Paper Citation Record · LEDGER

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach

As of 10 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2605.14663.

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pith.paper-citation-record.v1
2605.14663 v1

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measured 31 of 31 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-06-30T20:25:40.947453Z

measured 31 of 31 standing notices

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31 of 31 outbound references displayed

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Outbound references

Observation b5a5b6ae-481e-45a3-aa2b-67d606190d9e · outbound

This paper cites Convergence of the iterates of descent methods for analytic cost functions.SIAM Journal on Optimization, 16(2):531–547, 2005.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Convergence of the iterates of descent methods for analytic cost functions.SIAM Journal on Optimization, 16(2):531–547, 2005

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:11.026713Z

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Observation 6f9ec62a-9f52-4447-b7bd-30b76a0812b3 · outbound

This paper cites Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:11.011034Z

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Observation 3db86477-6269-4cbb-ba59-3a3766cfa2d9 · outbound

This paper cites Dynamics of stochastic approximation algorithms.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Dynamics of stochastic approximation algorithms

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:11.016196Z

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Observation a226eabc-3950-4756-b282-22f7e16839c2 · outbound

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

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Optimization methods for large-scale machine learning

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:11.002047Z

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Observation 803a6e1d-5e7d-433c-b4aa-b95662bc4bc6 · outbound

This paper cites If a smooth function is globally P L and coercive, then it has a unique minimizer.https://www.racetothebottom.xyz/posts/PL-smooth-unique/, 2025.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach If a smooth function is globally P L and coercive, then it has a unique minimizer.https://www.racetothebottom.xyz/posts/PL-smooth-unique/, 2025

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:11.006358Z

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Observation 54cbbab9-ecfc-4107-8ca1-86ec3c774bb4 · outbound

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

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Central limit theorems for stochastic gradient descent with averaging for stable manifolds.Electron

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:11.021054Z

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Observation e0ecb5e8-df13-46fe-b2cd-0e57d5aada53 · outbound

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

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Convergence of stochastic gradient descent schemes for Lojasiewicz- landscapes.J

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:11.034674Z

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Observation 572dcfd3-40cd-416c-9df1-22f5d07ec2ce · outbound

This paper cites On the Morse–Bott property of analytic functions on banach spaces with Lojasiewicz exponent one half.Calc.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach On the Morse–Bott property of analytic functions on banach spaces with Lojasiewicz exponent one half.Calc

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:11.039827Z

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Observation 2c6ae7a0-a012-45b5-b404-7c5c166681c4 · outbound

This paper cites Fehrman, B.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Fehrman, B

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:11.043924Z

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Observation b2122d3e-1ad3-42e1-a71c-99c2ed46ae9f · outbound

This paper cites Optimal local linear convergence of nesterov’s accelerated gradient method forc 2 functions under the Polyak– Lojasiewicz inequality.arXiv preprint arXiv:2603.21516, 2026.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Optimal local linear convergence of nesterov’s accelerated gradient method forc 2 functions under the Polyak– Lojasiewicz inequality.arXiv preprint arXiv:2603.21516, 2026

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:35:47.506065Z

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Observation ca3ee808-83d6-46a5-a11c-b9b36d489284 · outbound

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

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Handbook of Convergence Theorems for (Stochastic) Gradient Methods

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:35:47.508979Z

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Observation 194267da-e784-445c-9f3b-a736d17e945e · outbound

This paper cites Exponential convergence rates for momentum stochastic gradient descent in the overparametrized setting.Mathematical Programming, pages 1–37, 2026.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Exponential convergence rates for momentum stochastic gradient descent in the overparametrized setting.Mathematical Programming, pages 1–37, 2026

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:10.981354Z

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Observation 2c3e4ae5-3b59-40e4-ad3a-503f00f9801c · outbound

This paper cites Nesterov acceleration in benignly non-convex landscapes.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Nesterov acceleration in benignly non-convex landscapes

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:10.984622Z

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Observation 7f997a43-c907-44ec-a692-16de4bbb6d0f · outbound

This paper cites Karimi, J.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Karimi, J

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:10.993032Z

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Observation e21beca1-1e16-41a7-82dc-42f63a7ac0c1 · outbound

This paper cites Polyak’s heavy ball method achieves accelerated local rate of convergence under Polyak-Lojasiewicz inequality.arXiv preprint arXiv:2410.16849, 2024.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Polyak’s heavy ball method achieves accelerated local rate of convergence under Polyak-Lojasiewicz inequality.arXiv preprint arXiv:2410.16849, 2024

