Paper Citation Record · LEDGER

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points

As of 21 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:1907.01849.

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

pith.paper-citation-record.v1
1907.01849 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-25T09:52:34.427619Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-14T12:38:57.567840Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-14T12:38:57.831183Z

Reference resolution

33 of 33 outbound references displayed

verified exact7
verified fuzzy25
unresolved1
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b48a4f93-a4e2-4912-b7b8-fb1bd251e2f9 · outbound

This paper cites Diffusion learning in non-con vex envi- ronments.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Diffusion learning in non-con vex envi- ronments

Reference 1

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7fc2d9e7-7602-4768-be60-930e2a0058d2 · outbound

This paper cites Distributed learning in non-c onvex environments – Part I: Agreement at a Linear rate.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Distributed learning in non-c onvex environments – Part I: Agreement at a Linear rate

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.540341Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 68478ee1-8b2e-4a67-b114-1feb0434a667 · outbound

This paper cites Distributed subgradient meth ods for multi- agent optimization.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Distributed subgradient meth ods for multi- agent optimization

Reference 3

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 316e4a13-7b8f-472a-9b13-23917e042de6 · outbound

This paper cites Adaptation, learning, and optimization ov er networks.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Adaptation, learning, and optimization ov er networks

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.472180Z

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Observation 054fd8ab-ad45-4fb5-8b0a-fa3d2a1aca05 · outbound

This paper cites On the learning behavior of adapt ive networks - Part I: Transient analysis.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points On the learning behavior of adapt ive networks - Part I: Transient analysis

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.508303Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation aeb10823-31d9-4e33-8477-82bee007b204 · outbound

This paper cites Distributed stochastic optimization with gradient tracking over strongly-connected networks.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Distributed stochastic optimization with gradient tracking over strongly-connected networks

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-05-25T09:55:36.547979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 5038ee11-3696-4bfa-bcd0-0877d6ea455a · outbound

This paper cites Stochastic g radient descent with ﬁnite samples sizes.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Stochastic g radient descent with ﬁnite samples sizes

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.530406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation cd48a971-c22b-4a01-913e-c7c5ea25dcfc · outbound

This paper cites Extra: An exact ﬁrst-or der algorithm for decentralized consensus optimization.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Extra: An exact ﬁrst-or der algorithm for decentralized consensus optimization

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.520387Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d62ab078-21fe-4c62-ba04-64adede71c61 · outbound

This paper cites Exact diffusio n for distributed optimization and learning – Part II: Convergen ce analysis.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Exact diffusio n for distributed optimization and learning – Part II: Convergen ce analysis

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.486612Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0c20271b-39be-49a4-803a-73a16291bb4d · outbound

This paper cites Diffusion strategies o utperform consensus strategies for distributed estimation over adap tive networks.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Diffusion strategies o utperform consensus strategies for distributed estimation over adap tive networks

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.461398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2843d5d0-896f-4f3a-986e-abe818053e56 · outbound

This paper cites On the learning behavior of adap tive networks – Part II: Performance analysis.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points On the learning behavior of adap tive networks – Part II: Performance analysis

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.465038Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4c998181-afde-417e-991a-f912615cf525 · outbound

This paper cites Prox imal multitask learning over networks with sparsity-inducing coregulari zation.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Prox imal multitask learning over networks with sparsity-inducing coregulari zation

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.454374Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4f6b0855-766b-41c5-b91b-4b7edc9250a9 · outbound

This paper cites Adaptive penalty-based dis tributed stochastic convex optimization.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Adaptive penalty-based dis tributed stochastic convex optimization

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.493268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 57215295-3b71-4dbc-b592-da9dd75e1233 · outbound

This paper cites Performance limits of stochast ic sub-gradient learning, Part II: Multi-agent case.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Performance limits of stochast ic sub-gradient learning, Part II: Multi-agent case

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.523847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 742f2b60-05b7-45ec-944d-3342a1fda7df · outbound

This paper cites Cubic regularization of n ewton method and its global performance.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Cubic regularization of n ewton method and its global performance

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.500221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 82766bba-8757-48a2-8f79-116451616ada · outbound

This paper cites SPIDER: Near-opt imal non- convex optimization via stochastic path-integrated differential estimator.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points SPIDER: Near-opt imal non- convex optimization via stochastic path-integrated differential estimator

