In this work we introduce a multi-species generalization of the Hopfield model for associative memory, where neurons are divided into groups and both inter-groups and intra-groups pair-wise interactions are considered, with different intensities. Thus, this system contains two of the main ingredients of modern deep neural-network architectures: Hebbian interactions to store patterns of information and multiple layers coding different levels of correlations. The model is completely solvable in the low-load regime with a suitable generalization of the Hamilton–Jacobi technique, despite the Hamiltonian can be a non-definite quadratic form of the Mattis magnetizations. The family of multi-species Hopfield model includes, as special cases, the 3-layers Restricted Boltzmann Machine with Gaussian hidden layer and the Bidirectional Associative Memory model.

Non-convex Multi-species Hopfield Models

Tantari, Daniele
2018

Abstract

In this work we introduce a multi-species generalization of the Hopfield model for associative memory, where neurons are divided into groups and both inter-groups and intra-groups pair-wise interactions are considered, with different intensities. Thus, this system contains two of the main ingredients of modern deep neural-network architectures: Hebbian interactions to store patterns of information and multiple layers coding different levels of correlations. The model is completely solvable in the low-load regime with a suitable generalization of the Hamilton–Jacobi technique, despite the Hamiltonian can be a non-definite quadratic form of the Mattis magnetizations. The family of multi-species Hopfield model includes, as special cases, the 3-layers Restricted Boltzmann Machine with Gaussian hidden layer and the Bidirectional Associative Memory model.
Agliari, Elena; Migliozzi, Danila; Tantari, Daniele
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/718067
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