Abstract
The more realistic neural soma and synaptic nonlinear relations and an alternative mean field theory (MFT) approach relevant for strongly interconnected systems as a cortical matter are considered. The general procedure of averaging the quenched random states in the fully-connected networks for MFT, as usually, is based on the Boltzmann Machine learning. But this approach requires an unrealistically large number of samples to provide a reliable performance. We suppose an alternative MFT with deterministic features instead of stochastic nature of searching a solution a set of large number equations. Of course, this alternative theory will not be strictly valid for infinite number of elements. Another property of generalization is an inclusion of the additional member in the effective Hamiltonian allowing to improve the stochastic hill-climbing search of the solution not dropping into local minima of the energy function. Especially, we pay attention to increasing of neural networks retrieval capability transforming the replica-symmetry model by including of different nonlinear elements. Some results of numerical modeling as well as the wide discussion of neural systems storage capacity are presented.
Highlights
The nonlinearities in the nature especially in the biology or neuroanatomy as well as in artificial technical systems and even social life play a marked role in the behavior either small separate particles or large-scale, massive, strongly interconnected systems
That a presence of synaptic nonlinearities positive influence to retrieval capabilities, requires an essential foundation based upon consideration of concrete nonlinear characteristics of main components of neural networks
The proposed alternative mean field theory model generalizes the process of averaging over random observable elements of fully connected artificial neural networks by a large number of equations with deterministic features
Summary
The nonlinearities in the nature especially in the biology or neuroanatomy as well as in artificial technical systems and even social life play a marked role in the behavior either small separate particles or large-scale, massive, strongly interconnected systems. An influence of nonlinearities to the formation different kinds of metastable states, retrieval, spin-glass, and mixture ones has been analyzed by Sompolinsky (1986). In another work (Matus and Perez, 1990), the state dependance of synaptic strengths expressed by squared, polynomial function was analyzed and shown by computational experiments, that the number of spurious states is reduced and the stability of retrieval states has been improved. In both of last works, the nonlinearities were not realistic, artificially idealized ones. The MFT approach we propose is based on analytical presentation of a state dependent Boltzman distribution and partition functions represented by correspond manipulate the summations as a MFT approximation and inclusion of the effective energy function that has a smoother landscape due to the extra terms
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