Brains as optimal emergent Turing Machines

Abstract

The theory and experiments outlined in Weng 2015 [1] modeled brains as naturally emerging Turing Machines (TMs) inside Developmental Networks (DNs) — a new class of brain inspired neural networks. However, TMs originally proposed by Alan Turing 1936 [2] were deterministic. If they involved probability to handle uncertainty, the probability was in the mind of the human programmer for a specific task. Although the task-specific program will run on a Universal TM — a model of the popular Von Neumann Computers — the Universal TM itself had no imbedded probability. Yet, each brain samples from infinitely many stimuli and actions through the real word, unlike a TM that deals with only tape-symbols from a finite and static alphabet. Computationally, is a brain optimal? If the answer is yes, in what sense? This theoretical work reports the overall brain optimality. It shows that a biological brain, modeled by the DN, is optimal in the sense of maximum likelihood, conditioned on (1) the genome program — the Developmental Program (DP) that regulates the development of body, sensors, effectors and the limited computational resource (e.g., brain size and types of neural transmitters), and (2) the incremental lifetime experience — including teaching from the environments and self exploration and discovery through the real world.