201 citations · 465 across the 10 of their papers we have counts for
10 papers
The Convergence of AI code and Cortical Functioning -- a Commentary
David Mumford
Neural nets, one of the oldest architectures for AI programming, are loosely based on biological neurons and their properties. Recent work on language applications has made the AI…
Geodesic Completeness for Sobolev Metrics on the Space of Immersed Plane Curves
Martins Bruveris, Peter W. Michor, David Mumford
We study properties of Sobolev-type metrics on the space of immersed plane curves. We show that the geodesic equation for Sobolev-type metrics with constant coefficients of order 2…
A zoo of diffeomorphism groups on
Peter W. Michor, David Mumford
We consider the groups , , and of smooth…
Sobolev Metrics on Diffeomorphism Groups and the Derived Geometry of Spaces of Submanifolds
Mario Micheli, Peter W. Michor, David Mumford
Given a finite dimensional manifold , the group of diffeomorphism of which fall suitably rapidly to the identity, acts on the manifold…
Sectional Curvature in terms of the Cometric, with Applications to the Riemannian Manifolds of Landmarks
Mario Micheli, Peter W. Michor, David Mumford
This paper deals with the computation of sectional curvature for the manifolds of landmarks (or feature points) in D dimensions, endowed with the Riemannian metric induced by t…
A Metric on Shape Space with Explicit Geodesics
Peter W. Michor, David Mumford, Jayant Shah +1
This paper studies a specific metric on plane curves that has the property of being isometric to classical manifold (sphere, complex projective, Stiefel, Grassmann) modulo change o…