Before revision:  This framework builds upon a formulation of PD metrics as optimal transport (OT) problems , for which recent computational advances , in particular entropic regularization and its convolutional formulation on regular grids, can all be leveraged to provide efficient and (GPU) scalable computations .
After revision:  This framework builds upon a reformulation of PD metrics as optimal transport (OT) problems , for which recent computational advances , in particular entropic regularization and its convolutional formulation on regular grids, can all be leveraged to provide efficient and (GPU) scalable computations .