Hopfield networks are recurrent neural networks with dynamical trajectories converging to fixed point attractor states and described by an energy function. The state of each model neuron is defined by a time-dependent variable , which can be chosen to be either discrete or continuous. A complete model describes the mathematics of how the future state of activity of each neuron depends on the known present or previous activity of all the neurons.
| Attributes | Values |
|---|
| rdfs:label
| - Modern Hopfield network (en)
|
| rdfs:comment
| - Hopfield networks are recurrent neural networks with dynamical trajectories converging to fixed point attractor states and described by an energy function. The state of each model neuron is defined by a time-dependent variable , which can be chosen to be either discrete or continuous. A complete model describes the mathematics of how the future state of activity of each neuron depends on the known present or previous activity of all the neurons. (en)
|
| foaf:depiction
| |
| dcterms:subject
| |
| Wikipage page ID
| |
| Wikipage revision ID
| |
| Link from a Wikipage to another Wikipage
| |
| sameAs
| |
| dbp:wikiPageUsesTemplate
| |
| thumbnail
| |
| has abstract
| - Hopfield networks are recurrent neural networks with dynamical trajectories converging to fixed point attractor states and described by an energy function. The state of each model neuron is defined by a time-dependent variable , which can be chosen to be either discrete or continuous. A complete model describes the mathematics of how the future state of activity of each neuron depends on the known present or previous activity of all the neurons. In the original Hopfield model of associative memory, the variables were binary, and the dynamics were described by a one-at-a-time update of the state of the neurons. An energy function quadratic in the was defined, and the dynamics consisted of changing the activity of each single neuron only if doing so would lower the total energy of the system. This same idea was extended to the case of being a continuous variable representing the output of neuron , and being a monotonic function of an input current. The dynamics became expressed as a set of first-order differential equations for which the "energy" of the system always decreased. The energy in the continuous case has one term which is quadratic in the (as in the binary model), and a second term which depends on the gain function (neuron's activation function). While having many desirable properties of associative memory, both of these classical systems suffer from a small memory storage capacity, which scales linearly with the number of input features. Dense Associative Memories (also known as the modern Hopfield networks) are generalizations of the classical Hopfield networks that break the linear scaling relationship between the number of input features and the number of stored memories. This is achieved by introducing stronger non-linearities (either in the energy function or neurons’ activation functions) leading to super-linear (even an exponential) memory storage capacity as a function of the number of feature neurons. The network still requires a sufficient number of hidden neurons. The key theoretical idea behind the Modern Hopfield networks is to use an energy function and an update rule that is more sharply peaked around the stored memories in the space of neuron’s configurations compared to the classical Hopfield network. (en)
|
| prov:wasDerivedFrom
| |
| page length (characters) of wiki page
| |
| foaf:isPrimaryTopicOf
| |
| is Link from a Wikipage to another Wikipage
of | |
| is Wikipage redirect
of | |
| is foaf:primaryTopic
of | |
![[RDF Data]](/fct/images/sw-rdf-blue.png)
![[cxml]](/fct/images/cxml_doc.png)
![[csv]](/fct/images/csv_doc.png)
![[text]](/fct/images/ntriples_doc.png)
![[turtle]](/fct/images/n3turtle_doc.png)
![[ld+json]](/fct/images/jsonld_doc.png)
![[rdf+json]](/fct/images/json_doc.png)
![[rdf+xml]](/fct/images/xml_doc.png)
![[atom+xml]](/fct/images/atom_doc.png)
![[html]](/fct/images/html_doc.png)
