Paper Citation Record · LEDGER

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives

As of 9 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 1 inbound Pith citation observation for arXiv:2509.11236.

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

pith.paper-citation-record.v1
2509.11236 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T17:01:57.128540Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T10:18:45.227744Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

34 of 34 outbound references displayed

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External citation measurements

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Outbound references

Observation 445a2c8b-fe91-4ab2-addc-88b069199bfd · outbound

This paper cites Optimization algorithms on matrix manifolds.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Optimization algorithms on matrix manifolds

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:56.976330Z

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Unavailable: canonical work link unavailable.

Observation 8ca696f9-7f06-4ec2-82ae-6161ec2fd188 · outbound

This paper cites A continuous-time perspective for modeling acceleration in riemannian optimization.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives A continuous-time perspective for modeling acceleration in riemannian optimization

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:56.981812Z

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Observation e2b5382d-39db-4c5a-a96b-f01906d7abc4 · outbound

This paper cites Walter de Gruyter GmbH & Co KG, 2014.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Walter de Gruyter GmbH & Co KG, 2014

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:56.987031Z

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Observation cacd3cec-d213-46e0-b44d-4e45a5367a6f · outbound

This paper cites Stochastic gradient descent on riemannian manifolds.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Stochastic gradient descent on riemannian manifolds

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:56.992030Z

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Observation a29505c6-1cd9-494b-8459-640f1aae0c83 · outbound

This paper cites Cambridge University Press, 2023.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Cambridge University Press, 2023

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:56.996737Z

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Observation 767a1c0a-24d8-4abb-9196-9d256a92cf22 · outbound

This paper cites Decentralized Online Riemannian Optimization with Dynamic Environments.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Decentralized Online Riemannian Optimization with Dynamic Environments

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.001317Z

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Observation 6067fc61-6354-493e-aa50-c3ce6ab33ce1 · outbound

This paper cites Decentralized riemannian gradient descent on the stiefel manifold.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Decentralized riemannian gradient descent on the stiefel manifold

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.006816Z

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Observation fa6d5f72-241a-4190-a43e-c365a1a2a25e · outbound

This paper cites Riemannian dictionary learning and sparse coding for positive definite matrices.IEEE transactions on neural networks and learning systems, 28(12):2859–2871, 2016.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Riemannian dictionary learning and sparse coding for positive definite matrices.IEEE transactions on neural networks and learning systems, 28(12):2859–2871, 2016

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.011079Z

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Observation eba555f0-eb6c-4165-84cd-2c33e5efc4da · outbound

This paper cites Horospherically Convex Optimization on Hadamard Manifolds Part I: Analysis and Algorithms.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Horospherically Convex Optimization on Hadamard Manifolds Part I: Analysis and Algorithms

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.015490Z

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Observation d7d9a172-dc02-44db-8c05-78e41d7c4d59 · outbound

This paper cites The geometry of algorithms with orthogonality constraints.SIAM journal on Matrix Analysis and Applications, 20(2):303–353, 1998.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives The geometry of algorithms with orthogonality constraints.SIAM journal on Matrix Analysis and Applications, 20(2):303–353, 1998

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.020114Z

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Observation d4e9a26d-5835-4ca1-8ad5-e6eac281f78a · outbound

This paper cites A subgradient splitting algorithm for optimization on nonpos- itively curved metric spaces.arXiv preprint arXiv:2412.06730, 2024.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives A subgradient splitting algorithm for optimization on nonpos- itively curved metric spaces.arXiv preprint arXiv:2412.06730, 2024

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.024597Z

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Observation ffc4140d-1106-4201-b470-1c02d045ef98 · outbound

This paper cites Introduction to online convex optimization.Founda- tions and Trends® in Optimization, 2(3-4):157–325, 2016.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Introduction to online convex optimization.Founda- tions and Trends® in Optimization, 2(3-4):157–325, 2016

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.028920Z

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Observation 6c7a8913-6333-4f99-9b92-1766c7621a64 · outbound

