Paper Citation Record · LEDGER

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning

As of 8 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 2 inbound Pith citation observations for arXiv:2505.22085.

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

pith.paper-citation-record.v1
2505.22085 v1

Coverage vector

measured 55 of 55 reference resolution

Typed states for the displayed outbound observations.

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measured 57 of 57 standing notices

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measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T10:09:36.912553Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T07:29:38.373231Z

Reference resolution

55 of 55 outbound references displayed

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External citation measurements

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Outbound references

Observation 0ede2bde-50d0-4e6b-b914-b26768d3a5f4 · outbound

This paper cites Adam with model exponential moving average is effective for nonconvex optimization.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Adam with model exponential moving average is effective for nonconvex optimization

Reference 1

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This paper cites General framework for online-to-nonconvex conversion: Schedule-free SGD is also effective for nonconvex optimization.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning General framework for online-to-nonconvex conversion: Schedule-free SGD is also effective for nonconvex optimization

Reference 2

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PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Unresolved cited work

Reference 3

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Observation f655e2b0-de84-4ab0-aca7-6b406d49b244 · outbound

This paper cites Learning Theory from First Principles.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Learning Theory from First Principles

Reference 4

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Observation 003918ea-9e35-4d1e-ac82-3ef4f2fff3e5 · outbound

This paper cites Convergence and dynamical behavior of the Adam algorithm for nonconvex stochastic optimization.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Convergence and dynamical behavior of the Adam algorithm for nonconvex stochastic optimization

Reference 5

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Observation 66f837b2-360b-4c7a-9b98-1a88ab5c6eb6 · outbound

This paper cites Solving the Kolmogorov PDE by means of deep learning.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Solving the Kolmogorov PDE by means of deep learning

Reference 6

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Observation 603fecab-d84e-4768-8b14-0f59c951ab3d · outbound

This paper cites An overview on deep learning-based approximation methods for partial differential equations.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning An overview on deep learning-based approximation methods for partial differential equations

Reference 7

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Observation a9c69ac5-8cb3-460f-9215-91f249d6b530 · outbound

This paper cites Solving high-dimensional optimal stopping problems using deep learning.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Solving high-dimensional optimal stopping problems using deep learning

Reference 8

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PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Unresolved cited work

Reference 9

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Observation 10695ec8-d505-4f1c-ab3c-475bc9ce6d2b · outbound

This paper cites G., Suau Cuadros, X., and Webb, R.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning G., Suau Cuadros, X., and Webb, R

Reference 10

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Observation 0cf9b7d8-f3cb-4c5b-b55e-232ad0c71007 · outbound

This paper cites Scientific machine learning through physics-informed neural networks: where we are and what’s next.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Scientific machine learning through physics-informed neural networks: where we are and what’s next

Reference 11

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Observation a8dddf37-23af-43f4-b8ac-005545f927e8 · outbound

This paper cites The Road Less Scheduled.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning The Road Less Scheduled

Reference 12

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Observation 51a48e79-e6d9-435a-9995-498bf0e27a9b · outbound

This paper cites A Simple Convergence Proof of Adam and Adagrad.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning A Simple Convergence Proof of Adam and Adagrad

Reference 13

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Observation c3cb9ab0-2fc9-45ed-ad59-5f53b7904919 · outbound

This paper cites General multilevel adaptations for stochastic approximation algorithms II: CLTs.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning General multilevel adaptations for stochastic approximation algorithms II: CLTs

Reference 14

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Observation 7561269f-221b-42ab-b3e7-386f24565866 · outbound

This paper cites Convergence rates for the Adam optimizer.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Convergence rates for the Adam optimizer

Reference 15

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Observation 48240a19-5a1f-4a6d-9ae4-a7e6e0a34b9d · outbound

This paper cites On the existence of minimizers in shallow residual relu neural network optimization landscapes.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning On the existence of minimizers in shallow residual relu neural network optimization landscapes

Reference 16

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Observation 87d7e869-f19e-427e-8c0a-7b832eba50bc · outbound

