Abstract neural automata on compact Riemannian manifold

By means of topological conjugate transformation, the previous theory of abstract neural automata (ANA) on d‐dimensional (d≥1) integer lattice is extended to compact Riemannian manifold. This paper points out emphatically that intelligence of ANA is related to the geometrical features. The greater the volume of relative plane, the stronger the intelligence; curved Riemannian manifold X˜ configuration space of ANA are locally flat such that the cognitive process of NAN limits the Gibbs' probability measure for a sufficiently small time i.e. the cognitive process of ANA can determine the solution in a sufficiently small time the problem. This hypothesis was supported by studying the human brain, in particular by studying Einstein's brain.