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.458020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 06f3657f-478e-49c5-b592-f0610d175db7 · outbound

This paper cites NEON2: Finding local minima via ﬁrst-order oracles.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points NEON2: Finding local minima via ﬁrst-order oracles

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.514731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ab8b234e-b097-4e46-b094-f2a82f731aa1 · outbound

This paper cites Natasha 2: Faster non-convex optimizat ion than SGD.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Natasha 2: Faster non-convex optimizat ion than SGD

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.504800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4c0eaf1c-3d5b-4977-88c4-c35b5373320a · outbound

This paper cites Gra dient descent only converges to minimizers.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Gra dient descent only converges to minimizers

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.468777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6c34fe7f-4161-41e9-b56a-68284cebf116 · outbound

This paper cites Second-order Guarantees of Distributed Gradient Algorithms.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Second-order Guarantees of Distributed Gradient Algorithms

Reference 20

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4f9e72c3-b0d9-4275-8902-525fe888f135 · outbound

This paper cites Recursive stochastic algori thms for global optimization in Rd.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Recursive stochastic algori thms for global optimization in Rd

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.527046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation fa750ff3-8adb-4157-901d-060a54b32945 · outbound

This paper cites Annealing for Distributed Global Optimization.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Annealing for Distributed Global Optimization

Reference 22

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ae68b1fe-c06e-4521-938c-ce79b762be27 · outbound

This paper cites Gradient Descent Can Take Exponential Time to Escape Saddle Points.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Gradient Descent Can Take Exponential Time to Escape Saddle Points

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-05-25T09:55:36.580148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9c6d6388-d678-4a14-a063-4253aeb467ca · outbound

This paper cites Escaping from saddl e pointsonline stochastic gradient for tensor decompositio n.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Escaping from saddl e pointsonline stochastic gradient for tensor decompositio n

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.475791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 805ccb71-6ad2-4016-b956-177d2e925d90 · outbound

This paper cites How to escape saddle points efﬁciently.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points How to escape saddle points efﬁciently

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.533920Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2f123d49-9a9a-4cf4-9cc6-d8625eafd6d8 · outbound

This paper cites On Nonconvex Optimization for Machine Learning: Gradients, Stochasticity, and Saddle Points.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points On Nonconvex Optimization for Machine Learning: Gradients, Stochasticity, and Saddle Points

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-05-25T09:55:36.558456Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 85764c71-8e8a-4851-a604-b71696123d09 · outbound

This paper cites Escaping Saddles with Stochastic Gradients.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Escaping Saddles with Stochastic Gradients

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-05-25T09:55:36.553099Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 041a77e5-032c-4dc6-9e2a-596207357959 · outbound

This paper cites Sharp Analysis for Nonconvex SGD Escaping from Saddle Points.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Sharp Analysis for Nonconvex SGD Escaping from Saddle Points

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-05-25T09:55:36.574587Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 66924e47-7c68-4a7c-b9f1-c7826423c92e · outbound

This paper cites NEXT: in-network nonconv ex optimiza- tion.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points NEXT: in-network nonconv ex optimiza- tion

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.489878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 83cdc552-a956-4c58-b943-f6fb0acbaf41 · outbound

This paper cites Global convergence of ADMM in nonconvex nonsmooth optimization.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Global convergence of ADMM in nonconvex nonsmooth optimization

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.479621Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a44234ce-d806-47a3-adb5-4a453aeea293 · outbound

This paper cites Non-convex distributed opt imization.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Non-convex distributed opt imization

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.496742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 603a6f8b-5639-4766-8293-d92d94968cd8 · outbound

This paper cites an unresolved cited work.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-05-25T09:55:37.511460Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9389384a-aef7-419d-ab52-31f969588a3b · outbound

This paper cites The Perron-Frobenius theorem: Some of its applications.

Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points The Perron-Frobenius theorem: Some of its applications

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T09:55:37.483136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

Observation 0685eacb-e7e5-4049-baaa-dd1c8d2a990d · inbound

Second-Order Guarantees of Stochastic Gradient Descent in Non-Convex Optimization cites this paper.

Second-Order Guarantees of Stochastic Gradient Descent in Non-Convex Optimization Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-14T12:38:57.836541Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.