Notes

Hopfield, John J. "Neural networks and physical systems with emergent collective computational abilities." Proceedings of the national academy of sciences 79.8 (1982): 2554-2558.

NeuralNetworksPhysical

Large networks of simple components, such as those in biological and physical systems, can show collective computational properties. We investigate whether memory-related computational properties in neuronal networks arise collectively from the interaction of elementary neurons. We introduce in this paper a model where the interactions between the neuronal components mimic the neurobiological processes. The time evolution of the state of the model is calculated by an asynchronous parallel processing algorithm. This, in turn, enables the description of the phase space flow of the system state. The model shows how networks store memories as stable states of the system. Hence, this model describes a content-addressable memory that accurately retrieves entire memories from any reasonably sized subpart. We performed numerical simulations of the system dynamics by Monte Carlo calculations to demonstrate that additional collective computational properties arose in the neuronal network. For instance, errors resolve on a statistical basis. Properties of categorization, generalization and time ordering of memories follow from the nature of the flow in phase space determined by the processing algorithm. In addition, these properties showed to be only weakly dependent on precise details of the modelling. Hence, suggesting that they will be consistent in neurobiologically richer models. Finally, the implementation of this model by integrated circuit hardware would address soft-failure and element-failure problems in classical circuits.