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Paper Citation Record · LEDGER

Hopfield Neural Network Flow: A Geometric Viewpoint

As of 17 August 2026, this Paper Citation Record lists 68 of 68 outbound references and 0 inbound Pith citation observations for arXiv:1908.01270.

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

pith.paper-citation-record.v1
1908.01270 v2

Coverage vector

measured 68 of 68 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T15:32:37.980430Z

measured 68 of 68 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+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

68 of 68 outbound references displayed

  • verified exact1
  • verified fuzzy67
  • unresolved0
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8599d347-c854-4ac4-99d6-0d8c75121db4 · outbound

This paper cites Neural networks and physical systems with emerging collective computational abilities.

Hopfield Neural Network Flow: A Geometric Viewpoint Neural networks and physical systems with emerging collective computational abilities

Reference 1

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 5e1060b5-62af-4616-af13-cc389f35d3ac · outbound

This paper cites Neurons with graded response have collective computa- tional properties like those of two-state neurons.

Hopfield Neural Network Flow: A Geometric Viewpoint Neurons with graded response have collective computa- tional properties like those of two-state neurons

Reference 2

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 9797621a-a9ff-4183-bcf2-62b32eac9490 · outbound

This paper cites Simple ‘neural’ optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit.

Hopfield Neural Network Flow: A Geometric Viewpoint Simple ‘neural’ optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit

Reference 3

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 4e2f9045-d3be-41b4-b60a-335af75bde3c · outbound

This paper cites Neural networks for nonlinear program- ming.

Hopfield Neural Network Flow: A Geometric Viewpoint Neural networks for nonlinear program- ming

Reference 4

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 7de77d35-4c37-4fb9-aef2-55efaa8b83a2 · outbound

This paper cites Identification and control of dy- namical systems using neural networks.

Hopfield Neural Network Flow: A Geometric Viewpoint Identification and control of dy- namical systems using neural networks

Reference 5

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 876cf07c-03f2-4e86-9227-385f0adcf985 · outbound

This paper cites Hopfield neural networks for affine invariant matching.

Hopfield Neural Network Flow: A Geometric Viewpoint Hopfield neural networks for affine invariant matching

Reference 6

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation ea189c57-0389-4547-8a65-e481afd7b7f8 · outbound

This paper cites Dual Hopfield methods for large-scale mixed-integer programming.

Hopfield Neural Network Flow: A Geometric Viewpoint Dual Hopfield methods for large-scale mixed-integer programming

Reference 7

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation d14e82e4-888f-4d44-bc56-86d51662c2f8 · outbound

This paper cites Aluffi-Pentini, V.

Hopfield Neural Network Flow: A Geometric Viewpoint Aluffi-Pentini, V

Reference 27

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 09748c24-2452-44c5-a19c-061038f47f0f · outbound

This paper cites Stochastic neural networks.

Hopfield Neural Network Flow: A Geometric Viewpoint Stochastic neural networks

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.803973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation e0bbdc03-ce0b-48ad-a132-abdf4520a4cb · outbound

This paper cites Robust stability for interval Hopfield neural networks with time delay.

Hopfield Neural Network Flow: A Geometric Viewpoint Robust stability for interval Hopfield neural networks with time delay

Reference 29

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 44f87295-6988-4a4b-8665-4165e5fae972 · outbound

This paper cites Hopfield neural networks for optimization: study of the different dynamics.

Hopfield Neural Network Flow: A Geometric Viewpoint Hopfield neural networks for optimization: study of the different dynamics

Reference 30

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 04fe5e25-aa7d-441f-8021-aef7e4062a27 · outbound

This paper cites Natural gradient works efficiently in learning.

Hopfield Neural Network Flow: A Geometric Viewpoint Natural gradient works efficiently in learning

Reference 31

Resolution
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raw_fallback, observed 2026-08-14T15:32:38.768025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation c16fc81f-fb91-48aa-bb4e-77d5d6bc3402 · outbound

This paper cites Nemirovskii, and D.B.

Hopfield Neural Network Flow: A Geometric Viewpoint Nemirovskii, and D.B

Reference 33

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation d76bfad6-6b59-4ebd-971d-92b1bc148261 · outbound

This paper cites do Carmo, Riemannian Geometry , Birkh ¨auser, 1992.

Hopfield Neural Network Flow: A Geometric Viewpoint do Carmo, Riemannian Geometry , Birkh ¨auser, 1992

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.709307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.731316Z digest=sha256:20dbceb99cb284828753e478178fc762ca0fc33164b9067fac969825e31a89f6

Observation a610dc9a-1283-4dfb-9f19-366833ab466a · outbound

This paper cites Convex optimization: algorithms and convexity.

