Paper Citation Record · LEDGER

Sharp higher order convergence rates for the Adam optimizer

As of 19 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 4 inbound Pith citation observations for arXiv:2504.19426.

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

pith.paper-citation-record.v1
2504.19426 v1

Coverage vector

measured 41 of 41 reference resolution

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measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:42:54.670505Z

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Source: arxiv_reference, observed 2026-05-21T10:30:00.239783Z

Reference resolution

41 of 41 outbound references displayed

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Outbound references

Observation 1e545ef3-3bc4-48e7-8ca9-5d27c75a4428 · outbound

This paper cites Learning Theory from First Principles , ﬁrst edition ed.

Sharp higher order convergence rates for the Adam optimizer Learning Theory from First Principles , ﬁrst edition ed

Reference 1

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This paper cites Convergence Analysis of a Momentum Algorithm with Adaptive Step Size for Non Convex Optimization.

Sharp higher order convergence rates for the Adam optimizer Convergence Analysis of a Momentum Algorithm with Adaptive Step Size for Non Convex Optimization

Reference 2

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

Sharp higher order convergence rates for the Adam optimizer Convergence and dynamical behavior of the Adam algorithm for nonconvex stochastic optimization

Reference 3

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This paper cites Stochastic optimization with momentum: convergence, ﬂuctuations, an d traps avoidance.

Sharp higher order convergence rates for the Adam optimizer Stochastic optimization with momentum: convergence, ﬂuctuations, an d traps avoidance

Reference 4

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This paper cites S., and von Wurstemberge r, P.

Sharp higher order convergence rates for the Adam optimizer S., and von Wurstemberge r, P

Reference 5

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Observation c226eefd-014e-434d-a565-0bad11a6b358 · outbound

This paper cites A Proof of Local Convergence for the Adam Optimizer.

Sharp higher order convergence rates for the Adam optimizer A Proof of Local Convergence for the Adam Optimizer

Reference 6

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This paper cites Méthode générale pour la résolution des systèmes d’équatio ns si- multanées.

Sharp higher order convergence rates for the Adam optimizer Méthode générale pour la résolution des systèmes d’équatio ns si- multanées

Reference 7

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Observation d04069a4-3cbd-4265-bc64-8e5f25673c14 · outbound

This paper cites On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization.

Sharp higher order convergence rates for the Adam optimizer On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization

Reference 8

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This paper cites Non-convergence of stochas- tic gradient descent in the training of deep neural networks.

Sharp higher order convergence rates for the Adam optimizer Non-convergence of stochas- tic gradient descent in the training of deep neural networks

Reference 9

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Observation 78f34057-0ea6-4265-b2e4-ee8d9fc8e44f · outbound

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

Sharp higher order convergence rates for the Adam optimizer A Simple Convergence Proof of Adam and Adagrad

Reference 10

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Observation 92dd69be-8d6a-467e-a83f-5d3eb6327a2a · outbound

This paper cites Non-convergence of Adam and other adaptive stochastic gradient descent optimization methods for non-vanishing learning rates.

Sharp higher order convergence rates for the Adam optimizer Non-convergence of Adam and other adaptive stochastic gradient descent optimization methods for non-vanishing learning rates

Reference 11

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This paper cites Convergence rates for the Adam optimizer.

Sharp higher order convergence rates for the Adam optimizer Convergence rates for the Adam optimizer

Reference 12

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This paper cites Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses.

Sharp higher order convergence rates for the Adam optimizer Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses

Reference 13

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This paper cites Convergence of stochastic gradient descent schemes for Lojasiewicz-landscapes.

Sharp higher order convergence rates for the Adam optimizer Convergence of stochastic gradient descent schemes for Lojasiewicz-landscapes

Reference 14

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This paper cites Non-convergence to global minimizers in data driven supervised deep learning: Adam and stochastic gradient descent optimization provably fail to converge to global minimizers in the training of deep neural networks with ReLU activation.

Sharp higher order convergence rates for the Adam optimizer Non-convergence to global minimizers in data driven supervised deep learning: Adam and stochastic gradient descent optimization provably fail to converge to global minimizers in the training of deep neural networks with ReLU activation

Reference 15

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This paper cites On the oracle complexity of smooth strongly convex minimization.

Sharp higher order convergence rates for the Adam optimizer On the oracle complexity of smooth strongly convex minimization

Reference 16

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Observation 6a5ec2e9-e7cd-4cb5-87a2-067fcb5b66fd · outbound

This paper cites Adaptive subgradient methods for online learning and stochastic optimization.

Sharp higher order convergence rates for the Adam optimizer Adaptive subgradient methods for online learning and stochastic optimization

Reference 17

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This paper cites Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't.

Sharp higher order convergence rates for the Adam optimizer Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't

Reference 18

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

Sharp higher order convergence rates for the Adam optimizer Blow up phenomena for gradient descent optimization methods in the training of artificial neural networks

Reference 19

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This paper cites Handbook of Convergence Theorems for (Stochastic) Gradient Methods.

