Boolean Models Guide Intentionally Continuous Information and Computation Inside the Brain

Abstract

In 1943 Machculloch and Pitts create the formal neuron where many input signals are linearly composed with different weights on the neuron soma. When the soma electrical signal goes over a specific threshold an output is produced. The main topic in this model is that the response is the same response as in a Boolean function used a lot for the digital computer. Logic functions can be simplified with the formal neuron. But there is the big problem for which not all logic functions, as XOR , cannot be designed in the formal neuron. After a long time the back propagation and many other neural models overcame the big problem in some cases but not in all cases creating a lot of uncertainty. The model proposed does not consider the formal neuron but the natural network controlled by a set of differential equations for neural channels that model the current and voltage on the neuron surface. The steady state of the probabilities is the activation state continuous function whose maximum and minimum are the values of the Boolean function associated with the activation time of spikes of the neuron. With this method the activation function can be designed when the Boolean functions are known. Moreover the neuron differential equation can be designed in order to realize the wanted Boolean function in the neuron itself. The activation function theory permits to compute the neural parameters in agreement with the intention.