Paper Citation Record · LEDGER

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis

As of 20 August 2026, this Paper Citation Record lists 52 of 52 outbound references and 3 inbound Pith citation observations for arXiv:2509.08483.

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

pith.paper-citation-record.v1
2509.08483 v1

Coverage vector

measured 52 of 52 reference resolution

Typed states for the displayed outbound observations.

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measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-07T15:43:58.446157Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-07T15:53:54.525321Z

Reference resolution

52 of 52 outbound references displayed

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External citation measurements

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Outbound references

Observation cc9e9185-bd96-4769-b210-7f6073b3a704 · outbound

This paper cites Edge of Stochastic Stability: Revis- iting the Edge of Stability for SGD.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Edge of Stochastic Stability: Revis- iting the Edge of Stability for SGD

Reference 1

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This paper cites Post-groups, (Lie-)Butcher groups and the Yang–Baxter equation.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Post-groups, (Lie-)Butcher groups and the Yang–Baxter equation

Reference 2

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This paper cites Implicit Gradient Regularization.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Implicit Gradient Regularization

Reference 3

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This paper cites On the Trajectories of SGD Without Replacement.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis On the Trajectories of SGD Without Replacement

Reference 4

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This paper cites Old Optimizer, New Norm: An Anthology.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Old Optimizer, New Norm: An Anthology

Reference 5

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This paper cites Numerical methods for dynamical systems.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Numerical methods for dynamical systems

Reference 6

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This paper cites Optimization methods for large-scale machine learning.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Optimization methods for large-scale machine learning

Reference 7

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This paper cites An algebraic theory of integration methods.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis An algebraic theory of integration methods

Reference 8

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This paper cites Modified equations for ODEs.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Modified equations for ODEs

Reference 9

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This paper cites On the Implicit Bias of Adam.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis On the Implicit Bias of Adam

Reference 10

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This paper cites How Memory in Optimization Algorithms Im- plicitly Modifies the Loss.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis How Memory in Optimization Algorithms Im- plicitly Modifies the Loss

Reference 11

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This paper cites Algebraic structures of B-series.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Algebraic structures of B-series

Reference 12

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This paper cites Numerical integrators based on mod- ified differential equations.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Numerical integrators based on mod- ified differential equations

Reference 13

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This paper cites Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 14

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This paper cites Enumerating a class of lattice paths.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Enumerating a class of lattice paths

Reference 15

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This paper cites Aspects of backward error analysis of numerical ODEs.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Aspects of backward error analysis of numerical ODEs

Reference 16

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Observation 25eb5ce2-01c8-4f49-83a4-abf2c943700b · outbound

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Unresolved cited work

Reference 17

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This paper cites Multiscale analysis of accelerated gradient methods.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Multiscale analysis of accelerated gradient methods

Reference 18

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This paper cites Rooted tree graphs and the Butcher group: Combinatorics of elementary perturbation theory.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Rooted tree graphs and the Butcher group: Combinatorics of elementary perturbation theory

Reference 19

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Formal power series and numerical algorithms for dynamical systems

Reference 20

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Persistence and smoothness of invariant manifolds for flows

Reference 21

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Observation c31315ca-a17b-49fa-b827-c10ef3e0f104 · outbound

This paper cites Sharpness-aware Minimization for Efficiently Improving Generaliza- tion.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Sharpness-aware Minimization for Efficiently Improving Generaliza- tion

Reference 22

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Observation fa6a7f24-80db-4912-af09-2b5ad8f5cddb · outbound

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Implicit regularization in Heavy-ball momentum accelerated stochas- tic gradient descent

Reference 23

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Unresolved cited work

Reference 24

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis On the scope of the method of modified equations

Reference 25

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Observation 07648af0-061e-4065-b3c3-c2bcbdf18d71 · outbound

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Shampoo: Preconditioned Stochas- tic Tensor Optimization

Reference 26

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This paper cites Backward analysis of numerical integrators and symplectic methods.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Backward analysis of numerical integrators and symplectic methods

Reference 27

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This paper cites On the Butcher group and general multi-value meth- ods.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis On the Butcher group and general multi-value meth- ods

Reference 28

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Deep residual learning for image recognition

Reference 29

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Bag of tricks for image classification with convolutional neural networks

