  The mass distribution of dark matter haloes is the result of the hierarchical
growth of initial density perturbations through mass accretion and mergers. We
use an interpretable machine-learning framework to provide physical insights
into the origin of the spherically-averaged mass profile of dark matter haloes.
We train a gradient-boosted-trees algorithm to predict the final mass profiles
of cluster-sized haloes, and measure the importance of the different inputs
provided to the algorithm. We find two primary scales in the initial conditions
(ICs) that impact the final mass profile: the density at approximately the
scale of the haloes' Lagrangian patch $R_L$ ($R\sim 0.7\, R_L$) and that in the
large-scale environment ($R\sim 1.7~R_L$). The model also identifies three
primary time-scales in the halo assembly history that affect the final profile:
(i) the formation time of the virialized, collapsed material inside the halo,
(ii) the dynamical time, which captures the dynamically unrelaxed, infalling
component of the halo over its first orbit, (iii) a third, most recent
time-scale, which captures the impact on the outer profile of recent massive
merger events. While the inner profile retains memory of the ICs, this
information alone is insufficient to yield accurate predictions for the outer
profile. As we add information about the haloes' mass accretion history, we
find a significant improvement in the predicted profiles at all radii. Our
machine-learning framework provides novel insights into the role of the ICs and
the mass assembly history in determining the final mass profile of
cluster-sized haloes.
