  Infrared and collinear (IRC) safety has long been used a proxy for robustness
when developing new jet substructure observables. This guiding philosophy has
been carried into the deep learning era, where IRC-safe neural networks have
been used for many jet studies. For graph-based neural networks, the most
straightforward way to achieve IRC safety is to weight particle inputs by their
energies. However, energy-weighting by itself does not guarantee that
perturbative calculations of machine-learned observables will enjoy small
non-perturbative corrections. In this paper, we demonstrate the sensitivity of
IRC-safe networks to non-perturbative effects, by training an energy flow
network (EFN) to maximize its sensitivity to hadronization. We then show how to
construct Lipschitz Energy Flow Networks (L-EFNs), which are both IRC safe and
relatively insensitive to non-perturbative corrections. We demonstrate the
performance of L-EFNs on generated samples of quark and gluon jets, and
showcase fascinating differences between the learned latent representations of
EFNs and L-EFNs.
