Hopfield Networks as Models of Emergent Function in Biology | Paper Citation Record

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This paper cites Williams.

Hopfield Networks as Models of Emergent Function in Biology Williams

Reference 1

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This paper cites Tolerance versus synaptic noise in dense associative memories.

Hopfield Networks as Models of Emergent Function in Biology Tolerance versus synaptic noise in dense associative memories

Reference 2

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This paper cites Dense hebbian neural networks: A replica symmetric picture of supervised learning.Physica A: Statistical Mechanics and its Applications, 626:129076, September 2023.

Hopfield Networks as Models of Emergent Function in Biology Dense hebbian neural networks: A replica symmetric picture of supervised learning.Physica A: Statistical Mechanics and its Applications, 626:129076, September 2023

Reference 3

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This paper cites The cell as a collection of protein machines: preparing the next generation of molecular biologists.cell, 92(3):291–294, 1998.

Hopfield Networks as Models of Emergent Function in Biology The cell as a collection of protein machines: preparing the next generation of molecular biologists.cell, 92(3):291–294, 1998

Reference 4

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This paper cites Cambridge university press, 1989.

Hopfield Networks as Models of Emergent Function in Biology Cambridge university press, 1989

Reference 5

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This paper cites Storing infinite numbers of patterns in a spin-glass model of neural networks.Physical Review Letters, 55(14):1530, 1985.

Hopfield Networks as Models of Emergent Function in Biology Storing infinite numbers of patterns in a spin-glass model of neural networks.Physical Review Letters, 55(14):1530, 1985

Reference 7

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This paper cites A new mechanical approach to handle generalized hopfield neural networks.Neural Networks, 106:205–222, October 2018.

Hopfield Networks as Models of Emergent Function in Biology A new mechanical approach to handle generalized hopfield neural networks.Neural Networks, 106:205–222, October 2018

Reference 8

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This paper cites Princeton University Press, 2012.

Hopfield Networks as Models of Emergent Function in Biology Princeton University Press, 2012

Reference 9

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This paper cites Waddington landscape for prototype learning in generalized hopfield networks.

Hopfield Networks as Models of Emergent Function in Biology Waddington landscape for prototype learning in generalized hopfield networks

Reference 10

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This paper cites Liquid hopfield model: Retrieval and localization in multicomponent liquid mixtures.Proceedings of the National Academy of Sciences, 121(48):e2320504121, 2024.

Hopfield Networks as Models of Emergent Function in Biology Liquid hopfield model: Retrieval and localization in multicomponent liquid mixtures.Proceedings of the National Academy of Sciences, 121(48):e2320504121, 2024

Reference 11

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This paper cites Learn- ing and inference in a lattice model of multicomponent condensates.

Hopfield Networks as Models of Emergent Function in Biology Learn- ing and inference in a lattice model of multicomponent condensates

Reference 12

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This paper cites The specious art of single-cell genomics.PLOS Computational Biology, 19(8):e1011288, 2023.

Hopfield Networks as Models of Emergent Function in Biology The specious art of single-cell genomics.PLOS Computational Biology, 19(8):e1011288, 2023

Reference 13

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This paper cites On a model of associative memory with huge storage capacity.Journal of Statistical Physics, 168:288–299, 2017.

Hopfield Networks as Models of Emergent Function in Biology On a model of associative memory with huge storage capacity.Journal of Statistical Physics, 168:288–299, 2017

Reference 14

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This paper cites Pattern recog- nition in the nucleation kinetics of non-equilibrium self-assembly.Nature, 625(7995):500–507, 2024.

Hopfield Networks as Models of Emergent Function in Biology Pattern recog- nition in the nucleation kinetics of non-equilibrium self-assembly.Nature, 625(7995):500–507, 2024

Reference 15

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This paper cites Not just a colourful metaphor: modelling the landscape of cellular development using hopfield networks.

Hopfield Networks as Models of Emergent Function in Biology Not just a colourful metaphor: modelling the landscape of cellular development using hopfield networks

Reference 16

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This paper cites Bistability, bifurcations, and waddington’s epigenetic landscape.Current biology, 22(11):R458–R466, 2012.

