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On the storage capacity of generalized Hopfield models
Generalized Hopfield model with Curie-Weiss patterns
Results about the Curie-Weiss model
Introduction to the standard Hopfield model
Storage capacity of the standard Hopfield model for a perfect retrieval
The standard Hopfield model as a spin glass model
Generalized Hopfield model with i.i.d. patterns
Generalized dynamics with a polynomial interaction function
Generalized dynamics with an exponential interaction function
Generalized Hopfield model with Curie-Weiss patterns
Introduction to the Curie-Weiss model
Results about the Curie-Weiss model
Central Limit Theorem for the magnetization
The Gibbs measure of a Curie-Weiss model as a de Finetti type measure
Laplace's method and the correlation of spins
Central Limit Theorem for the overlap of spins
Main Result for Curie-Weiss patterns and the polynomial dynamics
Conclusions about the polynomial dynamics
Generalized Hopfield model with weights
The hierarchical Hopfield model
The inhomogeneous Hopfield model
The Hopfield model with weights on a deterministic graph
Lattice structure on a torus
Regular tree graph
Conclusions about the inhomogeneous Hopfield model on a deterministic graph
The Hopfield model with weights on a random graph
General results about the Galton-Watson process
The inhomogeneous Hopfield model on a Galton-Watson tree
Conclusions about the inhomogeneous Hopfield model on a Galton-Watson tree
Appendices
References
List of symbols
Dissertation
On the storage capacity of generalized Hopfield models
Entstehung
2019
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