Paper Citation Record · LEDGER

Extending the step-size restriction for gradient descent to avoid strict saddle points

As of 22 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:1908.01753.

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

pith.paper-citation-record.v1
1908.01753 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T15:14:53.476868Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

30 of 30 outbound references displayed

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verified fuzzy22
unresolved8
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 29ae7032-b00a-4d10-8842-0a386eb62ffa · outbound

This paper cites Convergence of the iterates of descent methods for analytic cost functions.

Extending the step-size restriction for gradient descent to avoid strict saddle points Convergence of the iterates of descent methods for analytic cost functions

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.859374Z

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Observation d0179db1-fe1d-4f32-8038-69751b073bbd · outbound

This paper cites Eﬃcient approaches f or escaping higher order saddle points in non-convex optimization.

Extending the step-size restriction for gradient descent to avoid strict saddle points Eﬃcient approaches f or escaping higher order saddle points in non-convex optimization

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.847173Z

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Observation 7c0557ab-f4cf-4651-8ec9-c4982dbce18e · outbound

This paper cites Global optimality of local search for low rank matrix recovery.

Extending the step-size restriction for gradient descent to avoid strict saddle points Global optimality of local search for low rank matrix recovery

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.834224Z

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Observation 638e688a-abe4-4302-8976-d22c94fefdef · outbound

This paper cites Accelerated methods for nonconvex optimization.

Extending the step-size restriction for gradient descent to avoid strict saddle points Accelerated methods for nonconvex optimization

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.821794Z

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Observation aabc920b-e4f1-4f99-94fd-24139aee4d49 · outbound

This paper cites an unresolved cited work.

Extending the step-size restriction for gradient descent to avoid strict saddle points Unresolved cited work

Reference 5

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Observation cea6893c-5bbe-4052-95c5-81bdb7284e4d · outbound

This paper cites Identifying and attacking the saddle point p roblem in high-dimensional non- convex optimization.

Extending the step-size restriction for gradient descent to avoid strict saddle points Identifying and attacking the saddle point p roblem in high-dimensional non- convex optimization

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.798609Z

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Observation b6312465-f5fa-4758-8d42-bd82c5a27abd · outbound

This paper cites Gradient descent can take exponential time to escape saddle points.

Extending the step-size restriction for gradient descent to avoid strict saddle points Gradient descent can take exponential time to escape saddle points

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.786108Z

Source-reported events for the cited work

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Observation 1a0d68a8-f4f1-45ed-ba10-def9cf9ba760 · outbound

This paper cites Escaping fr om saddle points–online stochas- tic gradient for tensor decomposition.

Extending the step-size restriction for gradient descent to avoid strict saddle points Escaping fr om saddle points–online stochas- tic gradient for tensor decomposition

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.774992Z

Source-reported events for the cited work

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Observation 7ad297b2-54b5-452e-a441-dc9c098fb7ab · outbound

This paper cites No spurious local minima in nonconvex low rank problems: A uniﬁed geometric analysis.

Extending the step-size restriction for gradient descent to avoid strict saddle points No spurious local minima in nonconvex low rank problems: A uniﬁed geometric analysis

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.763085Z

Source-reported events for the cited work

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Observation 8ee16840-204f-4d18-9d3f-45277d82b851 · outbound

This paper cites Matrix completion ha s no spurious local minimum.

Extending the step-size restriction for gradient descent to avoid strict saddle points Matrix completion ha s no spurious local minimum

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.749640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation fecb838c-37ba-4ed4-8a0b-a4c20a571273 · outbound

This paper cites Newton-type methods fo r unconstrained and linearly con- strained optimization.

Extending the step-size restriction for gradient descent to avoid strict saddle points Newton-type methods fo r unconstrained and linearly con- strained optimization

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.735525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 41668baf-312f-4e18-ad8f-189f381f8d68 · outbound

This paper cites How to escape saddle points eﬃciently.

Extending the step-size restriction for gradient descent to avoid strict saddle points How to escape saddle points eﬃciently

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.723144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7ebca6af-14f5-4c01-97d9-b30cd4af1701 · outbound

This paper cites On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima.

Extending the step-size restriction for gradient descent to avoid strict saddle points On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima

Reference 13

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Source-reported events for the cited work

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Observation 50aaf26f-96d6-42ba-a530-eb26bbd29da0 · outbound

This paper cites First-order Methods Almost Always Avoid Saddle Points.

Extending the step-size restriction for gradient descent to avoid strict saddle points First-order Methods Almost Always Avoid Saddle Points

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-14T15:14:53.411614Z

Source-reported events for the cited work

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Observation d24a5c19-d881-4ccb-aa6f-f20cd63c5b88 · outbound

This paper cites Gradient descent only converges to minimizers.

Extending the step-size restriction for gradient descent to avoid strict saddle points Gradient descent only converges to minimizers

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.711069Z

Source-reported events for the cited work

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Observation e3cb2e78-9597-4f99-a721-0464f3c2609e · outbound

This paper cites The Power of Normalization: Faster Evasion of Saddle Points.

