Paper Citation Record · LEDGER

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations

As of 8 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2607.23012.

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pith.paper-citation-record.v1
2607.23012 v1

Coverage vector

measured 40 of 40 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-01T03:56:21.101169Z

measured 40 of 40 standing notices

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Reference resolution

40 of 40 outbound references displayed

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Outbound references

Observation e6a54760-2fd8-4f60-887a-0868b284635a · outbound

This paper cites Towards understanding sharpness-aware minimization.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Towards understanding sharpness-aware minimization

Reference 1

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Observation 00dc9a5f-8fe0-45b7-ae4b-21cb38430a9b · outbound

This paper cites Bartlett, Philip M.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Bartlett, Philip M

Reference 2

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Observation 80216976-5913-4641-ae20-3dc87737dd85 · outbound

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

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Gradient descent on neural networks typically occurs at the edge of stability

Reference 3

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Observation 794c4eba-f0fa-4eed-8475-b2f183f1d103 · outbound

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Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Unresolved cited work

Reference 4

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This paper cites Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 5

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This paper cites Suspicious Alignment of SGD: A Fine-Grained Step Size Condition Analysis.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Suspicious Alignment of SGD: A Fine-Grained Step Size Condition Analysis

Reference 6

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Observation bb696665-4b3c-4114-9a6c-f18d35b4d4b6 · outbound

This paper cites Sharp minima can gen- eralize for deep nets.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Sharp minima can gen- eralize for deep nets

Reference 7

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This paper cites Sharpness-aware min- imization for efficiently improving generalization.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Sharpness-aware min- imization for efficiently improving generalization

Reference 8

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Observation 358d7975-eef5-4b2f-bf53-ff4d3281cd66 · outbound

This paper cites An investigation into neural net opti- mization via hessian eigenvalue density.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations An investigation into neural net opti- mization via hessian eigenvalue density

Reference 9

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This paper cites Roberts, and Ethan Dyer.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Roberts, and Ethan Dyer

Reference 10

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This paper cites Flat minima.Neural Computation, 9(1):1–42, 01.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Flat minima.Neural Computation, 9(1):1–42, 01

Reference 11

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Observation 727ec6b2-84fa-4766-8046-0713230dbd68 · outbound

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

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Three factors influencing minima in SGD, 2018

Reference 12

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Observation 79ab3069-a99d-44b5-8fda-1fd5395f5375 · outbound

This paper cites Fan- tasticgeneralizationmeasuresandwheretofindthem.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Fan- tasticgeneralizationmeasuresandwheretofindthem

Reference 13

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Observation cd13ec03-0a45-4fe1-a497-d74257330f1b · outbound

This paper cites On large-batch training for deep learning: Generalization gap and sharp minima.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations On large-batch training for deep learning: Generalization gap and sharp minima

Reference 14

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Reference 15

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This paper cites Learning multiple layers of features from tiny images.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Learning multiple layers of features from tiny images

Reference 16

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Observation 36d34437-dfc4-479f-92ef-bd9abb3ac232 · outbound

This paper cites Asam: Adaptivesharpness- aware minimization for scale-invariant learning of deep neural networks.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Asam: Adaptivesharpness- aware minimization for scale-invariant learning of deep neural networks

Reference 17

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This paper cites Lecun, L.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Lecun, L

Reference 18

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Observation 38e76fd0-8364-486a-a51b-b66b3dc3df7a · outbound

This paper cites Stochastic modified equations and adaptive stochastic gradient algorithms.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Stochastic modified equations and adaptive stochastic gradient algorithms

Reference 19

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Observation 46b0244f-9475-43f5-a707-93ee353018bd · outbound

This paper cites Stochasticmodifiedequationsanddynamicsofstochas- tic gradient algorithms i: Mathematical foundations.Journal of Machine Learning Research , 20(40):1–47, 2019.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Stochasticmodifiedequationsanddynamicsofstochas- tic gradient algorithms i: Mathematical foundations.Journal of Machine Learning Research , 20(40):1–47, 2019

Reference 20

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This paper cites On the validity of modeling SGD with stochastic differential equations (SDEs).