This paper cites Averaged Adam accelerates stochastic optimization in the training of deep neural network approximations for partial differential equation and optimal control problems.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Averaged Adam accelerates stochastic optimization in the training of deep neural network approximations for partial differential equation and optimal control problems

Reference 17

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Observation 080081b6-b3f0-4147-9f37-997a168118e0 · outbound

This paper cites Central limit theorems for stochastic gradient descent with averaging for stable manifolds.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Central limit theorems for stochastic gradient descent with averaging for stable manifolds

Reference 18

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Observation e29d8abd-3823-40d6-97db-4159f880da90 · outbound

This paper cites On the existence of optimal shallow feedforward networks with ReLU activation.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning On the existence of optimal shallow feedforward networks with ReLU activation

Reference 19

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Observation a998fdc4-adee-4388-aae0-cab3df4962ea · outbound

This paper cites General multilevel adaptations for stochastic approximation algorithms of Robbins-Monro and Polyak-Ruppert type.Numer.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning General multilevel adaptations for stochastic approximation algorithms of Robbins-Monro and Polyak-Ruppert type.Numer

Reference 20

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Observation 7765285a-e5f8-44e7-8862-38d86e513211 · outbound

This paper cites Uniform convergence guarantees for the deep ritz method for nonlinear problems.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Uniform convergence guarantees for the deep ritz method for nonlinear problems

Reference 21

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Observation 2e25f9d3-d276-4245-8d69-89a207cbf049 · outbound

This paper cites Deep learning-based numerical methods for high- dimensional parabolic partial differential equations and backward stochastic differential equations.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Deep learning-based numerical methods for high- dimensional parabolic partial differential equations and backward stochastic differential equations

Reference 22

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Observation dd51ade3-a143-42ee-869d-c433c46f5dce · outbound

This paper cites Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning

Reference 23

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This paper cites The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems

Reference 24

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Observation 91ddcca1-97a5-4f04-9fca-01d5749814f3 · outbound

This paper cites Optimal non-asymptotic bound of the Ruppert-Polyak averaging without strong convexity.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Optimal non-asymptotic bound of the Ruppert-Polyak averaging without strong convexity

Reference 25

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This paper cites Blow up phenomena for gradient descent optimization methods in the training of artificial neural networks.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Blow up phenomena for gradient descent optimization methods in the training of artificial neural networks

Reference 26

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This paper cites Neural networks-based algorithms for stochastic control and PDEs in finance.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Neural networks-based algorithms for stochastic control and PDEs in finance

Reference 27

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This paper cites Stochastic weight averaging revisited.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Stochastic weight averaging revisited

Reference 28

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PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Unresolved cited work

Reference 29

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Observation dd6775d0-2b8e-4823-ac1a-76cdd95391a3 · outbound

This paper cites Recent developments in machine learning methods for stochastic control and games.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Recent developments in machine learning methods for stochastic control and games

Reference 30

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This paper cites Averaging Weights Leads to Wider Optima and Better Generalization.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Averaging Weights Leads to Wider Optima and Better Generalization

Reference 31

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This paper cites Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory

Reference 32

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This paper cites On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks

Reference 33

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Observation 71cdcc58-6054-416f-b9c1-e954c0495dd4 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Adam: A Method for Stochastic Optimization

Reference 34

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This paper cites SAD Neural Net- works: Divergent Gradient Flows and Asymptotic Optimality via o-minimal Structures.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning SAD Neural Net- works: Divergent Gradient Flows and Asymptotic Optimality via o-minimal Structures

Reference 35

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This paper cites Convergence of Adam Under Relaxed Assumptions.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Convergence of Adam Under Relaxed Assumptions

Reference 36

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Observation 8102fa5d-3cb1-4def-8a85-973b59d35ec3 · outbound

This paper cites Understanding SGD with Exponential Moving Average: A Case Study in Linear Regression.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Understanding SGD with Exponential Moving Average: A Case Study in Linear Regression

Reference 37

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This paper cites Summary of ChatGPT-Related Research and Perspective Towards the Future of Large Language Models.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Summary of ChatGPT-Related Research and Perspective Towards the Future of Large Language Models