Reference 30

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Invariant manifolds

Reference 31

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Unresolved cited work

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Observation 8f3757b6-04fe-4fe2-a6cd-e103fac19b0a · outbound

This paper cites On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima

Reference 33

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Observation cbe5e6e1-3268-4776-a0ee-b54fd079ae7c · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Adam: A Method for Stochastic Optimization

Reference 34

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This paper cites Continuous Time Analysis of Momentum Methods.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Continuous Time Analysis of Momentum Methods

Reference 35

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis ImageNet Classification with Deep Convolutional Neural Networks

Reference 36

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Revisiting Small Batch Training for Deep Neural Networks

Reference 37

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This paper cites Toward Equation of Motion for Deep Neural Networks: Continuous-time Gradient Descent and Discretization Error Analysis.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Toward Equation of Motion for Deep Neural Networks: Continuous-time Gradient Descent and Discretization Error Analysis

Reference 38

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This paper cites Some methods of speeding up the convergence of iteration methods.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Some methods of speeding up the convergence of iteration methods

Reference 39

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Observation 9f77d9cb-a8e8-4ff4-a397-10db2478920c · outbound

This paper cites Prince.Understanding Deep Learning.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Prince.Understanding Deep Learning

Reference 40

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Observation 63ee9cad-3d4f-4391-82f4-1fb3eaa0be2a · outbound

This paper cites Backward error analysis for numerical integrators.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Backward error analysis for numerical integrators

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:32.366399Z

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This paper cites On a continuous time model of gradient descent dynamics and instability in deep learning.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis On a continuous time model of gradient descent dynamics and instability in deep learning

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:32.353171Z

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This paper cites Understanding the acceleration phenomenon via high-resolution differential equations.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Understanding the acceleration phenomenon via high-resolution differential equations

Reference 43

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This paper cites On the Generalization Benefit of Noise in Stochastic Gradient Descent.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis On the Generalization Benefit of Noise in Stochastic Gradient Descent

Reference 44

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Observation c70974cc-1b3f-4fbb-83e4-c8e970de7576 · outbound

This paper cites On the Origin of Implicit Regularization in Stochastic Gradient Descent.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 45

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Unresolved cited work

Reference 46

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Observation c6ace5ee-cf8f-4e18-92b5-6e9eee694b87 · outbound

This paper cites On the importance of initialization and momentum in deep learning.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis On the importance of initialization and momentum in deep learning

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:32.285583Z

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Observation 6dd2614d-26eb-4202-9f42-3511bea1eab3 · outbound

This paper cites The modified equation approach to the stability and accuracy analysis of finite-difference methods.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis The modified equation approach to the stability and accuracy analysis of finite-difference methods

Reference 48

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Unresolved cited work

Reference 49

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Observation 5ceaab9d-e2e9-4d46-a80f-9df6478dce0b · outbound

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Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Error analysis of floating-point computation

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:32.241232Z

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Observation bbc17dbd-b467-4c87-9b57-0d611e78fe56 · outbound

This paper cites Aggregated residual transformations for deep neural networks.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Aggregated residual transformations for deep neural networks

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:32.226716Z

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Observation 318fd572-7e07-4486-86c5-9171a5632780 · outbound

This paper cites Penalizing Gradient Norm for Efficiently Im- proving Generalization in Deep Learning.

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis Penalizing Gradient Norm for Efficiently Im- proving Generalization in Deep Learning

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:32.212579Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Pith citing papers

Observation 4ca4f547-2f58-42fb-a328-998492640079 · inbound

The Effect of Mini-Batch Noise on the Implicit Bias of Adam cites this paper.

The Effect of Mini-Batch Noise on the Implicit Bias of Adam Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-16T08:07:34.259449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b6716020-942a-4296-809b-6e405b099197 · inbound

Do Deep Networks Forget Initialization? A Forgetting-Time View of Practical Inductive Bias cites this paper.

Do Deep Networks Forget Initialization? A Forgetting-Time View of Practical Inductive Bias Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis

Reference 107

Resolution: verified exact; arxiv_id, observed 2026-06-29T13:23:28.025496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b1c8667b-498d-4f09-9078-41fb22c56e67 · inbound

Approximate Minimax Estimation of a Bounded Normal Mean via Stochastic Mirror Ascent cites this paper.

Approximate Minimax Estimation of a Bounded Normal Mean via Stochastic Mirror Ascent Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-07-07T15:53:54.526919Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.