Hopfield Neural Network Flow: A Geometric Viewpoint Convex optimization: algorithms and convexity

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.685645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.738304Z digest=sha256:f67412ea4bf40cf4a86b4680f5f4222ace808f4d1d73af3bc4427326f164ae21

Observation b74d02ab-bcaf-41c3-a07b-af2a3c2d194d · outbound

This paper cites Rockafeller, Convex Analysis , Princeton University Press, 1970.

Hopfield Neural Network Flow: A Geometric Viewpoint Rockafeller, Convex Analysis , Princeton University Press, 1970

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.673231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.741862Z digest=sha256:ed0f996b9af8680a82f25935ef23ff7749b28d5bdb063950f7dcf6e274189806

Observation b63b3689-53aa-40a9-8b09-fcfed0513202 · outbound

This paper cites Accelerated Mirror Descent in Continuous and Discrete Time.

Hopfield Neural Network Flow: A Geometric Viewpoint Accelerated Mirror Descent in Continuous and Discrete Time

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.660751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.745996Z digest=sha256:26c7e9ce32bd8991e68dc94561cb6c68dfddab0771b4d2ae72ddc05edbacb0d3

Observation 91625b8c-73e5-4882-a67a-da379dcdad47 · outbound

This paper cites Aluffi-Pentini, V.

Hopfield Neural Network Flow: A Geometric Viewpoint Aluffi-Pentini, V

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.553779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation adc0c654-98fc-45e7-a096-3806b6de50a0 · outbound

This paper cites Stochastic neural networks.

Hopfield Neural Network Flow: A Geometric Viewpoint Stochastic neural networks

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.489253Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 7dbe2135-892f-4d14-befd-2648eb1a1756 · outbound

This paper cites Robust stability for interval Hopfield neural networks with time delay.

Hopfield Neural Network Flow: A Geometric Viewpoint Robust stability for interval Hopfield neural networks with time delay

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.477223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation e9a2d6a3-884f-45dd-b493-49d1d3af18a5 · outbound

This paper cites Hopfield neural networks for optimization: study of the different dynamics.

Hopfield Neural Network Flow: A Geometric Viewpoint Hopfield neural networks for optimization: study of the different dynamics

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.466896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.801339Z digest=sha256:906d08715d7aa542c8603d8225abff672f9abf8ec212c066560f1b3a9910eaef

Observation c51dcdec-456e-493b-9dd9-df1d72a2d5f8 · outbound

This paper cites Natural gradient works efficiently in learning.

Hopfield Neural Network Flow: A Geometric Viewpoint Natural gradient works efficiently in learning

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.456268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.805382Z digest=sha256:8d8f9bcc7cbd8d7fce4bd449792d0efaa6ea67d3a52906448bc1b66eaf18e872

Observation e3724307-049e-4ba3-85b0-80f9e662da9e · outbound

This paper cites Shima, The Geometry of Hessian Structures , World Scientific, 2007.

Hopfield Neural Network Flow: A Geometric Viewpoint Shima, The Geometry of Hessian Structures , World Scientific, 2007

Reference 52

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 7586e0eb-b825-4214-b228-c9c739780d4c · outbound

This paper cites Nemirovskii, and D.B.

Hopfield Neural Network Flow: A Geometric Viewpoint Nemirovskii, and D.B

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.444443Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 6783f78a-1a39-4280-83ef-005c5f82feb2 · outbound

This paper cites Mirror descent and nonlinear projected subgradient methods for convex optimization.

Hopfield Neural Network Flow: A Geometric Viewpoint Mirror descent and nonlinear projected subgradient methods for convex optimization

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.732266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 5407216f-2c16-419d-9450-34c3c108ab79 · outbound

This paper cites The information geometry of mirror descent.

Hopfield Neural Network Flow: A Geometric Viewpoint The information geometry of mirror descent

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.720694Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.820863Z digest=sha256:2120c0e8fa694e55ee6767f53709f4a4d8e5b1d91dee9a715a9fa8380e8ef85a

Observation 3677b3e7-59e4-4ba2-b274-42626d5ab595 · outbound

This paper cites doCarmo, Riemannian Geometry, Birkh ¨auser, 1992.