Reference 38

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PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Decoupled Weight Decay Regularization

Reference 39

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This paper cites Gradient Descent Maximizes the Margin of Homogeneous Neural Networks.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Gradient Descent Maximizes the Margin of Homogeneous Neural Networks

Reference 40

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Observation f5a2318d-ef61-414c-80ee-bb1a7df5a500 · outbound

This paper cites Stochastic Gradient Descent as Approximate Bayesian Inference.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Stochastic Gradient Descent as Approximate Bayesian Inference

Reference 41

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This paper cites Exponential moving average of weights in deep learning: Dynamics and benefits.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Exponential moving average of weights in deep learning: Dynamics and benefits

Reference 42

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This paper cites Topological properties of the set of functions generated by neural networks of fixed size.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Topological properties of the set of functions generated by neural networks of fixed size

Reference 43

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This paper cites Continuous-time stochastic control and optimization with financial applications, vol.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Continuous-time stochastic control and optimization with financial applications, vol

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:20:52.189882Z

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PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Unresolved cited work

Reference 45

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Observation dd5bac77-c224-42ca-91f4-df1fe0e02d0c · outbound

This paper cites T., and Juditsky, A.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning T., and Juditsky, A

Reference 46

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This paper cites Zero-Shot Text-to-Image Generation.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Zero-Shot Text-to-Image Generation

Reference 47

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This paper cites On the Convergence of Adam and Beyond.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning On the Convergence of Adam and Beyond

Reference 48

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Observation 5ceea0a7-d7e6-42e1-83a8-f50dc56cd332 · outbound

This paper cites High-Resolution Image Synthesis with Latent Diffusion Models.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning High-Resolution Image Synthesis with Latent Diffusion Models

Reference 49

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Observation 08ca1edf-a5b2-41d6-998e-8c2c25e34313 · outbound

This paper cites An overview of gradient descent optimization algorithms.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning An overview of gradient descent optimization algorithms

Reference 50

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Observation b7389969-55b8-4b52-9f5c-8df99e018d28 · outbound

This paper cites Efficient estimations from a slowly convergent Robbins-Monro process.Cor- nell University Operations Research and Industrial Engineering, hdl.handle.net/1813/8664 (1988), 1–34.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Efficient estimations from a slowly convergent Robbins-Monro process.Cor- nell University Operations Research and Industrial Engineering, hdl.handle.net/1813/8664 (1988), 1–34

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:20:51.601182Z

Source-reported events for the cited work

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Observation 9ae9a0e3-f7c2-4cd3-a529-38c93cbaaf54 · outbound

This paper cites Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-07T13:20:49.372617Z

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Observation 59a99ae4-2b76-4bb0-ad7f-ecea03b0c639 · outbound

This paper cites Training trajectories, mini-batch losses and the curious role of the learning rate.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Training trajectories, mini-batch losses and the curious role of the learning rate

Reference 53

Resolution: unresolved; no resolver link, observed 2026-08-07T13:20:49.539468Z

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Observation 503a1d71-526c-4b3a-8797-e03a34ddf718 · outbound

This paper cites On Margin Maximization in Linear and ReLU Networks.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning On Margin Maximization in Linear and ReLU Networks

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-07T13:20:49.699637Z

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Observation de806598-2911-43d2-bd22-b44927348aae · outbound

This paper cites Deep learning with Elastic Averaging SGD.

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning Deep learning with Elastic Averaging SGD

Reference 55

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:20:50.167971Z

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Pith citing papers

Observation c4250ee0-78b1-45b3-8508-61ed43f75d3c · inbound

On the Provable Suboptimality of Momentum SGD in Nonstationary Stochastic Optimization cites this paper.

On the Provable Suboptimality of Momentum SGD in Nonstationary Stochastic Optimization PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T10:09:36.912553Z

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Observation b0941b4b-8e5c-49ff-ba18-6a59519f5548 · inbound

Central limit theorem for the averaged Adam optimizer cites this paper.

Central limit theorem for the averaged Adam optimizer PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-07-04T07:29:38.374677Z

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