Hopfield networks

E46142

associative memory model content-addressable memory system recurrent artificial neural network

Hopfield networks are recurrent artificial neural networks that serve as content-addressable memory systems, storing patterns as stable states and retrieving them through dynamics that minimize an energy function.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

All labels observed (5)

Label	Occurrences
Hopfield network	2
Hopfield networks canonical	2
Neural networks and physical systems with emergent collective computational abilities	1
continuous Hopfield network	1
modern Hopfield network	1

How this entity was disambiguated

This entity first appeared as the object of triple T364218 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Hopfield networks
Context triple: [Boltzmann machines, relatedTo, Hopfield networks]

A. “Learning representations by back-propagating errors”
“Learning representations by back-propagating errors” is a landmark 1986 research paper that popularized the backpropagation algorithm for training multi-layer neural networks, helping to launch the modern field of deep learning.
B. Boltzmann machines
Boltzmann machines are stochastic recurrent neural networks used for learning complex probability distributions, foundational in unsupervised learning and energy-based models.
C. “A fast learning algorithm for deep belief nets”
“A fast learning algorithm for deep belief nets” is a seminal 2006 paper by Geoffrey Hinton that introduced an efficient unsupervised pretraining method for deep neural networks using stacked restricted Boltzmann machines.
D. SyNAPSE neuromorphic computing program
The SyNAPSE neuromorphic computing program is a DARPA initiative to develop brain-inspired electronic systems that emulate neural architectures for highly efficient, scalable cognitive computing.
E. RBM
RBM is a global partnership initiative dedicated to coordinating and scaling up efforts to prevent, control, and ultimately eliminate malaria worldwide.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Hopfield networks
Target entity description: Hopfield networks are recurrent artificial neural networks that serve as content-addressable memory systems, storing patterns as stable states and retrieving them through dynamics that minimize an energy function.

A. “Learning representations by back-propagating errors”
“Learning representations by back-propagating errors” is a landmark 1986 research paper that popularized the backpropagation algorithm for training multi-layer neural networks, helping to launch the modern field of deep learning.
B. Boltzmann machines
Boltzmann machines are stochastic recurrent neural networks used for learning complex probability distributions, foundational in unsupervised learning and energy-based models.
C. “A fast learning algorithm for deep belief nets”
“A fast learning algorithm for deep belief nets” is a seminal 2006 paper by Geoffrey Hinton that introduced an efficient unsupervised pretraining method for deep neural networks using stacked restricted Boltzmann machines.
D. SyNAPSE neuromorphic computing program
The SyNAPSE neuromorphic computing program is a DARPA initiative to develop brain-inspired electronic systems that emulate neural architectures for highly efficient, scalable cognitive computing.
E. RBM
RBM is a global partnership initiative dedicated to coordinating and scaling up efforts to prevent, control, and ultimately eliminate malaria worldwide.
F. None of above. chosen

Statements (50)

Predicate	Object
instanceOf	associative memory model ⓘ content-addressable memory system ⓘ recurrent artificial neural network ⓘ
belongsToField	computational neuroscience ⓘ machine learning ⓘ neural networks ⓘ statistical physics ⓘ
convergesTo	local energy minima ⓘ
dynamicsMinimize	energy function ⓘ
hasActivationFunction	sign function ⓘ threshold function ⓘ
hasApproximateCapacity	0.138N for random uncorrelated patterns ⓘ
hasCapacityProperty	storage capacity proportional to number of neurons ⓘ
hasConnectionType	no self-connections ⓘ symmetric weights ⓘ
hasEnergyFunction	Lyapunov function ⓘ
hasLearningRule	Hebbian learning ⓘ outer-product rule ⓘ
hasLimitation	limited storage capacity ⓘ sensitivity to correlated patterns ⓘ spurious attractors ⓘ
hasMathematicalRepresentation	binary quadratic form energy ⓘ
hasNodeType	Ising spin ⓘ binary neuron ⓘ
hasProperty	guaranteed convergence under symmetric weights and asynchronous updates ⓘ
hasStateSpace	binary vectors ⓘ
hasTopology	fully connected network ⓘ
hasUpdateDynamics	deterministic dynamics ⓘ
hasUpdateRule	asynchronous update ⓘ synchronous update ⓘ
hasVariant	Hopfield networks self-linksurface differs ⓘ surface form: continuous Hopfield network Hopfield networks self-linksurface differs ⓘ surface form: modern Hopfield network stochastic Hopfield network ⓘ
introducedBy	John Hopfield ⓘ
introducedInYear	1982 ⓘ
isRelatedTo	Boltzmann machines ⓘ surface form: Boltzmann machine Ising models ⓘ surface form: Ising Hopfield model Ising models ⓘ surface form: Ising model spin glass theory ⓘ
isUsedFor	associative memory tasks ⓘ combinatorial optimization ⓘ constraint satisfaction ⓘ optimization ⓘ
namedAfter	John Hopfield ⓘ
stableStatesRepresent	stored patterns ⓘ
supports	associative recall ⓘ content-addressable memory ⓘ error correction ⓘ pattern completion ⓘ robust retrieval from noisy inputs ⓘ

How these facts were elicited

Referenced by (7)

Full triples — surface form annotated when it differs from this entity's canonical label.

Boltzmann machines → relatedTo → Hopfield networks ⓘ

Hopfield networks → hasVariant → Hopfield networks self-linksurface differs ⓘ

subject surface form: Hopfield network

this entity surface form: continuous Hopfield network

Hopfield networks → hasVariant → Hopfield networks self-linksurface differs ⓘ

subject surface form: Hopfield network

this entity surface form: modern Hopfield network

Hebbian learning → usedIn → Hopfield networks ⓘ

John Hopfield → knownFor → Hopfield networks ⓘ

this entity surface form: Hopfield network

John Hopfield → notableWork → Hopfield networks ⓘ

this entity surface form: Neural networks and physical systems with emergent collective computational abilities

John Hopfield → developed → Hopfield networks ⓘ