Paper Citation Record · LEDGER

A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks

As of 21 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 3 inbound Pith citation observations for arXiv:2412.09579.

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

pith.paper-citation-record.v1
2412.09579 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T17:03:15.006612Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:40:11.874369Z

measured 1 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

12 of 12 outbound references displayed

verified exact1
verified fuzzy7
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 9bfb00c3-0980-44d9-b131-77160545e473 · outbound

This paper cites Lemma 6 shows that this feature map, based on the initial weights, separates the dataset with a margin of order O(γ), provided the number of neurons is of the order O 1 γ2.

A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks Lemma 6 shows that this feature map, based on the initial weights, separates the dataset with a margin of order O(γ), provided the number of neurons is of the order O 1 γ2

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:03:15.166047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation cd9e38c6-ee6b-4f4c-a545-bb1dae305527 · outbound

This paper cites To describe the statement in Lemma 7, we first introduce some additional notations and quantities.

A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks To describe the statement in Lemma 7, we first introduce some additional notations and quantities

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:03:15.157421Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a3ab2c41-5d37-4245-a6c0-c9e0461c3c22 · outbound

This paper cites This inequality allows us to upper-bound the KL divergence lossℓKL(pi, ft i (W )) for each i by the distance between the corresponding logits, |zi − f t i (W )|.

A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks This inequality allows us to upper-bound the KL divergence lossℓKL(pi, ft i (W )) for each i by the distance between the corresponding logits, |zi − f t i (W )|

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:03:15.149296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 57a4a18a-9b87-4a86-be0b-cb9e64338402 · outbound

This paper cites Helong Zhou, Liangchen Song, Jiajie Chen, Ye Zhou, Guoli Wang, Junsong Yuan, and Qian Zhang.

A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks Helong Zhou, Liangchen Song, Jiajie Chen, Ye Zhou, Guoli Wang, Junsong Yuan, and Qian Zhang

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:03:15.173935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3fdac3f8-a2cf-4e64-8d99-df453cbc9ac6 · outbound

This paper cites an unresolved cited work.

A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:03:15.140317Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 393535c0-daa3-40ae-a236-7af999d430c0 · outbound

This paper cites (29) This is satisfied when : T ≥ 9HB 2 β2.

A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks (29) This is satisfied when : T ≥ 9HB 2 β2

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:03:15.131461Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 62365c75-bf8d-454c-a08a-13846eea296f · outbound

This paper cites (31) This is satisfied when ℓKL(pi, µ(f t i (W ))) ≤ β 6 for each i ∈ [1, n].

A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks (31) This is satisfied when ℓKL(pi, µ(f t i (W ))) ≤ β 6 for each i ∈ [1, n]

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:03:15.119623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 40e4cb0b-3378-4ee0-b9e8-d8039a5d672d · outbound

This paper cites T ≥ 9HB 2 β2.

A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks T ≥ 9HB 2 β2

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:03:15.111403Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1ee10fdf-4947-4b11-bdd3-880ef5171b7e · outbound

This paper cites an unresolved cited work.

A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:03:15.104374Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation de559773-2b1c-4f3c-8332-036eba4deeac · outbound

This paper cites Zixiang Chen, Yuan Cao, Quanquan Gu, and Tong Zhang.

A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks Zixiang Chen, Yuan Cao, Quanquan Gu, and Tong Zhang

Reference 2017

Resolution: unresolved; no resolver link, observed 2026-08-11T17:03:14.977474Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ebf95605-15bc-4d57-8262-cfd88c848eeb · outbound

This paper cites doi: 10.1214/19-ejp338.

A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks doi: 10.1214/19-ejp338

Reference 2019

Resolution: verified exact; doi, observed 2026-08-11T17:03:15.027650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8cd5e136-3260-473f-afc7-62ba2e1184ea · outbound

This paper cites Ziwei Ji and Matus Telgarsky.

A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks Ziwei Ji and Matus Telgarsky

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-11T17:03:14.982779Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 87e17416-112e-46ed-ae8a-8abd2367798d · inbound

LGAI-EMBEDDING-Preview Technical Report cites this paper.

LGAI-EMBEDDING-Preview Technical Report A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T05:40:11.874369Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b39c9108-1cc3-4e77-a9fb-df2a3a8e4c83 · inbound

ASKD-Whisper: Adaptive Self-knowledge Distillation for Efficient and Low-Latency Automatic Speech Recognition cites this paper.

ASKD-Whisper: Adaptive Self-knowledge Distillation for Efficient and Low-Latency Automatic Speech Recognition A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-03T12:01:00.357052Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 32c1d394-d749-4385-91bf-a83422eb23d3 · inbound

Toward Calibrated, Fair, and accurate Deepfake Detection cites this paper.

Toward Calibrated, Fair, and accurate Deepfake Detection A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks

Reference 48

Resolution: verified exact; arxiv_id, observed 2026-06-28T07:11:45.324465Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.