  The astrophysical formation channels of binary black hole systems predict
correlations between their mass, spin, and redshift distributions, which can be
probed with gravitational-wave observations. Population-level analysis of the
latest LIGO-Virgo-KAGRA catalog of binary black hole mergers has identified
evidence for such correlations assuming linear evolution of the mean and width
of the effective spin distribution as a function of the binary mass ratio and
merger redshift. However, the complex astrophysical processes at play in
compact binary formation do not necessarily predict linear relationships
between the distributions of these parameters. In this work, we relax the
assumption of linearity and instead search for correlations using a more
flexible cubic spline model. Our results suggest a nonlinear correlation
between the width of the effective spin distribution and redshift. We also show
that the LIGO-Virgo-Kagra collaborations may find convincing Bayesian evidence
for nonlinear correlations by the end of the fourth observing run, O4. This
highlights the valuable role of flexible models in population analyses of
compact-object binaries in the era of growing catalogs.