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations On the validity of modeling SGD with stochastic differential equations (SDEs)

Reference 21

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This paper cites What happens after SGD reaches zero loss? –a mathematical framework.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations What happens after SGD reaches zero loss? –a mathematical framework

Reference 22

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This paper cites Stochastic Gradient Descent as Approximate Bayesian Inference.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Stochastic Gradient Descent as Approximate Bayesian Inference

Reference 23

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Observation cfe945f2-6d5f-4f6d-aa45-90c2f51429b6 · outbound

This paper cites Measurements of three-level hierarchical structure in the outliers in the spectrum of deepnet hessians.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Measurements of three-level hierarchical structure in the outliers in the spectrum of deepnet hessians

Reference 24

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Observation c6d56244-7aa9-41b3-8c2a-9c8697993535 · outbound

This paper cites Traces of class/cross-class structure pervade deep learning spectra.Journal of Machine Learning Research, 21(252):1–64, 2020.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Traces of class/cross-class structure pervade deep learning spectra.Journal of Machine Learning Research, 21(252):1–64, 2020

Reference 25

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This paper cites Eigenvalues of the hessian in deep learning: Singularity and beyond, 2017.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Eigenvalues of the hessian in deep learning: Singularity and beyond, 2017

Reference 26

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This paper cites Empirical Analysis of the Hessian of Over-Parametrized Neural Networks.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Empirical Analysis of the Hessian of Over-Parametrized Neural Networks

Reference 27

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This paper cites Recursive deep models for semantic compositionality over a sentiment treebank.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Recursive deep models for semantic compositionality over a sentiment treebank

Reference 28

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This paper cites Does SGD really happen in tiny subspaces? In The Thirteenth International Conference on Learning Representations, 2025.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Does SGD really happen in tiny subspaces? In The Thirteenth International Conference on Learning Representations, 2025

Reference 29

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This paper cites On the interplay between noise and curvature and its effect on optimizationandgeneralization.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations On the interplay between noise and curvature and its effect on optimizationandgeneralization

Reference 30

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This paper cites Attention is all you need.Advances in neural information processing systems, 30, 2017.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Attention is all you need.Advances in neural information processing systems, 30, 2017

Reference 31

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Observation 9ae7dc9c-fd0f-4fa7-b760-1e5ddeccfdba · outbound

This paper cites How sharpness-aware minimization minimizes sharpness? In The Eleventh International Conference on Learning Representations , 2023.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations How sharpness-aware minimization minimizes sharpness? In The Eleventh International Conference on Learning Representations , 2023

Reference 32

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This paper cites Wang, David Leo Wright Hall, Percy Liang, and Tengyu Ma.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Wang, David Leo Wright Hall, Percy Liang, and Tengyu Ma

Reference 33

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This paper cites An empirical study of stochastic gradient descent with structured covariance noise.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations An empirical study of stochastic gradient descent with structured covariance noise

Reference 34

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This paper cites The alignment property of sgd noise and how it helps select flat minima: A stability analysis.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations The alignment property of sgd noise and how it helps select flat minima: A stability analysis

Reference 35

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This paper cites Accelerating Neural Network Training Along Sharp and Flat Directions.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Accelerating Neural Network Training Along Sharp and Flat Directions

Reference 36

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This paper cites The anisotropic noise in stochastic gradient descent: Its behavior of escaping from sharp minima and regularization effects.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations The anisotropic noise in stochastic gradient descent: Its behavior of escaping from sharp minima and regularization effects

Reference 37

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This paper cites doi: 10.1162/neco.1997.9.1.1.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations doi: 10.1162/neco.1997.9.1.1

Reference 1997

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This paper cites Gradient Descent Happens in a Tiny Subspace.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Gradient Descent Happens in a Tiny Subspace

Reference 2018

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Reference 2022

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