On the Dynamics of Transforming Artificial Intelligence Systems

This paper investigates whether the description of artificial intelligence systems may be simplified by requiring that the laws governing changes in their effective states possess the same form under different admissible representations. Motivated by apparent asymmetries that can arise when equivalent computational transformations are described from different reference systems, we introduce two postulates: that the laws governing artificial intelligence are invariant under transformations between equivalent capability frames, and that there exists a characteristic rate of capability propagation which is independent of the particular frame in which it is measured. From these assumptions, transformation relations between capability coordinates and transformation variables are developed, together with consequences for the comparison of artificial intelligence systems undergoing relative change. The resulting framework is then applied to the transformation of capability fields and to the dynamics of individual capability contributions. The theory is intended not as an assertion that artificial intelligence obeys physical relativity, but as a mathematical investigation of whether an invariant description of artificial capability can be constructed from a small number of operational principles. Its validity must ultimately depend upon whether the proposed invariances and transformation relations can be given reproducible empirical meaning in artificial intelligence systems. The mathematical construction developed below is motivated by Einstein's transformation-based treatment of inertial reference systems, while replacing physical spacetime quantities with operational quantities proposed for artificial-intelligence systems [1].