Zeta Distribution and Transfer Learning Problem
  We explore the relations between the zeta distribution and algorithmic
information theory via a new model of the transfer learning problem. The
program distribution is approximated by a zeta distribution with parameter near
$1$. We model the training sequence as a stochastic process. We analyze the
upper temporal bound for learning a training sequence and its entropy rates,
assuming an oracle for the transfer learning problem. We argue from empirical
evidence that power-law models are suitable for natural processes. Four
sequence models are proposed. Random typing model is like no-free lunch where
transfer learning does not work. Zeta process independently samples programs
from the zeta distribution. A model of common sub-programs inspired by genetics
uses a database of sub-programs. An evolutionary zeta process samples mutations
from Zeta distribution. The analysis of stochastic processes inspired by
evolution suggest that AI may be feasible in nature, countering no-free lunch
sort of arguments.
