resolution
unresolved
no resolver link, observed 2026-08-07T05:45:57.994758Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T05:45:57.994758Z digest=sha256:97fe21e30efc383c6bfbc4526a7eb4d7bc28e36eeb7d0b4d73bf5569f69f7a21

Observation 8e5d2508-6888-4f6b-88d0-b84eaf19986e · outbound

This paper cites Conditional Generative Adversarial Nets.

Minimax Optimal Rates for Regression on Manifolds and Distributions Conditional Generative Adversarial Nets

Reference 2018

Resolution
unresolved
no resolver link, observed 2026-08-07T05:45:58.002606Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T05:45:58.002606Z digest=sha256:72309bc31dfb5745cd77770d8d430df0504b0efe21db6dc2a0ec7e026d6bea64

Observation 54a2ed4a-6a03-460d-a877-e6ecf25deb25 · outbound

This paper cites Minimax Optimal Rates for Regression on Manifolds and Distributions.

Minimax Optimal Rates for Regression on Manifolds and Distributions Minimax Optimal Rates for Regression on Manifolds and Distributions

Reference 2019

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:45:59.281501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:45:58.014820Z digest=sha256:a7017f541df2e8e9a1560a78d4b39e1de8cb4f75d5d0010ceac9040757b1dc9a

Observation bcba965b-2753-430c-bd71-34e0aec5429b · outbound

This paper cites Wasserstein Auto-Encoders.

Minimax Optimal Rates for Regression on Manifolds and Distributions Wasserstein Auto-Encoders

Reference 2021

Resolution
unresolved
no resolver link, observed 2026-08-07T05:45:58.008164Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T05:45:58.008164Z digest=sha256:757b7319f3e1948aea5337d69eccd7b7b7a48f0b57aff14f40d4f36fc48c0c79

Pith citing papers

Observation b545a0df-3538-4765-9e9b-de8138b951a7 · inbound

Semi-Supervised Conditional Diffusion via Label Augmentation cites this paper.

Semi-Supervised Conditional Diffusion via Label Augmentation Minimax Optimal Rates for Regression on Manifolds and Distributions

Reference 37

Resolution
unresolved
no resolver link, observed 2026-08-01T20:21:45.303967Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-01T20:21:45.303967Z digest=sha256:ca2cc19812fd09fe574873614d98c392b73cb79a695bd5fb45de8a408b216668