Sharp higher order convergence rates for the Adam optimizer Handbook of Convergence Theorems for (Stochastic) Gradient Methods

Reference 20

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Sharp higher order convergence rates for the Adam optimizer Non asymptotic analysis of Adaptive stochastic gradient algorithms and applications

Reference 21

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Observation 449966e4-f16d-4285-a2b5-8a5db4a37bcd · outbound

This paper cites Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case.

Sharp higher order convergence rates for the Adam optimizer Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case

Reference 22

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This paper cites Lecture 6e: Rm- sprop: Divide the gradient by a running average of its recent magnitude.

Sharp higher order convergence rates for the Adam optimizer Lecture 6e: Rm- sprop: Divide the gradient by a running average of its recent magnitude

Reference 23

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Sharp higher order convergence rates for the Adam optimizer Revisiting Convergence of AdaGrad with Relaxed Assumptions

Reference 24

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Sharp higher order convergence rates for the Adam optimizer A., and Johnson, C

Reference 25

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This paper cites Strong error analysis for stochastic gradient descent opti mization algorithms.

Sharp higher order convergence rates for the Adam optimizer Strong error analysis for stochastic gradient descent opti mization algorithms

Reference 26

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

Sharp higher order convergence rates for the Adam optimizer Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory

Reference 27

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This paper cites Non-convergence to global minimizers for Adam and stochastic gradient descent optimization and constructions of local minimizers in the training of artificial neural networks.

Sharp higher order convergence rates for the Adam optimizer Non-convergence to global minimizers for Adam and stochastic gradient descent optimization and constructions of local minimizers in the training of artificial neural networks

Reference 28

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This paper cites Lower error bounds for the stochas- tic gradient descent optimization algorithm: sharp conver gence rates for slowly and fast decaying learning rates.

Sharp higher order convergence rates for the Adam optimizer Lower error bounds for the stochas- tic gradient descent optimization algorithm: sharp conver gence rates for slowly and fast decaying learning rates

Reference 29

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Sharp higher order convergence rates for the Adam optimizer Adam: A Method for Stochastic Optimization

Reference 30

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Sharp higher order convergence rates for the Adam optimizer Convergence of Adam Under Relaxed Assumptions

Reference 31

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Sharp higher order convergence rates for the Adam optimizer Dying ReLU and Initialization: Theory and Numerical Exampl es

Reference 32

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This paper cites A method of solving a convex programming problem with conver - gence rate o(1/k2).

Sharp higher order convergence rates for the Adam optimizer A method of solving a convex programming problem with conver - gence rate o(1/k2)

Reference 33

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This paper cites Introductory lectures on convex optimization , vol.

Sharp higher order convergence rates for the Adam optimizer Introductory lectures on convex optimization , vol

Reference 34

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Sharp higher order convergence rates for the Adam optimizer Gradient methods for the minimisation of functionals

Reference 35

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Sharp higher order convergence rates for the Adam optimizer Some methods of speeding up the convergence of iteration met hods

Reference 36

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This paper cites On the Convergence of Adam and Beyond.

Sharp higher order convergence rates for the Adam optimizer On the Convergence of Adam and Beyond

Reference 37

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Sharp higher order convergence rates for the Adam optimizer An overview of gradient descent optimization algorithms

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Sharp higher order convergence rates for the Adam optimizer Optimization for deep learning: theory and algorithms

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Sharp higher order convergence rates for the Adam optimizer Adam Can Converge Without Any Modification On Update Rules

Reference 40

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This paper cites A Sufficient Condition for Convergences of Adam and RMSProp.

Sharp higher order convergence rates for the Adam optimizer A Sufficient Condition for Convergences of Adam and RMSProp

Reference 41

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Pith citing papers

Observation 4d82e7a9-7249-454b-a4c3-3b8045202f8a · inbound

Adaptive Preconditioners Trigger Loss Spikes in Adam cites this paper.

Adaptive Preconditioners Trigger Loss Spikes in Adam Sharp higher order convergence rates for the Adam optimizer

Reference 14

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Observation 914b32af-e72b-4420-9a8d-1fbd7a790794 · inbound

Global Stability and Step Size Robustness of RMSProp cites this paper.

Global Stability and Step Size Robustness of RMSProp Sharp higher order convergence rates for the Adam optimizer

Reference 11

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Adam-SHANG: A Convergent Adam-Type Method for Stochastic Smooth Convex Optimization cites this paper.

Adam-SHANG: A Convergent Adam-Type Method for Stochastic Smooth Convex Optimization Sharp higher order convergence rates for the Adam optimizer

Reference 13

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Unified convergence analysis for gradient descent optimization methods in the training of deep neural networks cites this paper.

Unified convergence analysis for gradient descent optimization methods in the training of deep neural networks Sharp higher order convergence rates for the Adam optimizer

Reference 21

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