Hopfield Neural Network Flow: A Geometric Viewpoint doCarmo, Riemannian Geometry, Birkh ¨auser, 1992

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.432820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.824795Z digest=sha256:366d9ea9b802260eb746814a3381958ba82a07f41c68808c899ab141a78ff6f5

Observation 5a904a64-00a6-4756-945a-4a5c5512489b · outbound

This paper cites The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming.

Hopfield Neural Network Flow: A Geometric Viewpoint The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.697858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 0c6087a2-91ff-42f8-bcb1-7ccae2646908 · outbound

This paper cites Convex optimization: algorithms and convexity.

Hopfield Neural Network Flow: A Geometric Viewpoint Convex optimization: algorithms and convexity

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.420578Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.832053Z digest=sha256:061842a4448afdabc718014737ac768e4a507cc846d889640ff92ffad44a6c0e

Observation c0649eaf-f640-4c1b-a3b8-a133d527dad5 · outbound

This paper cites Rockafeller, Convex Analysis, Princeton University Press, 1970.

Hopfield Neural Network Flow: A Geometric Viewpoint Rockafeller, Convex Analysis, Princeton University Press, 1970

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.408551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.836171Z digest=sha256:22aa1fe0f7fbf69f3e79bd301ff2d95dc8efb0ea1b3fd52dfdec775c19327106

Observation c68f5c7a-8095-4669-b6f4-22fc3a9bcfef · outbound

This paper cites Accelerated Mirror Descent in Continuous and Discrete Time.

Hopfield Neural Network Flow: A Geometric Viewpoint Accelerated Mirror Descent in Continuous and Discrete Time

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.396510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.840467Z digest=sha256:7c541246cbb8930784b992d3ab5c5165f5347a7aa5d0fa68472aadcd44e2abdd

Observation 0c6d083c-159c-415e-b7bd-846a34fb24ca · outbound

This paper cites Characterization of the subdifferentials of convex functions.

Hopfield Neural Network Flow: A Geometric Viewpoint Characterization of the subdifferentials of convex functions

Reference 61

Resolution
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raw_fallback, observed 2026-08-14T15:32:38.647928Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.844474Z digest=sha256:651e89c531db04146ab16513fa8b9ee1f607fd154bda46985ec75c9b616b9517

Observation 20ec66f4-07fa-469e-8717-658de95b43c3 · outbound

This paper cites On Bregman V oronoi diagrams.

Hopfield Neural Network Flow: A Geometric Viewpoint On Bregman V oronoi diagrams

Reference 62

Resolution
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raw_fallback, observed 2026-08-14T15:32:38.635098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.847939Z digest=sha256:1414f64c48d01899b062ad747c3f7a1e8782f607b16e61d024d74bb2654dfcd6

Observation 84502f8d-a056-4e5c-acf7-ea36e4096ecf · outbound

This paper cites Clustering with Bregman divergences.

Hopfield Neural Network Flow: A Geometric Viewpoint Clustering with Bregman divergences

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.621245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.851584Z digest=sha256:dbc5116722fc15e9285ed621643874c97b278d47540a24a171c14b6df94e3318

Observation 3d25f76c-4393-4940-917c-3d191ee8cab1 · outbound

This paper cites Economic load dispatch for piecewise quadratic cost function using Hopfield neural network.

Hopfield Neural Network Flow: A Geometric Viewpoint Economic load dispatch for piecewise quadratic cost function using Hopfield neural network

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.384504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.855428Z digest=sha256:3c9a8f4edc8f298b685dd67e07d1b6e4b8404bb2a8ee134e19eb3dc16db79a68

Observation a67c2172-972c-4dcc-970e-45de5f212c9f · outbound

This paper cites Optimal environmental dispatching of electric power systems via an improved Hopfield neural network model.

Hopfield Neural Network Flow: A Geometric Viewpoint Optimal environmental dispatching of electric power systems via an improved Hopfield neural network model

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.373371Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.859946Z digest=sha256:132cc793c4ca1fd3c07e293e12cc9d3431fd70c514df000d01e2d133f1636ac1

Observation ceb7b024-3a3a-4373-a6e3-3f7ade5d9d4d · outbound

This paper cites Adaptive Hopfield neural networks for economic load dispatch.

Hopfield Neural Network Flow: A Geometric Viewpoint Adaptive Hopfield neural networks for economic load dispatch

Reference 66

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.361616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.863698Z digest=sha256:02b0cf2239eab78bda97927b9ce70cb78262b46da0a874fb73c36b7273a7b888

Observation c67fe6b3-93bb-4b2d-bdd1-faa48dd6e2ef · outbound

This paper cites Diffusions for global optimization.

