  Neural networks (NNs) hold great promise for advancing inverse design via
topology optimization (TO), yet misconceptions about their application persist.
This article focuses on neural topology optimization (neural TO), which
leverages NNs to reparameterize the decision space and reshape the optimization
landscape. While the method is still in its infancy, our analysis tools reveal
critical insights into the NNs' impact on the optimization process. We
demonstrate that the choice of NN architecture significantly influences the
objective landscape and the optimizer's path to an optimum. Notably, NNs
introduce non-convexities even in otherwise convex landscapes, potentially
delaying convergence in convex problems but enhancing exploration for
non-convex problems. This analysis lays the groundwork for future advancements
by highlighting: 1) the potential of neural TO for non-convex problems and
dedicated GPU hardware (the "good"), 2) the limitations in smooth landscapes
(the "bad"), and 3) the complex challenge of selecting optimal NN architectures
and hyperparameters for superior performance (the "ugly").
