Models of Innate Neural Attractors and Their Applications for Neural Information Processing

Abstract

In this work we reveal and explore a new class of attractor neural networks, based on inborn connections provided by model molecular markers, the molecular marker based attractor neural networks (MMBANN). Each set of markers has a metric, which is used to make connections between neurons containing the markers. We have explored conditions for the existence of attractor states, critical relations between their parameters and the spectrum of single neuron models, which can implement the MMBANN. Besides, we describe functional models (perceptron and SOM), which obtain significant advantages over the traditional implementation of these models, while using MMBANN. In particular, a perceptron, based on MMBANN, gets specificity gain in orders of error probabilities values, MMBANN SOM obtains real neurophysiological meaning, the number of possible grandma cells increases 1000-fold with MMBANN. MMBANN have sets of attractor states, which can serve as finite grids for representation of variables in computations. These grids may show dimensions of d = 0, 1, 2,…. We work with static and dynamic attractor neural networks of the dimensions d = 0 and 1. We also argue that the number of dimensions which can be represented by attractors of activities of neural networks with the number of elements N = 104 does not exceed 8.

Analytical estimates of efficiency of attractor neural networks with inborn connections

“…Usually, w = 1 and r = 0. In computational experiments [2] we have explored the methods for making inter-neuronal connections, which enable the neural networks to have attractor states (states which are transformed into themselves under the specified above rules of neural dynamics). The states of the neural network are N-dimensional vectors of ones (neuron is excited) and zeros (neuron is quiet).…”

“…As soon as the markers are distributed between the neurons, the latter are connected with excitatory synapses. The connections are symmetric and are set between two neurons, if they have markers, the distance between which is less, than another pre-determined value, į. Computational experiments have demonstrated that the two types of metrics marks, described above, yield the neural networks with the SAAS with d = 0 and the SAAS with d = 1, when the same for both cases conditions for marker distribution and connection setting have been used [2].…”

“…In present work, we complement computer simulations of [2] with a thorough mathematical analysis, which enables us to make analytical estimates of the network operational parameters.…”

“…The analysis yields a relation between the number of the stable theoretical attractor states and the number of neurons in the network. The analytical estimates are compared to the results of computational experiments [2]. Section 3.2 continues the analysis to get the trade-off relations for the numbers of attractor states, the number of neurons in the network and the number of active neurons in each attractor state.…”

“…Section 3.2 continues the analysis to get the trade-off relations for the numbers of attractor states, the number of neurons in the network and the number of active neurons in each attractor state. The results are compared with the computational experiments data [2], which are presented in Figs. 1 and 2.…”