Proton-proton collisions at the large hadron collider result in the creation of unstable particles. The decays of many of these particles produce collimated sprays of particles referred to as jets. To better understand the physics processes occurring in the collisions, one needs to classify the jets, a process known as jet tagging. Given the enormous amount of data generated during such experiments, and the subtleties between different signatures, jet tagging is of vital importance and allows us to discard events which are not of interest --- a critical part of dealing with such high-throughput data. We present a new approach to jet tagging that leverages topological properties of jets to capture their inherent shape. Our method respects underlying physical symmetries, is robust to noise, and exhibits predictive performance on par with more complex, heavily-parametrized approaches.