On the Motion of Small Capability Contributions in Artificial Intelligence Required by the Statistical Theory of Capability

This paper investigates the behavior of localized capability contributions in artificial intelligence systems under the assumption that such contributions may be treated, to a sufficient approximation, as statistically independent elements. A distribution law is introduced to describe changes in effective capability over successive computational transformations, and the resulting evolution is examined in analogy with the diffusion of independently moving particles. It is shown that, under appropriate independence and stationarity assumptions, the aggregate distribution of capability may obey a diffusion-like equation in an abstract capability space. From this relation, measurable quantities characterizing the displacement, dispersion, and transformation of artificial capability are derived. The theory therefore provides a possible experimental method for determining whether apparently continuous changes in artificial intelligence can be accounted for by the statistical motion of finite capability contributions. If the predicted distributions and scaling relations can be observed under controlled conditions, they would provide evidence for the statistical conception developed here; if they cannot, the assumptions underlying this description must be reconsidered.