Hopfield Networks as Models of Emergent Function in Biology Bistability, bifurcations, and waddington’s epigenetic landscape.Current biology, 22(11):R458–R466, 2012

Reference 17

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This paper cites Multiconnected neural network models.Journal of Physics A: Mathematical and General, 20(11):3453–3464, August 1987.

Hopfield Networks as Models of Emergent Function in Biology Multiconnected neural network models.Journal of Physics A: Mathematical and General, 20(11):3453–3464, August 1987

Reference 18

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Hopfield Networks as Models of Emergent Function in Biology Unresolved cited work

Reference 19

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This paper cites What is life? the physical aspect of the living cell: By erwin schr¨ odinger.

Hopfield Networks as Models of Emergent Function in Biology What is life? the physical aspect of the living cell: By erwin schr¨ odinger

Reference 20

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This paper cites Durable alveolar engraftment of psc-derived lung epithelial cells into immunocompetent mice.Cell Stem Cell, 30(9):1217–1234, 2023.

Hopfield Networks as Models of Emergent Function in Biology Durable alveolar engraftment of psc-derived lung epithelial cells into immunocompetent mice.Cell Stem Cell, 30(9):1217–1234, 2023

Reference 21

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This paper cites Neurons with graded response have collective computational properties like those of two-state neurons.Proceedings of the National Academy of Sciences, 81(10):3088–3092, 1984.

Hopfield Networks as Models of Emergent Function in Biology Neurons with graded response have collective computational properties like those of two-state neurons.Proceedings of the National Academy of Sciences, 81(10):3088–3092, 1984

Reference 22

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Hopfield Networks as Models of Emergent Function in Biology Unresolved cited work

Reference 23

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This paper cites Neural networks and physical systems with emergent collective computational abilities.Proceedings of the national academy of sciences, 79(8):2554–2558, 1982.

Hopfield Networks as Models of Emergent Function in Biology Neural networks and physical systems with emergent collective computational abilities.Proceedings of the national academy of sciences, 79(8):2554–2558, 1982

Reference 24

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This paper cites Neurodynamics of mental exploration.Proceedings of the National Academy of Sciences, 107(4):1648–1653, 2010.

Hopfield Networks as Models of Emergent Function in Biology Neurodynamics of mental exploration.Proceedings of the National Academy of Sciences, 107(4):1648–1653, 2010

Reference 25

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This paper cites Whatever happened to solid state physics?Annu.

Hopfield Networks as Models of Emergent Function in Biology Whatever happened to solid state physics?Annu

Reference 26

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This paper cites Hotelling.

Hopfield Networks as Models of Emergent Function in Biology Hotelling

Reference 27

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This paper cites The molecular and mathematical basis of waddington’s epigenetic landscape: A framework for post-darwinian biology?Bioessays, 34(2):149–157, 2012.

Hopfield Networks as Models of Emergent Function in Biology The molecular and mathematical basis of waddington’s epigenetic landscape: A framework for post-darwinian biology?Bioessays, 34(2):149–157, 2012

Reference 28

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This paper cites The in vivo genetic program of murine primordial lung epithelial progenitors.Nature communications, 11(1):635, 2020.

Hopfield Networks as Models of Emergent Function in Biology The in vivo genetic program of murine primordial lung epithelial progenitors.Nature communications, 11(1):635, 2020

Reference 29

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This paper cites Random Features Hopfield Networks generalize retrieval to previously unseen examples.

Hopfield Networks as Models of Emergent Function in Biology Random Features Hopfield Networks generalize retrieval to previously unseen examples

Reference 30

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This paper cites Kanter and H.

Hopfield Networks as Models of Emergent Function in Biology Kanter and H

Reference 31

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This paper cites Enhancernet: a predictive model of cell identity dynamics through enhancer selection.Development, 151(19):dev202997, 2024.

Hopfield Networks as Models of Emergent Function in Biology Enhancernet: a predictive model of cell identity dynamics through enhancer selection.Development, 151(19):dev202997, 2024

Reference 32

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This paper cites A new frontier for hopfield networks.Nature Reviews Physics, 5(7):366–367, 2023.