This paper cites Convex analysis on hadamard spaces and scaling problems.Foundations of Computational Mathematics, 24(6):1979– 2016, 2024.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Convex analysis on hadamard spaces and scaling problems.Foundations of Computational Mathematics, 24(6):1979– 2016, 2024

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.033561Z

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Observation d9c620a9-f784-41b7-9d03-338c8583745e · outbound

This paper cites Riemannian projection-free online learning.Advances in Neural Information Pro- cessing Systems, 36:41980–42014, 2023.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Riemannian projection-free online learning.Advances in Neural Information Pro- cessing Systems, 36:41980–42014, 2023

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.038169Z

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Observation eac34c23-3c8e-4ccc-9c6d-4dc4aa0f16d1 · outbound

This paper cites Horoballs and the subgradient method.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Horoballs and the subgradient method

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.042317Z

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Observation f301ebed-2a45-4cc9-a68b-e867a1491ed2 · outbound

This paper cites Cheap orthogonal constraints in neural networks: A simple parametrization of the or- thogonal and unitary group.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Cheap orthogonal constraints in neural networks: A simple parametrization of the or- thogonal and unitary group

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.047102Z

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Unavailable: canonical work link unavailable.

Observation c541adf1-87b6-42de-8e04-e95c359bb86c · outbound

This paper cites Tracking and regret bounds for online zeroth-order euclidean and riemannian optimization.SIAM Journal on Optimization, 32(2):445–469, 2022.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Tracking and regret bounds for online zeroth-order euclidean and riemannian optimization.SIAM Journal on Optimization, 32(2):445–469, 2022

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.051855Z

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Observation 91feb76a-9ebc-44b3-a7c4-1775bfbc81ad · outbound

This paper cites A differential geometric approach to the geometric mean of symmetric positive-definite matrices.SIAM journal on matrix analysis and applications, 26(3):735–747, 2005.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives A differential geometric approach to the geometric mean of symmetric positive-definite matrices.SIAM journal on matrix analysis and applications, 26(3):735–747, 2005

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.056035Z

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Observation bfa3547b-7024-47e8-8575-60b3f26d9914 · outbound

This paper cites Poincar ´e embeddings for learning hierarchical representations.Advances in neural information processing systems, 30, 2017.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Poincar ´e embeddings for learning hierarchical representations.Advances in neural information processing systems, 30, 2017

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.060408Z

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Observation 4fa5a365-a798-4875-afee-b40cfd68702a · outbound

This paper cites Decentralized Online Riemannian Optimization Beyond Hadamard Manifolds.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Decentralized Online Riemannian Optimization Beyond Hadamard Manifolds

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.066122Z

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Observation 9fb3f1d3-a47b-420a-8d07-afbef0db7ca0 · outbound

This paper cites Consensus optimization on manifolds.SIAM journal on Control and Optimization, 48(1):56–76, 2009.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Consensus optimization on manifolds.SIAM journal on Control and Optimization, 48(1):56–76, 2009

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.071188Z

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Observation d1380b04-30a7-4580-bab2-236a57e27239 · outbound

This paper cites an unresolved cited work.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.075426Z

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Observation 981fa927-fee6-4bc0-b6bd-de0e844df974 · outbound

This paper cites Riemannian optimization on unit sphere with p-norm and its applications.Computational Optimization and Applications, 85(3):897–935, 2023.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Riemannian optimization on unit sphere with p-norm and its applications.Computational Optimization and Applications, 85(3):897–935, 2023

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.079656Z

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Observation bd8c827c-32b6-471e-8ce5-3681a6f684bd · outbound

This paper cites Riemannian stochastic variance reduced gradient algorithm with retraction and vector transport.SIAM Journal on Optimization, 29(2):1444–1472, 2019.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Riemannian stochastic variance reduced gradient algorithm with retraction and vector transport.SIAM Journal on Optimization, 29(2):1444–1472, 2019

