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.
CITATION STYLE
Agliari, E., Migliozzi, D., & Tantari, D. (2018). Non-convex Multi-species Hopfield Models. Journal of Statistical Physics, 172(5), 1247–1269. https://doi.org/10.1007/s10955-018-2098-6
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