On higher order computations, rewiring the connectome, and non-von Neumann computer architecture

Abstract: Structural plasticity in the brain (i.e. rewiring the connectome) may be viewed as mechanisms for dynamic reconfiguration of neural circuits. First order computations in the brain are done by static neural circuits, whereas higher order computations are done by dynamic reconfigurations of the links (synapses) between the neural circuits. Static neural circuits correspond to first order computable functions. Synapse creation (activation) between them correspond to the mathematical notion of function composition. Functionals are higher order functions that take functions as their arguments. The construction of functionals is based on dynamic reconfigurations of function compositions. Perhaps the functionals correspond to rewiring mechanisms of the connectome. The architecture of human mind is different than the von Neumann computer architecture. Higher order computations in the human brain (based on functionals) may suggest a non-von Neumann computer architecture, a challenge posed by John Backus in 1977 \cite{Backus}. The presented work is a substantial extension and revision of the paper published in Proc. ICANN2016.