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.084019Z

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Observation a4ae544c-767d-4131-94ea-0d2786e8ddfe · outbound

This paper cites Riemannian optimal identification method for linear systems with symmetric positive-definite matrix.IEEE Transactions on Automatic Control, 65(11):4493–4508, 2019.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Riemannian optimal identification method for linear systems with symmetric positive-definite matrix.IEEE Transactions on Automatic Control, 65(11):4493–4508, 2019

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.088361Z

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Observation b1254e57-f932-472d-b198-d98c5e785ef3 · outbound

This paper cites Retraction-Free Decentralized Non-convex Optimization with Orthogonal Constraints.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Retraction-Free Decentralized Non-convex Optimization with Orthogonal Constraints

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.093557Z

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Unavailable: canonical work link unavailable.

Observation a880e50e-c0a7-4e0c-86c6-42e10c9069ca · outbound

This paper cites Policy optimization over subman- ifolds for linearly constrained feedback synthesis.IEEE Transactions on Automatic Control, 69(5):3024–3039, 2023.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Policy optimization over subman- ifolds for linearly constrained feedback synthesis.IEEE Transactions on Automatic Control, 69(5):3024–3039, 2023

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.098402Z

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Unavailable: canonical work link unavailable.

Observation 478e3656-ead9-4877-98a2-330a20d36adb · outbound

This paper cites Low-rank matrix completion by riemannian opti- mization.SIAM Journal on Optimization, 23(2):1214–1236, 2013.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Low-rank matrix completion by riemannian opti- mization.SIAM Journal on Optimization, 23(2):1214–1236, 2013

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.103285Z

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Observation 2bc6c7da-eb9a-47bb-9116-ef3d9b6178f6 · outbound

This paper cites Geodesic Convex Optimization: Differentiation on Manifolds, Geodesics, and Convexity.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Geodesic Convex Optimization: Differentiation on Manifolds, Geodesics, and Convexity

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.107300Z

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Unavailable: canonical work link unavailable.

Observation 5db898a7-1650-4c7e-9cc3-39e2af733286 · outbound

This paper cites Riemannian online learning.Foundations and Trends® in Optimization, 9(3):248–406, 2025.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Riemannian online learning.Foundations and Trends® in Optimization, 9(3):248–406, 2025

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.111921Z

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Unavailable: canonical work link unavailable.

Observation 955a19bc-2ef7-4a30-ae01-14b6396ad2ac · outbound

This paper cites Online optimization over riemannian manifolds.Journal of Machine Learning Research, 24(84):1–67, 2023.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Online optimization over riemannian manifolds.Journal of Machine Learning Research, 24(84):1–67, 2023

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.116739Z

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Unavailable: canonical work link unavailable.

Observation 5d858ddf-bb57-4085-a646-e8ffa9e7f0c0 · outbound

This paper cites Riemannian online optimistic algorithms with dynamic regret.IEEE Transactions on Automatic Control, 2025.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Riemannian online optimistic algorithms with dynamic regret.IEEE Transactions on Automatic Control, 2025

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.120696Z

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Observation 238ef623-5a02-4a4f-9b83-99e0384d551f · outbound

This paper cites Riemannian svrg: Fast stochastic optimization on riemannian manifolds.Advances in Neural Information Processing Systems, 29, 2016.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives Riemannian svrg: Fast stochastic optimization on riemannian manifolds.Advances in Neural Information Processing Systems, 29, 2016

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.124560Z

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Observation fceaf0dd-bf8b-4519-bd98-d31a4c9bc496 · outbound

This paper cites First-order methods for geodesically convex optimization.

Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives First-order methods for geodesically convex optimization

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-04T17:01:57.128540Z

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Pith citing papers

Observation 5ef9bba4-5747-45ca-ab63-2bb1f7be11ed · inbound

Decentralized Online Riemannian Optimization for Strongly Geodesically Convex Functions cites this paper.

Decentralized Online Riemannian Optimization for Strongly Geodesically Convex Functions Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-01T10:18:45.227744Z

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