Envision a smart connected city of the future. This is a city transformed by the Internet of Things (IoT). It relies on advanced wireless infrastructure to monitor traffic and air quality. It relies on smart autonomous public transportation that adapts to user concentration and includes aerial autonomous vehicles to aid public safety. If we zoom into the different components of this smart infrastructure we see different types of data. Some of which our current technology can handle adequately. Some of which present more of a challenge. For example, conventional cameras mounted on fixed masts or autonomous drones acquire images that we can process with CNNs. But autonomous vehicles also rely on omnidirectional cameras and LIDAR scans that are subtly yet fundamentally different from images. Likewise, environmental sensors acquire data that can be integrated with information from neighboring agents but unless agents are deployed in a regular grid their processing would be challenging given existing technology. Somewhat insidiously, the network itself on which all of these interactions occur is an entity that acquires information about traffic demand and channel states that we can use to adapt their operation.
Although we are not foreign to the processing of LIDAR scans and sensor network data or to the manipulation of wireless communication networks, it is fair to say that our ability to work with this rarer data feeds lags behind our ability to process Euclidean data. The ultimate goal of FINPenn is to develop tools for the processing of non-Euclidean data that can match the accuracy of CNNs on Euclidean data. To do so we will advance a fundamental theory to guide their design.