promised to catapult us into going into the end of the future right and what I'm gonna argue is splines provide a very natural framework for both describing what we've learned but also providing us avenues for extending both the design and analysis of a whole host of different deep learning systems and so I'm going to talk a little bit about a particular kind of spline today and then I'm gonna give you a whole bunch of apples of how we've been using it to describe and extend and of course we're not the first people to think about the