An Exactly Solvable Asymmetric Neural Network Model

1987/07/15 by Bernard Derrida, E. Gardner, Alfred Zippelius · 10 citations
Computer Science · Neuroscience · #Neural Networks and Applications #Neural dynamics and brain function #Neural Networks and Reservoir Computing

paper · doi:10.1209/0295-5075/4/2/007

openalex publication_date 1987/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We consider a diluted and nonsymmetric version of the Little-Hopfield model which can be solved exactly. We obtain the analytic expression of the evolution of one configuration having a finite overlap on one stored pattern. We show that even when the system remembers, two different configurations which remain close to the same pattern never become identical. Lastly, we show that when two stored patterns are correlated, there exists a regime for which the system remembers these patterns without being able to distinguish them.

Citations

• Zero temperature parallel dynamics for infinite range spin glasses and neural networks
• Statistical mechanics of neural networks near saturation
• The existence of persistent states in the brain

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• Elizabeth Gardner (physicist) [wikipedia]