Non-classical probabilities in pilot wave models and neural networks

Abstract

Non-classical probabilities can arise in many contexts even beyond quantum theory. In this article essentially two very general classes of classical physical scenarios are discussed, which both exhibit non-classical probabilistic behavior: (1) pilot wave models and (2) neural networks. In both cases, deviations from classical behavior can be attributed to a non-standard definition of “observables”. This is particularly important for neural networks where two completely different but natural ways of defining the concept of an observable are discussed. In addition, non-classical probabilities can also arise due to the way we associate “physical situations” with the mathematical concept of “events” and, in particular, how we combine these events in the sense of OR and AND. Several examples are discussed in order to illustrate the general concepts.