Infrared-safe energy weighting does not guarantee small nonperturbative effects
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 nonperturbative corrections. Here, in this paper, we demonstrate the sensitivity of IRC-safe networks to nonperturbative 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 nonperturbative 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.