Stochastic Artificial Neural Networks and random walks

Abstract

We showed in previous work how complex stochastic automata can be constructed from simple stochastic parts networked together. Here, we apply this modeling paradigm to create model automata that can mimic some aspects of the random walks animals make as they search for food or prey. We call these models Stochastic Artificial Neural Networks (ANNs). We focus on step lengths and create and study two models leading to two different distributions of step lengths. The first is an exponential (Brownian) distribution and the second is a truncated Levy distribution. Both distributions are observed in animal data. Our models are not unique (within the modeling paradigm) in their ability to mimic the observed distributions. Also, in order to keep the models simple and focused, we ignore some of the factors that may also influence random walk behavior. Therefore, we do not assert that our models have a direct correspondence with any real animal nervous systems. However, these models do suggest explanations for some of the characteristics of experimentally observed random walks. In particular, the model that gives the exponential distribution is extremely simple. This suggests that one reason exponential distributions are common, even in very simple animals, is that the neural mechanisms needed to produce them are extremely simple. The more complicated model that produces a truncated Levy distribution requires that the animal keep track of how far it has already come during any given step. This suggests that one reason a Levy distribution is often observed to be truncated is that the animal has a limited amount of this kind of memory.