Hopfield Networks as Models of Emergent Function in Biology A new frontier for hopfield networks.Nature Reviews Physics, 5(7):366–367, 2023

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This paper cites Large Associative Memory Problem in Neurobiology and Machine Learning.

Hopfield Networks as Models of Emergent Function in Biology Large Associative Memory Problem in Neurobiology and Machine Learning

Reference 34

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Observation 638908d1-45cb-4359-9a75-9f0ea4d57a14 · outbound

This paper cites Dense associative memory for pattern recognition.Ad- vances in neural information processing systems, 29, 2016.

Hopfield Networks as Models of Emergent Function in Biology Dense associative memory for pattern recognition.Ad- vances in neural information processing systems, 29, 2016

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This paper cites Epigenetic landscapes explain partially reprogrammed cells and identify key reprogramming genes.PLoS computational biology, 10(8): e1003734, 2014.

Hopfield Networks as Models of Emergent Function in Biology Epigenetic landscapes explain partially reprogrammed cells and identify key reprogramming genes.PLoS computational biology, 10(8): e1003734, 2014

Reference 36

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Observation 7801618f-e52c-404d-9c8b-bfc77f07bdd6 · outbound

This paper cites The exponential capacity of dense associative memories.

Hopfield Networks as Models of Emergent Function in Biology The exponential capacity of dense associative memories

Reference 37

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Observation 41b27ca7-5f76-4a6c-a631-33303bd475ee · outbound

This paper cites Characterizing cancer subtypes as attractors of hopfield networks.Bioinformatics, 30(9):1273–1279, 2014.

Hopfield Networks as Models of Emergent Function in Biology Characterizing cancer subtypes as attractors of hopfield networks.Bioinformatics, 30(9):1273–1279, 2014

Reference 38

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This paper cites UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction.

Hopfield Networks as Models of Emergent Function in Biology UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction

Reference 39

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This paper cites Day, Clint Richardson, Charles K.

Hopfield Networks as Models of Emergent Function in Biology Day, Clint Richardson, Charles K

Reference 40

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Observation 8e4ff59d-1d59-4972-ae79-43092337c27e · outbound

This paper cites Mean-field message-passing equations in the hopfield model and its generaliza- tions.Physical Review E, 95(2):022117, 2017.

Hopfield Networks as Models of Emergent Function in Biology Mean-field message-passing equations in the hopfield model and its generaliza- tions.Physical Review E, 95(2):022117, 2017

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This paper cites Transition states and cell fate deci- sions in epigenetic landscapes.Nature Reviews Genetics, 17(11):693–703, 2016.

Hopfield Networks as Models of Emergent Function in Biology Transition states and cell fate deci- sions in epigenetic landscapes.Nature Reviews Genetics, 17(11):693–703, 2016

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This paper cites Multifarious assembly mixtures: Systems allowing retrieval of diverse stored structures.Proceedings of the National Academy of Sciences, 112(1):54–59, 2015.

Hopfield Networks as Models of Emergent Function in Biology Multifarious assembly mixtures: Systems allowing retrieval of diverse stored structures.Proceedings of the National Academy of Sciences, 112(1):54–59, 2015

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Observation bba5b59e-6116-4f4d-9987-c3cc6e3843af · outbound

This paper cites Stor- age and learning phase transitions in the random-features hopfield model.Physical Review Letters, 131(25):257301, 2023.

Hopfield Networks as Models of Emergent Function in Biology Stor- age and learning phase transitions in the random-features hopfield model.Physical Review Letters, 131(25):257301, 2023

Reference 44

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This paper cites WH Freeman New York, 2004.

Hopfield Networks as Models of Emergent Function in Biology WH Freeman New York, 2004

Reference 45

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Observation 61396e01-3125-48ad-bc23-874d3d80eabe · outbound

This paper cites Design principles of 3d epigenetic memory systems.Science, 382(6672):eadg3053, 2023.

Hopfield Networks as Models of Emergent Function in Biology Design principles of 3d epigenetic memory systems.Science, 382(6672):eadg3053, 2023

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Observation 4343c5ab-069f-4f3d-831f-4e38afbee8ca · outbound

This paper cites Personnaz, I.

