  Estimating the region of attraction (${\tt RoA}$) for a robot controller is
essential for safe application and controller composition. Many existing
methods require a closed-form expression that limit applicability to
data-driven controllers. Methods that operate only over trajectory rollouts
tend to be data-hungry. In prior work, we have demonstrated that topological
tools based on ${\it Morse Graphs}$ (directed acyclic graphs that
combinatorially represent the underlying nonlinear dynamics) offer
data-efficient ${\tt RoA}$ estimation without needing an analytical model. They
struggle, however, with high-dimensional systems as they operate over a
state-space discretization. This paper presents ${\it Mo}$rse Graph-aided
discovery of ${\it R}$egions of ${\it A}$ttraction in a learned ${\it L}$atent
${\it S}$pace (${\tt MORALS}$). The approach combines auto-encoding neural
networks with Morse Graphs. ${\tt MORALS}$ shows promising predictive
capabilities in estimating attractors and their ${\tt RoA}$s for data-driven
controllers operating over high-dimensional systems, including a 67-dim
humanoid robot and a 96-dim 3-fingered manipulator. It first projects the
dynamics of the controlled system into a learned latent space. Then, it
constructs a reduced form of Morse Graphs representing the bistability of the
underlying dynamics, i.e., detecting when the controller results in a desired
versus an undesired behavior. The evaluation on high-dimensional robotic
datasets indicates data efficiency in ${\tt RoA}$ estimation.
