Rigorous results for the free energy in the Hopfield model

DOI10.1007/BF02096664zbMath0770.92003MaRDI QIDQ1208001

Brunello Tirozzi, Sergio A. Albeverio, Bogusław Zegarliński

Publication date: 16 May 1993

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

free energyHopfield modelasymptotic series expansion in inverse powers of the neurons numberfinite number of patterns

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items (7)

An almost sure central limit theorem for the overlap parameters in the Hopfield model ⋮ Non-convex multi-species Hopfield models ⋮ Fluctuation of the free energy in the Hopfield model ⋮ Spontaneous Replica Symmetry Breaking and Interpolation Methods for Complex Statistical Mechanics Systems ⋮ About the ergodic regime in the analogical Hopfield neural networks: Moments of the partition function ⋮ On the free energy of the Hopfield model ⋮ Free energy and some sample path properties of a random walk with random potential.

Cites Work

• Some rigorous results on the Hopfield neural network model
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• The thermodynamics of site-random mean-field quantum spin systems
• An improvement of Watson’s theorem on Borel summability
• Neural networks and physical systems with emergent collective computational abilities.
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