Paper Citation Record · LEDGER

Mixture of Experts Provably Detect and Learn the Latent Cluster Structure in Gradient-Based Learning

As of 8 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2506.01656.

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

pith.paper-citation-record.v1
2506.01656 v2

Coverage vector

measured 13 of 13 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:42:35.512866Z

measured 13 of 13 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

13 of 13 outbound references displayed

verified exact0
verified fuzzy4
unresolved7
parse uncertain0
malformed identifier1
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 92e711c6-47e6-4303-be66-d051aeead91a · outbound

This paper cites an unresolved cited work.

Mixture of Experts Provably Detect and Learn the Latent Cluster Structure in Gradient-Based Learning Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:42:35.782853Z

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.

Observation 0f35a798-4f0e-42ff-8f12-84988db3d926 · outbound

This paper cites an unresolved cited work.

Mixture of Experts Provably Detect and Learn the Latent Cluster Structure in Gradient-Based Learning Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:42:35.766011Z

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.

Observation dde08aa4-9c8c-4626-a43b-a17289197039 · outbound

This paper cites an unresolved cited work.

Mixture of Experts Provably Detect and Learn the Latent Cluster Structure in Gradient-Based Learning Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:42:35.747871Z

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.

Observation 6ef2b442-f849-4d1e-bd71-687d3340828e · outbound

This paper cites an unresolved cited work.

Mixture of Experts Provably Detect and Learn the Latent Cluster Structure in Gradient-Based Learning Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:42:35.731966Z

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.

Observation c47ef0c3-a17d-4193-8749-1e6b6651a0a1 · outbound

This paper cites learnable.

Mixture of Experts Provably Detect and Learn the Latent Cluster Structure in Gradient-Based Learning learnable

Reference 5

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T11:42:35.715227Z

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.

Observation e545c8d5-0f0f-4b40-b26a-a5656a02dd7d · outbound

This paper cites an unresolved cited work.

Mixture of Experts Provably Detect and Learn the Latent Cluster Structure in Gradient-Based Learning Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:42:35.697021Z

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.

Observation fe8347da-ad48-48af-b7a1-33b7e6d74f86 · outbound

This paper cites an unresolved cited work.

Mixture of Experts Provably Detect and Learn the Latent Cluster Structure in Gradient-Based Learning Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:42:35.679143Z

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.

Observation b5216c72-6794-4d03-aaaa-37a639e7f7dd · outbound

This paper cites Then, there existst l+1 ≲η −1J dAl(k∗−2) such that.

Mixture of Experts Provably Detect and Learn the Latent Cluster Structure in Gradient-Based Learning Then, there existst l+1 ≲η −1J dAl(k∗−2) such that

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:35.661195Z

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.

Observation 08a1fa3c-8b21-4120-b577-fb0520faff68 · outbound

This paper cites an unresolved cited work.

Mixture of Experts Provably Detect and Learn the Latent Cluster Structure in Gradient-Based Learning Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:42:35.642470Z

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.

Observation 729f53b1-ee98-457a-b4f5-330c42cdc53c · outbound

This paper cites Proof.Let|κ t m,j,c|≲d − k∗ −2 k∗ Al− 1 2k∗ ,t∈[t l, tl+1].

Mixture of Experts Provably Detect and Learn the Latent Cluster Structure in Gradient-Based Learning Proof.Let|κ t m,j,c|≲d − k∗ −2 k∗ Al− 1 2k∗ ,t∈[t l, tl+1]

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:35.624750Z

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.

Observation 3607ef29-fefb-4efa-980e-4f307c7f2e83 · outbound

This paper cites , J,c= 1,2, we have sup t≥0 |ξt m,j,g|≲ ˜O(d−1/2) with high probability.

Mixture of Experts Provably Detect and Learn the Latent Cluster Structure in Gradient-Based Learning , J,c= 1,2, we have sup t≥0 |ξt m,j,g|≲ ˜O(d−1/2) with high probability

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:35.605836Z

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.

Observation 423735db-36d0-4545-af3e-19b9d8d4afd1 · outbound

This paper cites Thus, κt c,m,j >1−ϵ holds for all t3,3 ≤t≤(T 3,1 −t 3,1) + (T3,2 −t 3,2) +T 3,3 until κt c,m,j >1− ϵ 3 holds.

Mixture of Experts Provably Detect and Learn the Latent Cluster Structure in Gradient-Based Learning Thus, κt c,m,j >1−ϵ holds for all t3,3 ≤t≤(T 3,1 −t 3,1) + (T3,2 −t 3,2) +T 3,3 until κt c,m,j >1− ϵ 3 holds

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:35.586850Z

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.

Observation 041102b9-2251-4a42-8ab1-c4229f97642f · outbound

This paper cites Gradient dynamics for low-rank fine-tuning beyond kernels.

Mixture of Experts Provably Detect and Learn the Latent Cluster Structure in Gradient-Based Learning Gradient dynamics for low-rank fine-tuning beyond kernels

Reference 1262

Resolution: metadata mismatch; local_arxiv, observed 2026-08-07T11:42:35.567643Z

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.

Pith citing papers

No inbound Pith citation observations are available.