Gradient flows on graphons: existence, convergence, continuity equations. (arXiv:2111.09459v2 [math.PR] UPDATED)

Wasserstein gradient flows on probability measures have found a host of
applications in various optimization problems. They typically arise as the
continuum limit of exchangeable particle systems evolving by some mean-field
interaction involving a gradient-type potential. However, in many problems,
such as in multi-layer neural networks, the so-called particles are edge
weights on large graphs whose nodes are exchangeable. Such large graphs are
known to converge to continuum limits called graphons as their size grow to
infinity. We show that …

arxiv convergence gradient math pr