Do ideas have shape? Idea registration as the continuous limit of artificial neural networks

Understand

We introduce a GP generalization of ResNets (including ResNets as a particular case).

• We show that ResNets (and their GP generalization) converge, in the infinite depth limit, to a generalization of image registration variational algorithms.
• Whereas computational anatomy aligns images via warping of the material space, this generalization aligns ideas (or abstract shapes as in Plato's theory of forms) via the warping of the RKHS of functions mapping the input space to the output space.
• While the Hamiltonian interpretation of ResNets is not new, it was based on an Ansatz.