On Asymmetric Distances
By Andrea Mennucci. 2013
68 citations recorded by the source corpus.
Abstract In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1e0de9ee3106341227c3d3408a96cbf422cae149
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Citations in the corpus
- The Dynamics of Differential Learning I: Information-Dynamics and Task Reachability (2018, background): “d on them, fail to capture that very different parameters can represent the exact same posterior distribution. In order to relate to transfer learning, a distance function would have to be asymmetric [14] as it is typically easier to fine-tune a simple task from a complex one than vice-versa. Such di”