  The stellar initial mass function (IMF) is commonly interpreted to be a
scale-invariant probability density distribution function (PDF) such that many
small clusters yield the same IMF as one massive cluster of the same combined
number of stars. Observations of the galaxy-wide IMF challenge this as dwarf
galaxies do not form as many massive stars as expected. This indicates a highly
self-regulated star formation process in which stellar masses are not
stochastically sampled from the IMF and are instead related to the environment
of star formation. Here, the nature of star formation is studied using the
relation between the most massive star born in a star cluster and its parental
stellar cluster mass (the $m_{\rm max}$--$M_{\rm ecl}$ relation). This relation
has been argued to be a statistical effect if stars are sampled randomly from
the IMF. By comparing the tightness of the observed $m_{\rm max}$--$M_{\rm
ecl}$ distribution with synthetic star clusters with stochastically sampled
stellar masses, we find that the expected dispersion of the mock observations
is much larger than the observed dispersion. Assuming that $m_{\rm max}$ and
$M_{\rm ecl}$ uncertainties from the literature are correct, our test rejects
the hypothesis that the IMF is a PDF at a more than $4.5\sigma$ confidence
level. Alternatively, we provide a deterministic stellar mass sampling tool
which reproduces the observed $m_{\rm max}$--$M_{\rm ecl}$ distribution and
compares well with the luminosities of star-forming molecular clumps. In
addition, we find that there is a significant flattening of the $m_{\rm
max}$--$M_{\rm ecl}$ relation near $m_{\rm max}=13~M_\odot$. This may suggest
strong feedback of stars more massive than about $13~M_\odot$ and/or the
ejections of the most massive stars from young clusters in the mass range 63 to
$400~M_\odot$ to be likely important physical processes in forming clusters.