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:35:47.503495Z

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Observation 515195cc-c0e1-4396-98a8-3a9f58ed9f13 · outbound

This paper cites Khaled and P.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Khaled and P

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:10.956858Z

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Observation eecc76cf-68a5-4cb6-b6f2-d2e2f31cc5a4 · outbound

This paper cites Springer.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Springer

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:10.937562Z

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Observation ebb5f599-0b5e-4589-96ac-b363d1e1e55c · outbound

This paper cites Aiming towards the mini- mizers: fast convergence of SGD for overparametrized problems.Advances in neural information processing systems, 36:60748–60767, 2023.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Aiming towards the mini- mizers: fast convergence of SGD for overparametrized problems.Advances in neural information processing systems, 36:60748–60767, 2023

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:10.934326Z

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Observation 48849827-292a-4c27-b215-0e519d712a98 · outbound

This paper cites Springer Science & Business Media, 1992.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Springer Science & Business Media, 1992

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:10.963617Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1aec215f-34af-45ba-9d72-429baaa454a0 · outbound

This paper cites Lojasiewicz.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Lojasiewicz

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:10.940941Z

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Observation 027fa486-7d63-4a3d-98fc-6cccfb24d5d5 · outbound

This paper cites The power of interpolation: Understanding the effectiveness of SGD in modern over-parametrized learning.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach The power of interpolation: Understanding the effectiveness of SGD in modern over-parametrized learning

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:10.953554Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 84443b0f-11ae-4efa-8a03-adcef732ce53 · outbound

This paper cites On the almost sure convergence of stochastic gradient descent in non-convex problems.Advances in Neural Information Processing Systems, 33:1117–1128.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach On the almost sure convergence of stochastic gradient descent in non-convex problems.Advances in Neural Information Processing Systems, 33:1117–1128

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:10.950373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1c931a7e-61a4-4b01-9d3f-1b65240cb3c1 · outbound

This paper cites Polyak- Lojasiewicz inequality is essentially no more general than strong convexity forC 2 functions.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Polyak- Lojasiewicz inequality is essentially no more general than strong convexity forC 2 functions

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:35:47.500839Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 977cfe63-ee21-4e5d-aa3b-987954b811c8 · outbound

This paper cites Local convergence of the Heavy-Ball method and iPiano for Non-convex optimization.Journal of Optimization Theory and Applications, 177:153–180, 2018.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Local convergence of the Heavy-Ball method and iPiano for Non-convex optimization.Journal of Optimization Theory and Applications, 177:153–180, 2018

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:10.945212Z

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Observation 77ececf7-ef79-459e-9e73-3db40d64822a · outbound

This paper cites an unresolved cited work.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-07-07T20:34:10.960297Z

Source-reported events for the cited work

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Observation 4f9b37cc-936f-41fe-97e6-287dc144e1b1 · outbound

This paper cites an unresolved cited work.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-07-07T20:34:10.971779Z

Source-reported events for the cited work

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Observation 65a2da8d-1713-4518-bf4e-7bdda0a4c7a2 · outbound

This paper cites Fast convergence to non-isolated minima: four equivalent conditions forC 2 functions.Math.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Fast convergence to non-isolated minima: four equivalent conditions forC 2 functions.Math

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:10.988968Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation aafd83d3-30c6-4ee9-91d8-0a1eb24d71be · outbound

This paper cites A stochastic approximation method.The annals of mathematical sta- tistics, pages 400–407, 1951.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach A stochastic approximation method.The annals of mathematical sta- tistics, pages 400–407, 1951

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:10.967725Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7e25687c-1c2b-491f-b37a-a7f9a554435b · outbound

This paper cites Convergence and convergence rate of stochastic gradient search in the case of multiple and non-isolated extrema.Stochastic Processes and their Applications, 125(5):1715–1755, 2015.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Convergence and convergence rate of stochastic gradient search in the case of multiple and non-isolated extrema.Stochastic Processes and their Applications, 125(5):1715–1755, 2015

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:10.976799Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 46c30150-e957-4741-a041-a7afe97be985 · outbound

This paper cites Vaswani, F.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Vaswani, F

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:10.997958Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c1cd3404-4467-4086-bde7-eed97ba14720 · outbound

This paper cites Wojtowytsch.

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach Wojtowytsch

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-07-07T20:34:11.048801Z

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