Neural Embedding: Learning the Embedding of the Manifold of Physics Data

Despite being high dimensional, physics datasets are highly structured since physical laws strictly govern the data generating process. Although the data is complicated, it is not hard to imagine that physics data can exist within low-dimensional manifolds inside a high-dimensional ambient space. There is a growing recent interest in endowing the space of collider events with a metric structure calculated directly in the space of its inputs. Metrics based on optimal transport, such as energy mover's distance (EMD) [1] and Hellinger distance [2], allow us to compare raw inputs directly and quantify the global structural difference between any pair of collider events. Since the advent of these studies, a broad range of use cases has been emerging for these metrics. These include event tagging, anomaly tagging[3-5], and measurements of Quantum Chromo Dynamical (QCD) properties. However, the input dimension is usually very large for collider data; thus, the induced manifold of the metric lives in a very high dimensional space, making it challenging to work with directly.