Hopfield Neural Network Flow: A Geometric Viewpoint Diffusions for global optimization

Reference 67

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.608234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.868419Z digest=sha256:623197b693e3b298dded62e88c31b4b0a3d9acdf78ac8c437a668c9777e4e58d

Observation e96fdbf5-efc5-4066-8fad-a97b11693b76 · outbound

This paper cites Analog optimization with Wong’s stochastic neural net- work.

Hopfield Neural Network Flow: A Geometric Viewpoint Analog optimization with Wong’s stochastic neural net- work

Reference 68

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.596878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.873328Z digest=sha256:a06a13ade5d932d0abbc67901ea6849d155bd6f8ac38a09ef9b43dac3599aba9

Observation 3d758ad9-29a2-4ed4-b5cb-4ec4ed107172 · outbound

This paper cites Global optimization via the Langevin equation.

Hopfield Neural Network Flow: A Geometric Viewpoint Global optimization via the Langevin equation

Reference 69

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.583957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.876751Z digest=sha256:c51489e24656cda5044d8485b1348ac86ea02120638f92a0281a77554bf0824a

Observation 7978efb8-a981-49e2-a216-65d7bfbe773c · outbound

This paper cites Global optimization and stochastic differential equations.

Hopfield Neural Network Flow: A Geometric Viewpoint Global optimization and stochastic differential equations

Reference 70

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.349499Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.880286Z digest=sha256:bd2289098b6f4f0d474d9ceceb83dbbfaccd2996e11fe56a706e5a7f1e07907b

Observation dfdd44aa-e4ee-4ee8-adf2-a73baf0742bc · outbound

This paper cites A learning algorithm for Boltzmann machines.

Hopfield Neural Network Flow: A Geometric Viewpoint A learning algorithm for Boltzmann machines

Reference 71

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.338401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.884049Z digest=sha256:99fe977efb25b5ea5cf4be063372d1671d0b51add14a86d43906b315c17add79

Observation b6eba591-ee49-40f7-afd4-0fbfe33b2781 · outbound

This paper cites Risken, The Fokker-Planck equation: Methods of solution and appli- cations.

Hopfield Neural Network Flow: A Geometric Viewpoint Risken, The Fokker-Planck equation: Methods of solution and appli- cations

Reference 72

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.327665Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.887834Z digest=sha256:c328cd0d0aad56c4e44ed284b6a42b07e0fe5f4e18aa6dce8d0a4d43996355a4

Observation 3886e565-f0ad-44e6-9fb1-dc0ad96a069a · outbound

This paper cites Exponential convergence to equilibrium for kinetic Fokker-Planck equations.

Hopfield Neural Network Flow: A Geometric Viewpoint Exponential convergence to equilibrium for kinetic Fokker-Planck equations

Reference 73

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.316842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.891712Z digest=sha256:05c36b1403918d2c7c98dcd872f14930deb66e5e09d0a9ea08cf9e372a2829a9

Observation 038bd84c-a0d1-4f13-be1c-b07f22271501 · outbound

This paper cites Oscillatory descent for function minimization.

Hopfield Neural Network Flow: A Geometric Viewpoint Oscillatory descent for function minimization

Reference 74

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.304987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.895782Z digest=sha256:c1cdd7da3f65559da1097428efe5669aae89c39aa3d72e67da28a5e80feabf90

Observation def33579-e910-4804-af02-9a4f5ee5c0bd · outbound

This paper cites Noisy recurrent neural networks: the continuous-time case.

Hopfield Neural Network Flow: A Geometric Viewpoint Noisy recurrent neural networks: the continuous-time case

Reference 75

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.292965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.899692Z digest=sha256:f80fbe7ad45f7edada1f044123325abd64dc548fb4de99ea680d8df4ed17a416

Observation 91f4f63f-d0da-4d6e-b1e3-d271a267bf41 · outbound

This paper cites Villani, Topics in optimal transportation , American Mathematical Society, Providence, RI, 2003.

Hopfield Neural Network Flow: A Geometric Viewpoint Villani, Topics in optimal transportation , American Mathematical Society, Providence, RI, 2003

Reference 76

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.280972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.904300Z digest=sha256:93ff91fe71cc1a9a86406e9d479486af3e71c3d7c632aa0997319fd5deb17861

Observation 10a3a684-544b-4266-b60e-e15d130074e7 · outbound

This paper cites Convex functionals of probability measures and non- linear diffusions on manifolds.

