Upgang, Sven: On the storage capacity of generalized Hopfield models. 2019
Inhalt
- 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
- 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