Paper Citation Record · LEDGER

Training Transformers with Enforced Lipschitz Constants

As of 15 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 13 inbound Pith citation observations for arXiv:2507.13338.

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

pith.paper-citation-record.v1
2507.13338 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:30:29.736609Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 13 of 13 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T00:10:40.139792Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T20:30:07.620341Z

Reference resolution

18 of 18 outbound references displayed

verified exact0
verified fuzzy7
unresolved11
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 687c26d1-9ad5-49ae-ae9d-63baefe3f812 · outbound

This paper cites an unresolved cited work.

Training Transformers with Enforced Lipschitz Constants Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:29.912986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5e8c0440-031d-4527-a83c-2b191601c891 · outbound

This paper cites an unresolved cited work.

Training Transformers with Enforced Lipschitz Constants Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:29.902432Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 800d4ee1-2b6c-4926-ad0b-f45252708abb · outbound

This paper cites Notably, the official implementation of LipsFormer uses ϵ = 0.

Training Transformers with Enforced Lipschitz Constants Notably, the official implementation of LipsFormer uses ϵ = 0

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:29.892385Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2269993b-a55b-4a34-9d09-25bed14e9559 · outbound

This paper cites Cited on page 17.

Training Transformers with Enforced Lipschitz Constants Cited on page 17

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:29.944020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5e572c38-43d0-40ab-8974-bc79a3aec972 · outbound

This paper cites an unresolved cited work.

Training Transformers with Enforced Lipschitz Constants Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:29.870569Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2d998148-b13f-4c71-a1e2-efd3c0dae7ba · outbound

This paper cites an unresolved cited work.

Training Transformers with Enforced Lipschitz Constants Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:29.858378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0d2d51cb-493b-4f8a-80cc-7e5070b89da3 · outbound

This paper cites an unresolved cited work.

Training Transformers with Enforced Lipschitz Constants Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:29.846751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2d41dc57-9e59-4314-b9e8-80d1aa01287b · outbound

This paper cites an unresolved cited work.

Training Transformers with Enforced Lipschitz Constants Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:29.835929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation cb5c344b-a678-479d-b335-468ba98f0758 · outbound

This paper cites an unresolved cited work.

Training Transformers with Enforced Lipschitz Constants Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:29.824953Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 78442691-7386-4be5-aac3-59818f4ebd98 · outbound

This paper cites an unresolved cited work.

Training Transformers with Enforced Lipschitz Constants Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:29.814445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 154d9e0c-67d4-4164-9445-7fd062f3c128 · outbound

This paper cites an unresolved cited work.

Training Transformers with Enforced Lipschitz Constants Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:29.880976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5bc5431a-ac4f-4172-ae1d-ff76507f567e · outbound

This paper cites Bounding the Lipschitz constant of LipsFormer.

Training Transformers with Enforced Lipschitz Constants Bounding the Lipschitz constant of LipsFormer

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:29.801607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e093f2e8-9117-4b8a-b998-79f0d27e5e78 · outbound

This paper cites Peter Bartlett, Dylan J.

Training Transformers with Enforced Lipschitz Constants Peter Bartlett, Dylan J

Reference 2016

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:29.964739Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f9c5be24-88e8-4f61-9050-e54653819eb4 · outbound

This paper cites Aladin Virmaux and Kevin Scaman.

Training Transformers with Enforced Lipschitz Constants Aladin Virmaux and Kevin Scaman

Reference 2017

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:29.923394Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9501cdd4-65af-401b-9a7e-d0ff44a7a64d · outbound

This paper cites Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin.

Training Transformers with Enforced Lipschitz Constants Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin

Reference 2018

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:29.933645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 03be3804-69cb-4512-ba0e-179f0a3625b1 · outbound

This paper cites A Spectral Condition for Feature Learning.

Training Transformers with Enforced Lipschitz Constants A Spectral Condition for Feature Learning

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-06T16:30:29.695101Z

Source-reported events for the cited work

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Observation 92e11f09-9bd4-46a0-8f42-cde8f32e151d · outbound

This paper cites The duality structure gradient descent algorithm: analysis and applications to neural networks.

Training Transformers with Enforced Lipschitz Constants The duality structure gradient descent algorithm: analysis and applications to neural networks

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-06T16:30:29.675581Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 89a1fb94-b6ee-4d17-bb24-57c2801331c8 · outbound

This paper cites I Can’t Believe It’s Not Better!.

Training Transformers with Enforced Lipschitz Constants I Can’t Believe It’s Not Better!

Reference 2025

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:29.954126Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

Observation 942aff20-0167-46f4-bc32-0f601a0d9253 · inbound

Understanding Rate-Distortion Performance in Distributed Transformer Inference cites this paper.