Hopfield Neural Network Flow: A Geometric Viewpoint Convex functionals of probability measures and non- linear diffusions on manifolds

Reference 77

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.269630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.908085Z digest=sha256:eff35902875a3079f2caeb62fa98db83143638c1b586b6d96805201135bfe76d

Observation 3c2aab32-5f53-4333-86af-c391c6ffc03a · outbound

This paper cites Gradient flows on Wasserstein spaces over compact Alexan- drov spaces.

Hopfield Neural Network Flow: A Geometric Viewpoint Gradient flows on Wasserstein spaces over compact Alexan- drov spaces

Reference 78

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.258324Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.912119Z digest=sha256:7955a2c1e299fc481cd8f39b03b5096f64c5b90b51468d9850f4ac5659dce756

Observation 8c990836-0efc-4814-bd85-2c1c390269f5 · outbound

This paper cites A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem.

Hopfield Neural Network Flow: A Geometric Viewpoint A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem

Reference 79

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.247033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.915500Z digest=sha256:757178d25a6aeb6340fd5cdc7299ce9555d8a8f2c66969fe535646ebe69982af

Observation 4b61885d-e371-43c4-a3e6-e8252db44da1 · outbound

This paper cites Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces.

Hopfield Neural Network Flow: A Geometric Viewpoint Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces

Reference 80

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.233579Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.918800Z digest=sha256:a2221e7b49c0d8144e2cebbd9d6fd3cb22a5dc03d157cc6ac6781a00d4e0947e

Observation ff2e856b-b9a2-48a7-b1da-29c1fe973bf9 · outbound

This paper cites The geometry of dissipative evolution equations: the porous medium equation.

Hopfield Neural Network Flow: A Geometric Viewpoint The geometry of dissipative evolution equations: the porous medium equation

Reference 81

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.222609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.921896Z digest=sha256:753cc97b83fdc16e7bcaafe9c19380b641aeadee8bc73c2443a8c39a8177cd4d

Observation a861a524-de43-409c-8ad3-9f53207ed546 · outbound

This paper cites Villani, Optimal transport: old and new, Springer Science & Business Media, V ol.

Hopfield Neural Network Flow: A Geometric Viewpoint Villani, Optimal transport: old and new, Springer Science & Business Media, V ol

Reference 82

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.211081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.925445Z digest=sha256:6eaa0568583b81e7a5daee583eedd3e8791677f46ce034291a8bad0be60e65a7

Observation a775ebcb-0cfd-4064-8dae-afeeb285e365 · outbound

This paper cites Ambrosio, N.

Hopfield Neural Network Flow: A Geometric Viewpoint Ambrosio, N

Reference 83

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.199956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.928530Z digest=sha256:65c6712d001627e1c4b3950b4b47a7924daef1534d2f04808f435914544f968d

Observation 16c6c42f-a3c9-49e2-b35b-4097671aaa99 · outbound

This paper cites Notes on stochastic processes on manifolds.

Hopfield Neural Network Flow: A Geometric Viewpoint Notes on stochastic processes on manifolds

Reference 84

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.190043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.931773Z digest=sha256:693e3ee57e020e46d90d04b5b829121a26e5f59bd71a0cc7113efb97ef5b1318

Observation 8946898d-3dab-45a8-b396-3f049b6a44b4 · outbound

This paper cites The variational formulation of the Fokker-Planck equation.

Hopfield Neural Network Flow: A Geometric Viewpoint The variational formulation of the Fokker-Planck equation

Reference 85

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.178828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.935361Z digest=sha256:bd0db0399793a42df0c86c669260b94f1cd4fc1917abcd8c1fa92ccd94e43f88

Observation 45059c9b-2782-461c-9e56-8e417f241e34 · outbound

This paper cites Constrained Steepest Descent in the 2- Wasserstein Metric.

Hopfield Neural Network Flow: A Geometric Viewpoint Constrained Steepest Descent in the 2- Wasserstein Metric

Reference 86

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.167427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.939122Z digest=sha256:8ab5234bea117147096efc4d77351b8081aa841647a2b0648010c71a146f5340

Observation 5259836b-f3d6-4e6e-9b3b-3872760e77a5 · outbound

This paper cites {Euclidean, metric, and Wasserstein} gradient flows: an overview.

Hopfield Neural Network Flow: A Geometric Viewpoint {Euclidean, metric, and Wasserstein} gradient flows: an overview

Reference 87

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.152119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.942573Z digest=sha256:cee3fe9ce95e7fabfb4eec64bcbd5363554b6cee8eaf042c90eb0ccbb8cfc2e1

Observation a46befee-125c-4311-8fd0-00db818309cf · outbound

This paper cites Proximit ´e et dualit ´e dans un espace hilbertien.

