We study the problem of discrimination between earthquakes and explosions on the basis of seismic signals detected at teleseismic distances (over 2000 km). Most work in the field of discrimination has been limited to signals detected within a few hundred kilometers which limits their utility from the perspective of sparse global seismic networks for either treaty monitoring or seismic hazard analysis. We show that existing Deep Learning architectures that have been proposed for discrimination or related tasks such as phase classification or signal detection can be repurposed for teleseismic discrimination. Using hyperparameter tuning methods we have been able to improve the performance relative to the original architectures while reducing the model complexity. We present empirical analysis of a number of different methods, and demonstrate that our proposed Deep Learning architecture performs the best at teleseismic discrimination and is able to reliably identify rockburst events.