Hopfield Networks as Models of Emergent Function in Biology Personnaz, I

Reference 47

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Observation d8028505-1f6e-4021-9252-a451fb3133db · outbound

This paper cites The biological frontier of physics.Physics Today, 59(5): 38–43, 2006.

Hopfield Networks as Models of Emergent Function in Biology The biological frontier of physics.Physics Today, 59(5): 38–43, 2006

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Observation d6efe1bc-744f-4d9f-b4be-3cbbae95deef · outbound

This paper cites Garland Science, 2012.

Hopfield Networks as Models of Emergent Function in Biology Garland Science, 2012

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:41:44.967429Z

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Observation e1839348-d3ef-4579-9643-1a2b710a7bdc · outbound

This paper cites Cellular reprogramming dynamics follow a simple 1d reaction coordinate.Physical Biology, 15(1):016001, 2017.

Hopfield Networks as Models of Emergent Function in Biology Cellular reprogramming dynamics follow a simple 1d reaction coordinate.Physical Biology, 15(1):016001, 2017

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Hopfield Networks as Models of Emergent Function in Biology Unresolved cited work

Reference 51

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Observation 68adc5cd-e711-4a41-9113-9a684d37785b · outbound

This paper cites Hopfield Networks is All You Need.

Hopfield Networks as Models of Emergent Function in Biology Hopfield Networks is All You Need

Reference 52

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Observation fe532a8f-1b47-4add-8b8a-abbd6d808955 · outbound

This paper cites Geom- etry of gene regulatory dynamics.Proceedings of the National Academy of Sciences, 118(38): e2109729118, 2021.

Hopfield Networks as Models of Emergent Function in Biology Geom- etry of gene regulatory dynamics.Proceedings of the National Academy of Sciences, 118(38): e2109729118, 2021

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:41:44.953522Z

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Observation d0d45ece-0494-45a9-91a2-280cf199e36c · outbound

This paper cites Daydreaming hopfield networks and their surprising effectiveness on correlated data.Neural Networks, 186:107216, June 2025.

Hopfield Networks as Models of Emergent Function in Biology Daydreaming hopfield networks and their surprising effectiveness on correlated data.Neural Networks, 186:107216, June 2025

Reference 54

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Observation bce60a37-b38d-4f3c-bd1c-6bcff807f08b · outbound

This paper cites Emergent properties of collective gene-expression patterns in multicellular systems.Cell Reports Physical Science, 4(2), 2023.

Hopfield Networks as Models of Emergent Function in Biology Emergent properties of collective gene-expression patterns in multicellular systems.Cell Reports Physical Science, 4(2), 2023

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:41:44.946480Z

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

Observation d8853c6e-77f3-433f-bff9-153a70693520 · outbound

This paper cites Information processing in dynamical systems: Foundations of harmony theory.

Hopfield Networks as Models of Emergent Function in Biology Information processing in dynamical systems: Foundations of harmony theory

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:41:44.939213Z

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Observation e670a3d4-5594-4e23-b1a9-35f609fab308 · outbound

This paper cites Cell cycle time series gene expression data encoded as cyclic attractors in hopfield systems.

Hopfield Networks as Models of Emergent Function in Biology Cell cycle time series gene expression data encoded as cyclic attractors in hopfield systems

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:41:44.931592Z

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Observation b54072a5-6033-44bf-b450-e621621e7906 · outbound

This paper cites Modeling the attractor landscape of disease progres- sion: a network-based approach.Frontiers in genetics, 8:48, 2017.

Hopfield Networks as Models of Emergent Function in Biology Modeling the attractor landscape of disease progres- sion: a network-based approach.Frontiers in genetics, 8:48, 2017

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:41:44.924600Z

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Observation 6a2d392a-8ecf-4f2d-83b2-be1e4e0abb34 · outbound

This paper cites Visualizing data using t-sne.Journal of machine learning research, 9(11), 2008.

Hopfield Networks as Models of Emergent Function in Biology Visualizing data using t-sne.Journal of machine learning research, 9(11), 2008

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:41:44.916949Z

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Observation 9b8c9436-e80f-416c-9960-1daed8357248 · outbound

This paper cites Van Hemmen, L.B.

