On a model of associative memory with huge storage capacity

Abstract

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. With this interaction we prove that model has an exponential storage capacity in the number of neurons, yet the basins of attraction are almost as large as in the standard Hopfield model.

13 pages

Cited by in corpus (16)

• Txt2Img-MHN: Remote Sensing Image Generation from Text Using Modern Hopfield Networks
• The Exponential Capacity of Dense Associative Memories
• Hypercomplex-Valued Recurrent Correlation Neural Networks
• Neural Distributed Autoassociative Memories: A Survey
• Input-Driven Dynamics for Robust Memory Retrieval in Hopfield Networks
• Quaternion-Valued Recurrent Projection Neural Networks on Unit Quaternions
• Daydreaming Hopfield Networks and their surprising effectiveness on correlated data
• Dense Hopfield Networks in the Teacher-Student Setting
• Explosive neural networks via higher-order interactions in curved statistical manifolds
• Dissipative Quantum Hopfield Network: A numerical analysis
• Hopfield Networks for Asset Allocation
• Dense Associative Memory in a Nonlinear Optical Hopfield Neural Network
• Computational models of learning and synaptic plasticity
• Statistical mechanics of vector Hopfield network near and above saturation
• Exact Replica Symmetric solution for transverse field Hopfield model under finite Trotter size
• Topological constraints on self-organisation in locally interacting systems