Paper Citation Record · LEDGER

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem

As of 16 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:1908.02747.

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

pith.paper-citation-record.v1
1908.02747 v2

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:46:14.645227Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

28 of 28 outbound references displayed

verified exact0
verified fuzzy23
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation feba2a95-02fb-471d-a837-648c3a39f2e6 · outbound

This paper cites Distributed optimization in sen sor networks,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Distributed optimization in sen sor networks,

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.591286Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7ed93cc2-665a-4b87-83bc-1c921136931d · outbound

This paper cites Diffusion adaptation strategie s for distributed optimization and learning over networks,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Diffusion adaptation strategie s for distributed optimization and learning over networks,

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.567399Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 85aa1e90-4219-4296-9da3-d6f25a4c9fcf · outbound

This paper cites An overview of recent pr ogress in the study of distributed multi-agent coordination,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem An overview of recent pr ogress in the study of distributed multi-agent coordination,

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.525743Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 111eadcb-7282-4d3f-ba0c-45a91abe2fb2 · outbound

This paper cites D istributed optimization and statistical learning via the alternating direction method of multipliers,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem D istributed optimization and statistical learning via the alternating direction method of multipliers,

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.502303Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c328482a-c6d6-4037-9a2e-9650a1261a72 · outbound

This paper cites Clustering with Distributed Data.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Clustering with Distributed Data

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-14T14:46:14.450230Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e73d378-d596-43a9-a03b-8c29615a33bf · outbound

This paper cites Distributed subgradient met hods for multi- agent optimization,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Distributed subgradient met hods for multi- agent optimization,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.468292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 966d0913-b6a8-4943-b970-c9880ff89c65 · outbound

This paper cites A distributed quasi-n ewton algo- rithm for empirical risk minimization with nonsmooth regul arization,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem A distributed quasi-n ewton algo- rithm for empirical risk minimization with nonsmooth regul arization,

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.432136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c798571b-07f1-4daa-b0c6-e2e3551b899a · outbound

This paper cites Distributed nonconvex opt imization over networks,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Distributed nonconvex opt imization over networks,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.408409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation cac629c5-4bda-4858-b366-05c4f66c4efd · outbound

This paper cites Distributed nonconv ex multiagent optimization over time-varying networks,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Distributed nonconv ex multiagent optimization over time-varying networks,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.374384Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 663c5b02-0735-4e24-bbd0-484ed282b16a · outbound

This paper cites Distributed Non-convex Optimization of Multi-agent Systems Using Boosting Functions to Escape Local Optima: Theory and Applications.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Distributed Non-convex Optimization of Multi-agent Systems Using Boosting Functions to Escape Local Optima: Theory and Applications

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-14T14:46:14.496490Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8ad49a3-258f-45ae-a685-e727987136de · outbound

This paper cites Convergence of a multi-a gent projected stochastic gradient algorithm for non-convex optimizatio n,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Convergence of a multi-a gent projected stochastic gradient algorithm for non-convex optimizatio n,

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.349918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation be5cd77b-25b9-4725-8d77-34c0920c3bb3 · outbound

This paper cites Next: In-network nonconv ex optimiza- tion,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Next: In-network nonconv ex optimiza- tion,

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.325880Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f2fc5e41-5345-48d4-a92d-c74eea202e6f · outbound

This paper cites Identifying and attacking the saddle point prob lem in high- dimensional non-convex optimization,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Identifying and attacking the saddle point prob lem in high- dimensional non-convex optimization,

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.297484Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4e735da1-0abd-42b9-a744-172874fd40c0 · outbound

This paper cites Gra dient descent only converges to minimizers,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Gra dient descent only converges to minimizers,

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.255436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ab79da0b-5640-4240-bb40-381049f26634 · outbound

This paper cites First-order methods almost always avoid strict s addle points,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem First-order methods almost always avoid strict s addle points,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.235482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 89e7a80e-4767-417a-98e7-b858bf61e981 · outbound

This paper cites Revisiting normaliz ed gradient descent: Fast evasion of saddle points,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Revisiting normaliz ed gradient descent: Fast evasion of saddle points,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.208483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 929ab326-f125-4187-89b2-ba5b1a9e6f06 · outbound

This paper cites Shub, Global stability of dynamical systems.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Shub, Global stability of dynamical systems

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.156416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b0fb7aef-fca9-446a-9003-da0aa722e516 · outbound

This paper cites an unresolved cited work.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-14T14:46:14.573980Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bc87bf5d-2bc1-45c6-b279-fae6e53ac2a6 · outbound

This paper cites Anneal ing for distributed global optimization,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Anneal ing for distributed global optimization,

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.114848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c873bbbf-946b-438a-b136-436609096c6f · outbound

This paper cites Non-convex distributed opt imization,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Non-convex distributed opt imization,

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.071366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7ed19cbd-b533-41ab-923b-c48755dfd309 · outbound

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

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Second-order Guarantees of Distributed Gradient Algorithms

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-14T14:46:14.593383Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ec08c84f-f25e-4a19-8eff-c8a9ab796e44 · outbound

This paper cites Distributed parame ter estimation in sensor networks: Nonlinear observation models and imper fect com- munication,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Distributed parame ter estimation in sensor networks: Nonlinear observation models and imper fect com- munication,

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.049829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d68341dc-5808-469c-841d-5ff3b4d127fd · outbound

This paper cites Constrained consensus and optimization in multi-agent networks,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Constrained consensus and optimization in multi-agent networks,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:15.019179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fcb55e3b-2207-4330-b8aa-5fe7cd724dcc · outbound

This paper cites Distributed optimization over time-varying directed graphs,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Distributed optimization over time-varying directed graphs,

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:14.972024Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 122f1847-bd54-4f74-9fc9-2998f8a45ee8 · outbound

This paper cites Gradient primal- dual al- gorithm converges to second-order stationary solutions fo r nonconvex distributed optimization,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Gradient primal- dual al- gorithm converges to second-order stationary solutions fo r nonconvex distributed optimization,

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:14.929726Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a5bbd946-bdfe-4194-9047-748ced98c066 · outbound

This paper cites an unresolved cited work.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-14T14:46:14.627430Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cc2f4a46-4ceb-406a-a53d-65464e2d8a40 · outbound

This paper cites Stochastic appr oximations and differential inclusions,.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Stochastic appr oximations and differential inclusions,

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:14.875461Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b5fc412e-6e35-4058-ad75-120e2322303c · outbound

This paper cites Lakshmikantham and S.

Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem Lakshmikantham and S

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:46:14.844825Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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