Hopfield Networks as Models of Emergent Function in Biology Van Hemmen, L.B

Reference 60

Resolution: verified exact; doi, observed 2026-08-07T00:41:44.531660Z

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Observation ed017a69-2bef-4c23-9c08-2999bdc72c11 · outbound

This paper cites Routledge, 2014.

Hopfield Networks as Models of Emergent Function in Biology Routledge, 2014

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-07T00:41:44.487377Z

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Observation 49a14c1b-b312-4ce1-8099-f19154df4e34 · outbound

This paper cites Riemondy, Michael Douglas, Kendall Foster, Nisha Patel, Norihito Kaku, Alexander Linsalata, Jean Nemzek, Brian M.

Hopfield Networks as Models of Emergent Function in Biology Riemondy, Michael Douglas, Kendall Foster, Nisha Patel, Norihito Kaku, Alexander Linsalata, Jean Nemzek, Brian M

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Resolution: verified exact; doi, observed 2026-08-07T00:41:44.905852Z

Source-reported events for the cited work

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Observation ec81981f-2f01-483a-8c7e-3ef1ad9023db · outbound

This paper cites Quantifying the waddington landscape and biological paths for development and differentiation.Proceedings of the National Academy of Sciences, 108(20):8257–8262, 2011.

Hopfield Networks as Models of Emergent Function in Biology Quantifying the waddington landscape and biological paths for development and differentiation.Proceedings of the National Academy of Sciences, 108(20):8257–8262, 2011

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:41:44.897575Z

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Observation 9d4623cc-0c77-4f11-b3c1-cdeb16ddab9f · outbound

This paper cites The tolman-eichenbaum machine: unifying space and relational memory through generalization in the hippocampal formation.Cell, 183(5):1249– 1263, 2020.

Hopfield Networks as Models of Emergent Function in Biology The tolman-eichenbaum machine: unifying space and relational memory through generalization in the hippocampal formation.Cell, 183(5):1249– 1263, 2020

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:41:44.890255Z

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Observation 44e1aed3-98ff-4776-8aad-55568bca210a · outbound

This paper cites Relating transformers to models and neural representations of the hippocampal formation.

Hopfield Networks as Models of Emergent Function in Biology Relating transformers to models and neural representations of the hippocampal formation

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-07T00:41:44.497730Z

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Observation e79a8601-9d38-4f76-ae24-4a486080c68a · outbound

This paper cites How to build a cognitive map.Nature neuroscience, 25(10):1257–1272, 2022.

Hopfield Networks as Models of Emergent Function in Biology How to build a cognitive map.Nature neuroscience, 25(10):1257–1272, 2022

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:41:44.882874Z

Source-reported events for the cited work

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Observation 2aa66b78-78de-4053-ad15-fc241f306d68 · outbound

This paper cites sctop: physics-inspired order parameters for cellular identification and visualization.

Hopfield Networks as Models of Emergent Function in Biology sctop: physics-inspired order parameters for cellular identification and visualization

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:41:44.875521Z

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 3b790a70-775a-4a37-b704-f2e34ae6505a · outbound

This paper cites Finding signatures of low- dimensional geometric landscapes in high-dimensional cell fate transitions.bioRxiv, 2025.

Hopfield Networks as Models of Emergent Function in Biology Finding signatures of low- dimensional geometric landscapes in high-dimensional cell fate transitions.bioRxiv, 2025

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:41:44.867787Z

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Observation eef99917-7983-4f4c-b50e-78ac0f49561a · outbound

This paper cites Associative pattern recognition through macro-molecular self-assembly.Journal of Statistical Physics, 167:806–826, 2017.

Hopfield Networks as Models of Emergent Function in Biology Associative pattern recognition through macro-molecular self-assembly.Journal of Statistical Physics, 167:806–826, 2017

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:41:44.860269Z

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Observation c58c53ec-2892-44c0-83ad-91cbfaaa2af7 · outbound

This paper cites The Exponential Capacity of Dense Associative Memories.

Hopfield Networks as Models of Emergent Function in Biology The Exponential Capacity of Dense Associative Memories

Reference 2023

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