Paper Citation Record · LEDGER

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games

As of 14 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2607.09950.

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

pith.paper-citation-record.v1
2607.09950 v1

Coverage vector

measured 28 of 28 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-07-14T14:22:06.385512Z

measured 28 of 28 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

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Reference resolution

28 of 28 outbound references displayed

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Outbound references

Observation 63350702-4884-40a2-a96e-5ff66b400df2 · outbound

This paper cites Arrow, Leonid Hurwicz, and Hirofumi Uzawa.Studies in Linear and Non-linear Programming.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Arrow, Leonid Hurwicz, and Hirofumi Uzawa.Studies in Linear and Non-linear Programming

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-14T14:22:06.385512Z

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Observation c1452d6a-9720-46a0-b82d-f1851d0b250a · outbound

This paper cites Fast and furious learning in zero-sum games: Vanishing regret with non- vanishing step sizes.Advances in Neural Information Processing Systems, 32, 2019.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Fast and furious learning in zero-sum games: Vanishing regret with non- vanishing step sizes.Advances in Neural Information Processing Systems, 32, 2019

Reference 2

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Observation 0afd933c-85a3-4f83-b6b6-756a9a309994 · outbound

This paper cites O (1/T) time-average convergence in a generalization of network zero-sum games via alternating gradient descent.European Journal of Operational Research, 2026.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games O (1/T) time-average convergence in a generalization of network zero-sum games via alternating gradient descent.European Journal of Operational Research, 2026

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-14T14:22:06.385512Z

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Observation 0c7efe77-445c-4aa2-a269-3d979f3109ad · outbound

This paper cites On the uniqueness of nash equilibria in polymatrix games.Optimization Letters, pages 1–18, 2026.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games On the uniqueness of nash equilibria in polymatrix games.Optimization Letters, pages 1–18, 2026

Reference 4

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Observation 5536d095-8c63-4ca2-838b-8aabd60192c3 · outbound

This paper cites Bailey, Gauthier Gidel, and Georgios Piliouras.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Bailey, Gauthier Gidel, and Georgios Piliouras

Reference 5

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Observation 91e26bd7-c9b3-45f3-a5dd-96f5039ba6f6 · outbound

This paper cites Bailey and Georgios Piliouras.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Bailey and Georgios Piliouras

Reference 6

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Observation 3354afb9-81e2-415e-8f6b-15f6878e672c · outbound

This paper cites Bailey and Georgios Piliouras.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Bailey and Georgios Piliouras

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-14T14:22:06.385512Z

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Observation 4d0e148e-2cf3-4a5b-914c-a8ac363fe790 · outbound

This paper cites an unresolved cited work.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Unresolved cited work

Reference 8

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Observation 8735b19d-2a0c-440a-90c6-86369fcdd12e · outbound

This paper cites Cambridge university press, 2006.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Cambridge university press, 2006

Reference 9

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Observation 591433be-5607-428d-9821-e4f39bb96198 · outbound

This paper cites Last-iterate convergence: Zero-sum games and constrained min-max opti- mization.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Last-iterate convergence: Zero-sum games and constrained min-max opti- mization

Reference 10

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Observation 912fefd2-d1e1-4e33-a65c-0c6d5d9a2e55 · outbound

This paper cites The limit points of (optimistic) gradient descent in min-max optimization.Advances in neural information processing systems, 31, 2018.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games The limit points of (optimistic) gradient descent in min-max optimization.Advances in neural information processing systems, 31, 2018

Reference 11

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Observation 6efbcbf8-09b5-477c-a5f6-cd603ae2d2bb · outbound

This paper cites Tabak, and Giulio Trigila.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Tabak, and Giulio Trigila

Reference 12

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Observation 22489178-ba74-40b4-9aca-c8af34d07380 · outbound

This paper cites MIT Press, 1991.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games MIT Press, 1991

Reference 13

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Observation 5499a2ea-3f0d-41b6-96be-b4d8326fb7c4 · outbound

This paper cites JHU press, 2013.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games JHU press, 2013

Reference 14

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Observation 1e1771cc-8844-43f8-958b-2e8b51a83d0a · outbound

This paper cites MIT Press, 2016.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games MIT Press, 2016

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-14T14:22:06.385512Z

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Observation e86fecdd-6909-4b8d-9a22-1261fa265e4b · outbound

This paper cites Generative adversarial nets.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Generative adversarial nets

Reference 16

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Observation 1876d7d6-4346-4800-ab59-06b9250c0bfd · outbound

This paper cites London Mathematical Society Lecture Note Series.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games London Mathematical Society Lecture Note Series

Reference 17

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Observation 9e4ba263-0e1c-4d28-a90e-c3da481291a3 · outbound

This paper cites Springer, 2 edition, 2006.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Springer, 2 edition, 2006

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-14T14:22:06.385512Z

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Observation 80771ae8-d208-4ecb-88fb-483e8e079dd5 · outbound

This paper cites Wiley, 1965.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Wiley, 1965

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-14T14:22:06.385512Z

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Observation 336c6131-7247-498a-b84f-c6838339de97 · outbound

This paper cites Characterizing Nash Equilibria in Zero-Sum Games: A Physics-Inspired, Parallelizable Approach with a Linear Number of Gradient Queries.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Characterizing Nash Equilibria in Zero-Sum Games: A Physics-Inspired, Parallelizable Approach with a Linear Number of Gradient Queries

Reference 20

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Observation 50b4ff7a-4282-498a-ba7b-2bde3a613a44 · outbound

This paper cites Kuhn and Albert W.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Kuhn and Albert W

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-14T14:22:06.385512Z

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Observation bbea15bc-3cb2-45b5-8dcb-ee7418d143b5 · outbound

This paper cites Cycles in adversarial regularized learning.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Cycles in adversarial regularized learning

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-14T14:22:06.385512Z

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Observation 3a053f45-5f9a-4dd2-a7b0-0fa43fce30ca · outbound

This paper cites A unified analysis of extra-gradient and optimistic gradient methods for saddle point problems: Proximal point approach.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games A unified analysis of extra-gradient and optimistic gradient methods for saddle point problems: Proximal point approach

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-14T14:22:06.385512Z

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Observation 82004832-cba5-4fad-a60d-d792ecac6eed · outbound

This paper cites Convergence rate of O(1/k) for optimistic gradient and extragradient methods in smooth convex-concave saddle point problems.SIAM Journal on Optimization, 30(4):3230–3251, 2020.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Convergence rate of O(1/k) for optimistic gradient and extragradient methods in smooth convex-concave saddle point problems.SIAM Journal on Optimization, 30(4):3230–3251, 2020

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-14T14:22:06.385512Z

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Observation 22b13744-dc9c-4b3a-b0d1-5b1a5c4aeb43 · outbound

This paper cites On theO(1/T)convergence of alternating gradient descent-ascent in bilinear games.arXiv preprint arXiv:2510.03855, 2025.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games On theO(1/T)convergence of alternating gradient descent-ascent in bilinear games.arXiv preprint arXiv:2510.03855, 2025

Reference 25

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Observation d18e1b91-cd61-4445-8596-381a4d27964e · outbound

This paper cites Online learning meets optimization in the dual.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Online learning meets optimization in the dual

Reference 26

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Observation 06bd0d69-baee-45ca-8057-1bab4c656394 · outbound

This paper cites On the Theory of Games of Strategy.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games On the Theory of Games of Strategy

Reference 27

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Observation 75d6b976-9833-4b34-af88-22d11b68c4ed · outbound

This paper cites Princeton University Press, 1944.

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games Princeton University Press, 1944

Reference 28

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