Paper Citation Record · LEDGER

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence

As of 9 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 3 inbound Pith citation observations for arXiv:2509.07972.

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

pith.paper-citation-record.v1
2509.07972 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T21:32:36.011814Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T12:38:58.891916Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-06-30T20:15:04.523466Z

Reference resolution

37 of 37 outbound references displayed

verified exact1
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External citation measurements

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Outbound references

Observation d4718808-baa3-4b27-ac4b-061ff6581a49 · outbound

This paper cites Qsgd: Communication- Efficient SGD via Gradient Quantization and Encoding.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Qsgd: Communication- Efficient SGD via Gradient Quantization and Encoding

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:41.308989Z

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Observation dc6aff50-060d-44e7-9c7a-b86e3e5caf38 · outbound

This paper cites Duchi, Dylan J.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Duchi, Dylan J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:40.966682Z

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Observation ca417af7-faa8-406f-bd36-1b52e48d41ac · outbound

This paper cites Curtis, and Jorge Nocedal.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Curtis, and Jorge Nocedal

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:40.749870Z

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Observation ec9e8a2e-59b2-4cf0-993b-e3cbc9711f6b · outbound

This paper cites Convex optimization.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Convex optimization

Reference 4

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Observation 9b97a3c6-abf5-4c56-9ca9-c68d227c8443 · outbound

This paper cites Gradient descent on neural networks typically occurs at the edge of stability.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Gradient descent on neural networks typically occurs at the edge of stability

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:40.409316Z

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Observation 4ee23d18-6703-4cd9-ac07-1b29ba8e725c · outbound

This paper cites Robustness to unbounded smoothness of generalized signsgd.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Robustness to unbounded smoothness of generalized signsgd

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:40.183963Z

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Observation ff52d472-7ba2-4df3-b8ab-a87f8c73c2f9 · outbound

This paper cites A loss curvature perspective on training instabilities of deep learning models.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence A loss curvature perspective on training instabilities of deep learning models

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:39.910840Z

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Observation 6ebaf8dc-8753-4f3b-817b-50221d9502ab · outbound

This paper cites A Closer Look at Deep Learning Heuristics: Learning rate restarts, Warmup and Distillation.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence A Closer Look at Deep Learning Heuristics: Learning rate restarts, Warmup and Distillation

Reference 8

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Observation ff8a23f2-32d0-4b8f-b34d-cdcf5d9b0fcd · outbound

This paper cites A closer look at deep learning heuristics: Learning rate restarts, warmup and distillation.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence A closer look at deep learning heuristics: Learning rate restarts, warmup and distillation

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:39.688153Z

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Observation cbcc7641-dd17-465f-87d8-f237f7ed0fbc · outbound

This paper cites SGD: General Analysis and Improved Rates.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence SGD: General Analysis and Improved Rates

Reference 10

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Observation d984b7e2-2db1-4594-be0e-ee657e728883 · outbound

This paper cites Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour

Reference 11

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Observation 7474a037-c114-41b5-a4b6-1033745c136a · outbound

This paper cites Deep residual learning for image recognition.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Deep residual learning for image recognition

Reference 12

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Observation 98a5cef4-ef28-45f2-9dd9-f922df3f1c56 · outbound

This paper cites Three factors influencing minima in SGD , 2018.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Three factors influencing minima in SGD , 2018

Reference 13

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Observation b47f25e8-7dcc-479d-8228-28461a978702 · outbound

This paper cites Why warmup the learning rate? underlying mechanisms and improvements.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Why warmup the learning rate? underlying mechanisms and improvements

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:39.070350Z

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Observation b7c5919c-8153-4c8a-b900-931a12fdc66c · outbound

This paper cites Better Theory for SGD in the Nonconvex World.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Better Theory for SGD in the Nonconvex World

Reference 15

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Observation afccdaec-29b4-4ae4-b533-bbf112fe3a6f · outbound

This paper cites Distributed learning with compressed gradients.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Distributed learning with compressed gradients

Reference 16

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Observation d3180bf2-e1fc-4b2d-82f1-9378c2df9ebb · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Adam: A Method for Stochastic Optimization

Reference 17

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Observation 07c72ed4-452d-47d7-8528-37717622a62c · outbound

This paper cites Analyzing & reducing the need for learning rate warmup in gpt training.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Analyzing & reducing the need for learning rate warmup in gpt training

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:38.616868Z

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Observation 314450eb-82f1-4de0-9886-746ee0df8559 · outbound

This paper cites Convex and Non -convex Optimization Under Generalized Smoothness.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Convex and Non -convex Optimization Under Generalized Smoothness

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:38.378429Z

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Observation 4ef6a172-b240-4d5d-8efd-4f75da586e6b · outbound

This paper cites Convergence of Adam Under Relaxed Assumptions.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Convergence of Adam Under Relaxed Assumptions

Reference 20

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Observation 8f0ad54b-13d1-488d-9177-1fb185bedf73 · outbound

This paper cites On the Variance of the Adaptive Learning Rate and Beyond.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence On the Variance of the Adaptive Learning Rate and Beyond