Understanding Rate-Distortion Performance in Distributed Transformer Inference Training Transformers with Enforced Lipschitz Constants

Reference 64

Resolution: verified exact; arxiv_id, observed 2026-05-16T10:02:42.585036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8202a399-6a0b-4638-8400-ded6a24c291e · inbound

Understanding Rate-Distortion Performance in Distributed Transformer Inference cites this paper.

Understanding Rate-Distortion Performance in Distributed Transformer Inference Training Transformers with Enforced Lipschitz Constants

Reference 64

Resolution: unresolved; no resolver link, observed 2026-08-03T06:51:19.172443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 708cf934-c3f3-469d-87eb-28add8d21cf1 · inbound

Understanding Rate-Distortion Performance in Distributed Transformer Inference cites this paper.

Understanding Rate-Distortion Performance in Distributed Transformer Inference Training Transformers with Enforced Lipschitz Constants

Reference 64

Resolution: unresolved; no resolver link, observed 2026-08-04T06:23:17.094050Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1fbf9e2e-5ec2-4236-af4a-31dd2bf32330 · inbound

The Geometric Alignment Tax: Tokenization vs. Continuous Geometry in Scientific Foundation Models cites this paper.

The Geometric Alignment Tax: Tokenization vs. Continuous Geometry in Scientific Foundation Models Training Transformers with Enforced Lipschitz Constants

Reference 31

Resolution: metadata mismatch; arxiv_id, observed 2026-05-13T16:53:00.026301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a245bdba-daa1-441b-85e6-c1938561e2f1 · inbound

DARE: Diffusion Language Model Activation Reuse for Efficient Inference cites this paper.

DARE: Diffusion Language Model Activation Reuse for Efficient Inference Training Transformers with Enforced Lipschitz Constants

Reference 21

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T03:26:19.691120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation cc58fdc8-164a-4513-9b55-90fc982ba4d1 · inbound

Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives cites this paper.

Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives Training Transformers with Enforced Lipschitz Constants

Reference 48

Resolution: verified exact; arxiv_id, observed 2026-05-13T05:37:19.215290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 4150efc1-40d0-48ed-a48c-232f2d366b67 · inbound

When Muon Optimizer Meets Adversarial Training: A Theoretical and Empirical Study cites this paper.

When Muon Optimizer Meets Adversarial Training: A Theoretical and Empirical Study Training Transformers with Enforced Lipschitz Constants

Reference 37

Resolution: verified exact; arxiv_id, observed 2026-06-29T19:43:54.581946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ee9916a3-2a41-432a-95d6-5d0ca598b8ae · inbound

Can Entry-Wise Clipping Give Spectral Control of Stochastic Gradients? cites this paper.

Can Entry-Wise Clipping Give Spectral Control of Stochastic Gradients? Training Transformers with Enforced Lipschitz Constants

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-06-29T18:33:50.859321Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c96ee673-61fb-4312-8a44-0f415df41bab · inbound

Improving Neural Network Training by Decoupling the Magnitude and Direction of Weight Vectors cites this paper.

Improving Neural Network Training by Decoupling the Magnitude and Direction of Weight Vectors Training Transformers with Enforced Lipschitz Constants

Reference 121

Resolution: metadata mismatch; arxiv_id, observed 2026-07-04T20:30:07.621861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 534031ee-960d-46db-9bdc-ca597439d79e · inbound

Improving Neural Network Training by Decoupling the Magnitude and Direction of Weight Vectors cites this paper.

Improving Neural Network Training by Decoupling the Magnitude and Direction of Weight Vectors Training Transformers with Enforced Lipschitz Constants

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-02T10:14:10.010967Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06bbfde3-0ba7-476c-a3f7-df339c6fac55 · inbound

Can Transformers Really Do It All? On the Compatibility of Inductive Biases Across Tasks cites this paper.

Can Transformers Really Do It All? On the Compatibility of Inductive Biases Across Tasks Training Transformers with Enforced Lipschitz Constants

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-01T17:31:48.492295Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a315921-82c4-43ed-bbce-ffb54c69629e · inbound

Multi-Horizon Consistency as Geometry: When Latent Dynamics Contract, and When They Do Not cites this paper.

Multi-Horizon Consistency as Geometry: When Latent Dynamics Contract, and When They Do Not Training Transformers with Enforced Lipschitz Constants

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T12:14:58.798163Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 280084ef-b7c5-4a29-aeab-fd2266f4ebc8 · inbound

ST-LoRA: Single Trajectory LoRA Ensemble for Uncertainty Aware Agricultural Segmentation cites this paper.

ST-LoRA: Single Trajectory LoRA Ensemble for Uncertainty Aware Agricultural Segmentation Training Transformers with Enforced Lipschitz Constants

Reference 200

Resolution: unresolved; no resolver link, observed 2026-08-06T00:10:40.139792Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.