D-GRIL: End-To-End Topological Learning with 2-Parameter Persistence

End-to-end topological learning using 1-parameter persistence is well-known. We show that the framework can be enhanced using 2-parameter persistence by adopting a recently introduced 2-parameter persistence based vectorization technique called GRIL. We establish a theory for gradient descent on GRIL producing D-GRIL. We show that D-GRIL can be used to learn a bifiltration function on benchmark graph datasets. Further, we exhibit that this framework can be applied in the context of bio-activity prediction in drug discovery.