Stochastic gradient descent (SGD) is one of the most popular algorithms in modern machine
learning. The noise encountered in these applications is different from that in many …

In this note, we study the cut locus of the free, step two Carnot groups $\mathbb {G} _k $ with
$ k $ generators, equipped with their left-invariant Carnot-Carathéodory metric. In particular …

We prove sectional and Ricci-type comparison theorems for the existence of conjugate
points along sub-Riemannian geodesics. In order to do that, we regard sub-Riemannian …

The representation of functions by artificial neural networks depends on a large number of
parameters in a non-linear fashion. Suitable parameters are found by minimizing a 'loss …

We consider the heat equation associated with a class of second order hypoelliptic
Hörmander operators with constant second order term and linear drift. We completely …

For a fat sub-Riemannian structure, we introduce three canonical Ricci curvatures in the
sense of Agrachev–Zelenko–Li. Under appropriate bounds we prove comparison theorems …

We solve a Kolmogorov-type hypoelliptic parabolic partial differential equation with a\lq\lq
side" boundary condition (in the direction of the weak H\" ormander condition). We construct …

We study the sub-Riemannian exponential for contact distributions on manifolds of
dimension greater than or equal to 5. We compute an approximation of the sub-Riemannian …

By adapting a technique of Molchanov, we obtain the heat kernel asymptotics at the sub-
Riemannian cut locus, when the cut points are reached by an r-dimensional parametric …

We consider specific sub-Finslerian structures in the neighborhood of 0 in ℝ 2 R^2, defined
by fixing a family of vector fields (F 1, F 2) and considering the norm defined on the non …