Analytical estimates of efficiency of attractor neural networks with inborn connections

The analysis is restricted to the features of neural networks endowed to the latter by the inborn (not learned) connections. We study attractor neural networks in which for almost all operation time the activity resides in close vicinity of a relatively small number of attractor states. The number of the latter, M , is proportional to the number of neurons in the neural network, N , while the total number of the states in it is 2 N . The unified procedure of growth/fabrication of neural networks with sets of all attractor states with dimensionality d =0 and d =1, based on model molecular markers, is studied in detail. The specificity of the networks ( d =0 or d =1) depends on topology (i.e., the set of distances between elements) which can be provided to the set of molecular markers by their physical nature. The neural networks parameters estimates and trade-offs for them in attractor neural networks are calculated analytically. The proposed mechanisms reveal simple and efficient ways of implementation in artificial as well as in natural neural networks of multiplexity, i.e. of using activity of single neurons in representation of multiple values of the variables, which are operated by the neural systems. It is discussed how the neuronal multiplexity provides efficient and reliable ways of performing functional operations in the neural systems.