69 citations · 316 across the 30 of their papers we have counts for
32 papers
Gradient extremals, talwegs, valleys, and directional alignment for generic gradient descent
Pascal Bégout, Jérôme Bolte, Thomas Mariotti +1
Gradient extremals are loci along which the gradient is an eigenvector of the Hessian. These objects provide a natural geometric framework connecting several notions, notably valle…
One-step differentiation of iterative algorithms
Jérôme Bolte, Edouard Pauwels, Samuel Vaiter
In appropriate frameworks, automatic differentiation is transparent to the user at the cost of being a significant computational burden when the number of operations is large. For…
Differentiating Nonsmooth Solutions to Parametric Monotone Inclusion Problems
Jérôme Bolte, Edouard Pauwels, Antonio Silveti-Falls
We leverage path differentiability and a recent result on nonsmooth implicit differentiation calculus to give sufficient conditions ensuring that the solution to a monotone inclusi…
On the complexity of nonsmooth automatic differentiation
Jérôme Bolte, Ryan Boustany, Edouard Pauwels +1
Using the notion of conservative gradient, we provide a simple model to estimate the computational costs of the backward and forward modes of algorithmic differentiation for a wide…
Automatic differentiation of nonsmooth iterative algorithms
Jérôme Bolte, Edouard Pauwels, Samuel Vaiter
Differentiation along algorithms, i.e., piggyback propagation of derivatives, is now routinely used to differentiate iterative solvers in differentiable programming. Asymptotics is…
Swarm gradient dynamics for global optimization: the density case
Jérôme Bolte, Laurent Miclo, Stéphane Villeneuve
Using jointly geometric and stochastic reformulations of nonconvex problems and exploiting a Monge-Kantorovich gradient system formulation with vanishing forces, we formally extend…