Understand
In [7] Krotov and Hopfield suggest a generalized version of the well-known Hopfield model of associative memory.
- In their version they consider a polynomial interaction function and claim that this increases the storage capacity of the model.
- We prove this claim and take the "limit" as the degree of the polynomial becomes infinite, i.e.
- an exponential interaction function.
Built on
Neural networks and physical systems with emergent collective computational abilities
J. J. Hopfield · 1982
Earlier work this paper cites.
Spin-glass models of neural networks
D. J. Amit, H. Gutfreund, and H. Sompolinsky · 1985
Earlier work this paper cites.
Storing infinite numbers of patterns in a spin-glass model of neural networks
D. J. Amit, H. Gutfreund, and H. Sompolinsky · 1985
Earlier work this paper cites.
The capacity of the Hopfield associative memory
R. J. McEliece, E. C. Posner, E. R. Rodemich, and S. S. Venkatesh · 1987
Earlier work this paper cites.
Memory capacity in neural network models: Rigorous lower bounds
C. M. Newman · 1988
Earlier work this paper cites.
Similar
Lower bounds on the restitution error in the Hopfield model
D. Loukianova · 1997
Cited alongside, same era.
Large deviations techniques and applications
A. Dembo and O. Zeitouni · 1998
Cited alongside, same era.
On the storage capacity of Hopfield models with correlated patterns
M. Löwe · 1998
Cited alongside, same era.
Rigorous results for the Hopfield model with many patterns
M. Talagrand · 1998
Cited alongside, same era.
Sharp upper bounds on perfect retrieval in the Hopfield model
A. Bovier · 1999
Cited alongside, same era.
Then
The storage capacity of generalized Hopfield models with semantically correlated patterns
M. Löwe · 1999
Later among the works it cites.
The spin-glass phase-transition in the Hopfield model with p p -spin interactions
A. Bovier and B. Niederhauser · 2001
Later among the works it cites.
The storage capacity of the Hopfield model and moderate deviations
M. Löwe and F. Vermet · 2005
Later among the works it cites.
The capacity of q q -state Potts neural networks with parallel retrieval dynamics
M. Löwe and F. Vermet · 2007
Later among the works it cites.
Dense associative memory for pattern recognition
D. Krotov and J. J. Hopfield · 2016
Later among the works it cites.
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