Hopfield Neural Network Flow: A Geometric Viewpoint Proximit ´e et dualit ´e dans un espace hilbertien

Reference 88

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.139130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.946208Z digest=sha256:6f04b8277bfe76a06bd0a57caa1cb387ebf46f7afad65d8e26ec19a88fcfa87e

Observation 9caffb30-b88e-4262-910d-eedd92100c4d · outbound

This paper cites Monotone operators and the proximal point algo- rithm.

Hopfield Neural Network Flow: A Geometric Viewpoint Monotone operators and the proximal point algo- rithm

Reference 89

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.124914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.949896Z digest=sha256:1325950ac94596ef41c3ec5e6177356926830ef1ef8159d200b2dc2318a12392

Observation 8f93a12b-a3da-47ba-a36d-868699c91b0b · outbound

This paper cites Bauschke, and P.L.

Hopfield Neural Network Flow: A Geometric Viewpoint Bauschke, and P.L

Reference 90

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.112878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.953788Z digest=sha256:355daa5e7428a0a73b7924a114287ee469e66f56545a11110490fa306c6500ca

Observation d53c6aa0-0524-409d-9d61-8b785f5cb2c9 · outbound

This paper cites Gradient flows in uncertainty propagation and filtering of linear Gaussian systems.

Hopfield Neural Network Flow: A Geometric Viewpoint Gradient flows in uncertainty propagation and filtering of linear Gaussian systems

Reference 91

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.100437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.957227Z digest=sha256:541642e136dd7a13065ab8d7213c2f91dc3d6c0e70329e45f6c4c426320c8100

Observation d5bc6db8-ad5d-4959-a61b-536eb8e4ede5 · outbound

This paper cites Gradient flows in filtering and Fisher- Rao Geometry.

Hopfield Neural Network Flow: A Geometric Viewpoint Gradient flows in filtering and Fisher- Rao Geometry

Reference 92

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.087964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.961177Z digest=sha256:80289a01e4434e39ada4aff9a207002c123aade8bae76a567cab6f9f6a26852f

Observation 05104e48-45ad-46c3-b881-b6d0bee5e384 · outbound

This paper cites Proximal recursion for solving the Fokker- Planck equation.

Hopfield Neural Network Flow: A Geometric Viewpoint Proximal recursion for solving the Fokker- Planck equation

Reference 93

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.075237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.964843Z digest=sha256:5fb9bc525f3d8c82a86fc462f1d5185163266a76f7c1d36df2f6abb3ab15c6c9

Observation ece47cd9-aa72-44ac-9896-b61213a2eb55 · outbound

This paper cites Gradient Flow Algorithms for Density Propagation in Stochastic Systems.

Hopfield Neural Network Flow: A Geometric Viewpoint Gradient Flow Algorithms for Density Propagation in Stochastic Systems

Reference 94

Resolution
verified exact
local_arxiv, observed 2026-08-14T15:32:38.022419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.968564Z digest=sha256:acc41e92b77555168fa9a730088ca8124eac4a3586eb443633786641a48bcb6a

Observation 424cb213-9b6d-4265-b5bd-ea2aea4a275f · outbound

This paper cites Proximal algorithms.

Hopfield Neural Network Flow: A Geometric Viewpoint Proximal algorithms

Reference 95

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.062271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.972917Z digest=sha256:40bd6b35e2fecefd33085ff0edd66353886c95c31ca13db8643a2e18693fd552

Observation 2a933314-494a-4bdf-b875-0b4f96096433 · outbound

This paper cites Himmelblau, Applied nonlinear programming , McGraw-Hill, 1972.

Hopfield Neural Network Flow: A Geometric Viewpoint Himmelblau, Applied nonlinear programming , McGraw-Hill, 1972

Reference 96

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.050080Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.976683Z digest=sha256:f34f59e75cf29d16016203e92f9c3772d5a93da9feb75378bc2bd95b7d032980

Observation 0a845180-8877-4894-9380-ff102c802376 · outbound

This paper cites Kloeden, and E.

Hopfield Neural Network Flow: A Geometric Viewpoint Kloeden, and E

Reference 97

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:32:38.034874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T15:32:37.980430Z digest=sha256:edc5550b8c1b296637c9fb4e7578ee2254800edb840b52a1295517a5850a7ccd

Pith citing papers

No inbound Pith citation observations are available.