  Monte Carlo criticality simulations are widely used in nuclear safety
demonstrations, as they offer an arbitrarily precise estimation of global and
local tallies while making very few assumptions. However, since the inception
of such numerical approaches, it is well known that bias might affect both the
estimation of errors on these tallies and the tallies themselves. In
particular, stochastic modeling approaches developed in the past decade have
shed light on the prominent role played by spatial correlations through a
phenomenon called neutron clustering. This effect is particularly of great
significance when simulating loosely coupled systems (i.e., with a high
dominance ratio). In order to tackle this problem, this paper proposes to
recast the power iteration technique of Monte Carlo criticality codes into a
variance reduction technique called Adaptative Multilevel Splitting. The
central idea is that iterating over neutron generations can be seen as pushing
a sub-population of neutrons towards a generational detector (instead of a
spatial detector as variance reduction techniques usually do). While both
approaches allow for neutron population control, the former blindly removes or
splits neutrons. In contrast, the latter optimizes spatial, generational, and
spectral attributes of neutrons when they are removed or split through an
adjoint flux estimation, hence tempering both generational and spatial
correlations. This is illustrated in the present article with a simple case of
a bare slab reactor in the one speed theory on which the Adaptive Multilevel
Splitting was applied and compared to variations of the Monte Carlo power
iteration method used in neutron transport. Besides looking at the resulting
efficiency of the methods, this work also aims at highlighting the main
mechanisms of the Adaptive Multilevel Splitting in criticality calculations.
