Paper Citation Record · LEDGER

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables

As of 19 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 3 inbound Pith citation observations for arXiv:2505.12473.

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

pith.paper-citation-record.v1
2505.12473 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:42:39.776348Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:06:08.750038Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-25T04:56:38.715423Z

Reference resolution

28 of 28 outbound references displayed

verified exact1
verified fuzzy15
unresolved11
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 25965cb3-610e-4f41-85a3-2e52102d33ba · outbound

This paper cites A kernel method for canonical correlation analysis.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables A kernel method for canonical correlation analysis

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T20:42:39.676329Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5ebf1fa3-c7db-47ce-a0fb-baee357697c7 · outbound

This paper cites Andrew, G., Arora, R., Bilmes, J., and Livescu, K.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables Andrew, G., Arora, R., Bilmes, J., and Livescu, K

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:42:40.210667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6ef8bc1a-8ef4-4367-8033-8ced1d52ba6b · outbound

This paper cites an unresolved cited work.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T20:42:39.701819Z

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Observation ba115941-12b0-4b64-9638-7b5df0b3a6e1 · outbound

This paper cites exp σ(f(X),g (eY )) τ !#) , EP logeqg(Y )|f(X)(V |U) pg(Y )(V ) = 1 τ EP{σ(f(X),g (Y ))}− E eY ( log EX.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables exp σ(f(X),g (eY )) τ !#) , EP logeqg(Y )|f(X)(V |U) pg(Y )(V ) = 1 τ EP{σ(f(X),g (Y ))}− E eY ( log EX

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:42:40.128660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3acfa6e1-dea7-49d9-8287-60ca3e7334c5 · outbound

This paper cites See proof in Section F.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables See proof in Section F

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:42:40.170604Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9c661668-5e5e-4b97-b718-491dec4c1d7a · outbound

This paper cites Unifying Visual-Semantic Embeddings with Multimodal Neural Language Models.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables Unifying Visual-Semantic Embeddings with Multimodal Neural Language Models

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T20:42:39.689343Z

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Observation 92a01af8-68de-4289-ab38-109701f3434d · outbound

This paper cites an unresolved cited work.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:42:40.160649Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7d55e8e8-f07c-47d8-9732-ff58285ce3a1 · outbound

This paper cites 23 See proof in Section F.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables 23 See proof in Section F

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:42:40.150490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d7721b3f-2fd9-4b96-bd55-42a6ced688de · outbound

This paper cites VisualBERT: A Simple and Performant Baseline for Vision and Language.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables VisualBERT: A Simple and Performant Baseline for Vision and Language

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T20:42:39.693817Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2b556839-0d1e-42e6-96f5-8533334fafe5 · outbound

This paper cites Here we defineH(U) as the entropy of random vectorU andUM = idM(U), where id is the identical map on Rd.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables Here we defineH(U) as the entropy of random vectorU andUM = idM(U), where id is the identical map on Rd

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:42:40.139192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 44a2d300-b687-46ce-8e51-1d6647899f51 · outbound

This paper cites an unresolved cited work.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:42:40.118246Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b5890345-ed4d-4e37-8ff5-fa9405904579 · outbound

This paper cites Pan, Y., Mei, T., Yao, T., Li, H., and Rui, Y.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables Pan, Y., Mei, T., Yao, T., Li, H., and Rui, Y

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:42:40.201002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1d52fc87-e1be-4e3c-87b7-4cc1b718fef5 · outbound

This paper cites exp ⟨f(X),g (eY )⟩ τ E∥f(X)∥E∥g(eY )∥ !#) + E eY ( log EX.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables exp ⟨f(X),g (eY )⟩ τ E∥f(X)∥E∥g(eY )∥ !#) + E eY ( log EX

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:42:40.106861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2598a32d-eef5-468e-ae53-ca5a5931c5d9 · outbound

This paper cites Particularly, for anyη >0, withτ =ε(η), it holds that lim sup M→+∞ L(fM,gM,ε (η)) + 2I∗ M(H) > lim sup M→+∞ L((f∗)M,gM,ε (η)) + 2I∗ M(H) ≥ 2η, for allη >0.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables Particularly, for anyη >0, withτ =ε(η), it holds that lim sup M→+∞ L(fM,gM,ε (η)) + 2I∗ M(H) > lim sup M→+∞ L((f∗)M,gM,ε (η)) + 2I∗ M(H) ≥ 2η, for allη >0

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:42:40.096331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 93bb4707-dfd3-4d3c-a4de-92cdd20df2d0 · outbound

This paper cites an unresolved cited work.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:42:40.085276Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 364098dd-78a6-4c3a-9e29-39b1bfedfe2f · outbound

This paper cites E.1.2 Extension of Proposition 2 We then turn to a general case whereX∈ eBd1 and Y ∈ eBd2, where eBd1 and eBd2 are bounded sets in Rd1 and Rd2, respectively.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables E.1.2 Extension of Proposition 2 We then turn to a general case whereX∈ eBd1 and Y ∈ eBd2, where eBd1 and eBd2 are bounded sets in Rd1 and Rd2, respectively