Extending the step-size restriction for gradient descent to avoid strict saddle points The Power of Normalization: Faster Evasion of Saddle Points

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-14T15:14:53.420939Z

Source-reported events for the cited work

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Observation 7f9cfa09-fa42-493c-a8f5-5ffb0a984ca9 · outbound

This paper cites On the use of directio ns of negative curvature in a modiﬁed newton method.

Extending the step-size restriction for gradient descent to avoid strict saddle points On the use of directio ns of negative curvature in a modiﬁed newton method

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.697355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4d60a9c7-8c09-40bf-965e-92acdd564fce · outbound

This paper cites Introductory lectures on convex optimization: A basic cours e, volume 87.

Extending the step-size restriction for gradient descent to avoid strict saddle points Introductory lectures on convex optimization: A basic cours e, volume 87

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.685525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b5daceb2-7715-4ee8-9139-f5f46630d2b3 · outbound

This paper cites Cubic regularizatio n of newton method and its global performance.

Extending the step-size restriction for gradient descent to avoid strict saddle points Cubic regularizatio n of newton method and its global performance

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.674255Z

Source-reported events for the cited work

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Observation 728e50bf-3ac5-4577-9107-dbef7f781751 · outbound

This paper cites Behavior of accel erated gradient methods near critical points of nonconvex functions.

Extending the step-size restriction for gradient descent to avoid strict saddle points Behavior of accel erated gradient methods near critical points of nonconvex functions

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.662985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b2a92c74-a9be-42bd-95d2-9c18102ac73a · outbound

This paper cites Gradient Descent Only Converges to Minimizers: Non-Isolated Critical Points and Invariant Regions.

Extending the step-size restriction for gradient descent to avoid strict saddle points Gradient Descent Only Converges to Minimizers: Non-Isolated Critical Points and Invariant Regions

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-14T15:14:53.442432Z

Source-reported events for the cited work

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Observation 829e4c88-3321-46df-815f-a0c66494a84d · outbound

This paper cites On the saddle point problem for non-convex optimization.

Extending the step-size restriction for gradient descent to avoid strict saddle points On the saddle point problem for non-convex optimization

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-14T15:14:53.446649Z

Source-reported events for the cited work

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Observation 41c6ae05-3103-4ae4-b34c-a5f40de5349f · outbound

This paper cites Nonconvergence to unstable points in u rn models and stochastic approxima- tions.

Extending the step-size restriction for gradient descent to avoid strict saddle points Nonconvergence to unstable points in u rn models and stochastic approxima- tions

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.650372Z

Source-reported events for the cited work

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Observation f8f7d45b-0dcc-40c5-bc77-328d6122ae86 · outbound

This paper cites A Generic Approach for Escaping Saddle points.

Extending the step-size restriction for gradient descent to avoid strict saddle points A Generic Approach for Escaping Saddle points

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-14T15:14:53.454597Z

Source-reported events for the cited work

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Observation d6c5486b-4f7c-4c47-a153-7dc1961f40a6 · outbound

This paper cites Complexity analy sis of second-order line-search algorithms for smooth nonconvex optimization.

Extending the step-size restriction for gradient descent to avoid strict saddle points Complexity analy sis of second-order line-search algorithms for smooth nonconvex optimization

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.637453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 725e6619-6743-4bc6-8d4e-9fb6928795bf · outbound

This paper cites Global stability of dynamical systems.

Extending the step-size restriction for gradient descent to avoid strict saddle points Global stability of dynamical systems

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-14T15:14:53.462822Z

Source-reported events for the cited work

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Observation e61ee051-f4ae-49ff-bdfb-4bc0055a24c9 · outbound

This paper cites Theoretical insights into the op- timization landscape of over-parameterized shallow neura l networks.

Extending the step-size restriction for gradient descent to avoid strict saddle points Theoretical insights into the op- timization landscape of over-parameterized shallow neura l networks

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.617166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1a9b39ce-c647-4dba-bfdb-f4bed8c074b3 · outbound

This paper cites Complete dictionary re covery over the sphere i: Overview and the geometric picture.

Extending the step-size restriction for gradient descent to avoid strict saddle points Complete dictionary re covery over the sphere i: Overview and the geometric picture

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.604849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5d0b4f4a-164b-46ca-aa34-f67e52621631 · outbound

This paper cites Complete dictionary re covery over the sphere ii: Recovery by riemannian trust-region method.

Extending the step-size restriction for gradient descent to avoid strict saddle points Complete dictionary re covery over the sphere ii: Recovery by riemannian trust-region method

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.592657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d0edd064-e6bf-445c-9e08-2d5b4122a3d7 · outbound

This paper cites A geometric analysis of phase retrieval.

Extending the step-size restriction for gradient descent to avoid strict saddle points A geometric analysis of phase retrieval

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:14:53.579724Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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