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:37.879480Z

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Observation 95096954-aea3-4c7a-9389-6f4fe541cb3c · outbound

This paper cites AdaGrad under Anisotropic Smoothness.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence AdaGrad under Anisotropic Smoothness

Reference 22

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Observation 5c9a1aa6-d925-4778-a765-04781f2f3c79 · outbound

This paper cites Revisiting the last-iterate convergence of stochastic gradient methods.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Revisiting the last-iterate convergence of stochastic gradient methods

Reference 23

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Observation fc032b57-383b-4fde-906c-ae001ac6363c · outbound

This paper cites SGDR : Stochastic gradient descent with warm restarts.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence SGDR : Stochastic gradient descent with warm restarts

Reference 24

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Observation 06ea6c50-4a2e-49d3-b6bc-fbbec7f9a9ad · outbound

This paper cites Adaptive Gradient Descent without Descent.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Adaptive Gradient Descent without Descent

Reference 25

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Observation 0d3c2c69-fdca-4b8f-afcf-3954453339b0 · outbound

This paper cites Lectures on convex optimization, volume 137.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Lectures on convex optimization, volume 137

Reference 26

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Observation d1d7617d-4e8b-4f70-bdbf-b8be3886a8d8 · outbound

This paper cites Global Convergence and Stability of Stochastic Gradient Descent.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Global Convergence and Stability of Stochastic Gradient Descent

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:37.355620Z

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Observation 2604dd10-241a-420a-9448-984bf0d78c36 · outbound

This paper cites Understanding Gradient Clipping In Incremental Gradient Methods.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Understanding Gradient Clipping In Incremental Gradient Methods

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:37.177582Z

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Observation a48916cd-bc8a-49db-94b1-08c7f8f83388 · outbound

This paper cites Smith, Pieter-Jan Kindermans, and Quoc V.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Smith, Pieter-Jan Kindermans, and Quoc V

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:37.062095Z

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Observation cbb4a111-831c-45db-83f1-ce519472d5c2 · outbound

This paper cites An elementary approach to tight worst case complexity analysis of gradient based methods.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence An elementary approach to tight worst case complexity analysis of gradient based methods

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:36.979005Z

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Observation b6f8f43b-f42d-48b6-99c4-75379aa3e0fd · outbound

This paper cites Llama 2: Open Foundation and Fine-Tuned Chat Models.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Llama 2: Open Foundation and Fine-Tuned Chat Models

Reference 31

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Observation 3b624295-8e1f-4767-99bf-3ffbf28c1104 · outbound

This paper cites Toward a Unified Theory of Gradient Descent under Generalized Smoothness.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Toward a Unified Theory of Gradient Descent under Generalized Smoothness

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:36.794213Z

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Observation 55ec8de5-bbd5-4992-8004-caac4d780bb8 · outbound

This paper cites Attention is all you need.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Attention is all you need

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-04T21:32:35.738963Z

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Observation 3e405299-3eb1-4fca-9f5b-0bc3331cc7b8 · outbound

This paper cites Understanding Warmup-Stable-Decay Learning Rates: A River Valley Loss Landscape Perspective.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Understanding Warmup-Stable-Decay Learning Rates: A River Valley Loss Landscape Perspective

Reference 34

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Observation 099ab271-6b10-4276-9f52-cfbd1bd47165 · outbound

This paper cites Improved analysis of clipping algorithms for non-convex optimization.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Improved analysis of clipping algorithms for non-convex optimization

Reference 35

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Observation 34286f8d-6728-41e9-8beb-e90599e97273 · outbound

This paper cites Why Gradient Clipping Accelerates Training : A Theoretical Justification for Adaptivity.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence Why Gradient Clipping Accelerates Training : A Theoretical Justification for Adaptivity

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:36.561393Z

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Observation 4b4e9247-268c-4084-a859-25ca2fecfb87 · outbound

This paper cites On the convergence and improvement of stochastic normalized gradient descent.

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence On the convergence and improvement of stochastic normalized gradient descent

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:32:36.404112Z

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Pith citing papers

Observation 89caaa2e-7bee-452a-9079-db1bb129da9e · inbound

Why Do We Need Warm-up? A Theoretical Perspective cites this paper.

Why Do We Need Warm-up? A Theoretical Perspective Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-04T12:38:58.891916Z

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Observation 1a80413b-21af-4eee-9d4f-a1b31709a47f · inbound

A Provably Robust Multi-Jet Framework applied to Active Flow Control of an Airfoil in Weakly Compressible Flow cites this paper.

A Provably Robust Multi-Jet Framework applied to Active Flow Control of an Airfoil in Weakly Compressible Flow Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence

Reference 57

Resolution: verified exact; arxiv_id, observed 2026-05-12T09:26:25.972480Z

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Observation 9c487ebe-6959-4395-86ea-d46ccef35102 · inbound

Avoiding Bias in Clipped SGD for Overparameterized Models under Generalized Smoothness cites this paper.

Avoiding Bias in Clipped SGD for Overparameterized Models under Generalized Smoothness Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence

Reference 36

Resolution: verified exact; arxiv_id, observed 2026-06-30T20:15:04.525674Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.