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:42:40.063138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 070fde9e-4da2-47ce-b96f-9f47c98f2480 · outbound

This paper cites LXMERT: Learning Cross-Modality Encoder Representations from Transformers.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables LXMERT: Learning Cross-Modality Encoder Representations from Transformers

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-15T20:42:39.713324Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 165f2d05-de04-46bf-bcf6-b796d0772f90 · outbound

This paper cites 40 Proposition3.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables 40 Proposition3

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:42:40.051260Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e2563912-40e7-4d33-ab4a-736ffb8a79e0 · outbound

This paper cites E.2 Alignment and uniformity with correctly specified dimension To begin with, recall that for any(f,g )∈A (H), it holds thatf(X)/E∥f(X)∥,g (Y )/E∥g(Y )∥∈S d−1.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables E.2 Alignment and uniformity with correctly specified dimension To begin with, recall that for any(f,g )∈A (H), it holds thatf(X)/E∥f(X)∥,g (Y )/E∥g(Y )∥∈S d−1

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:42:40.040151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 78e6023b-7944-4dcc-a6da-94b57aa9e9bd · outbound

This paper cites S., Sharma, Y., Schneider, S., Bethge, M., and Brendel, W.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables S., Sharma, Y., Schneider, S., Bethge, M., and Brendel, W

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:42:40.180907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3b9426d7-d8bd-4248-88b1-2bce31d81bc3 · outbound

This paper cites In addition, with the choice ofH∗, the uniformly distributed representation onSd∗−1 maximizes the entropy.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables In addition, with the choice ofH∗, the uniformly distributed representation onSd∗−1 maximizes the entropy

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:42:40.028014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0f590013-6ee5-4a91-b673-31fa086e1b4f · outbound

This paper cites exp ⟨fM(X),gM(eY )⟩ τ !#) + E eY ( log EX.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables exp ⟨fM(X),gM(eY )⟩ τ !#) + E eY ( log EX

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:42:40.013932Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c6894f33-87a8-4ede-aeff-e4e0158685e4 · outbound

This paper cites This is a photo of a/anlabel.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables This is a photo of a/anlabel

Reference 31

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T20:42:40.002853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f0f6ec58-9eaa-4508-8075-3118f320cfde · outbound

This paper cites Understanding Transferable Representation Learning and Zero-shot Transfer in CLIP.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables Understanding Transferable Representation Learning and Zero-shot Transfer in CLIP

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-15T20:42:39.685064Z

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Unavailable: canonical work link unavailable.

Observation 07a37c9f-a306-466b-92bc-e1666a62cdf2 · outbound

This paper cites and Mei, S.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables and Mei, S

Reference 36

Resolution: verified exact; raw_fallback, observed 2026-08-15T20:42:39.951963Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d1e0e41a-4c5f-41a7-8b92-1e08800784ca · outbound

This paper cites On the Importance of Contrastive Loss in Multimodal Learning.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables On the Importance of Contrastive Loss in Multimodal Learning

Reference 1253

Resolution: unresolved; no resolver link, observed 2026-08-15T20:42:39.709258Z

Source-reported events for the cited work

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Observation 965c0062-ba7f-478e-b2fa-17175122b60b · outbound

This paper cites 39 E.1.1 Proof of Proposition 2 We prove by showing thatY |=X|f∗(X).

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables 39 E.1.1 Proof of Proposition 2 We prove by showing thatY |=X|f∗(X)

Reference 2024

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:42:40.074426Z

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Observation 5f43eb1b-25af-41f9-9de3-36f5b3549bb4 · outbound

This paper cites an unresolved cited work.

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables Unresolved cited work

Reference 9939

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:42:40.190939Z

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Pith citing papers

Observation 0f940e70-c63c-4f67-b02a-99258dc01f6f · inbound

Is Dimensionality a Barrier for Retrieval Models? cites this paper.

Is Dimensionality a Barrier for Retrieval Models? Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables

Reference 158

Resolution: verified exact; arxiv_id, observed 2026-05-25T04:56:38.718532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0514509c-44da-48b1-a411-1e314d6c8e4b · inbound

DAIF: A Data-Driven Intermediate Fusion Framework for Multimodal Supervised Learning via Approximate Message Passing cites this paper.

DAIF: A Data-Driven Intermediate Fusion Framework for Multimodal Supervised Learning via Approximate Message Passing Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-15T15:06:08.750038Z

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Observation b7ce2b79-0041-4c0a-8648-736aa2262c20 · inbound

FiGuRO: Intrinsic Dimension Estimation for Multi-Modal Data cites this paper.

FiGuRO: Intrinsic Dimension Estimation for Multi-Modal Data Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-12T15:41:28.708834Z

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Unavailable: canonical work link unavailable.