7 citations · 16 across the 5 of their papers we have counts for
17 papers
Path differentiability of ODE flows
Swann Marx, Edouard Pauwels
We consider flows of ordinary differential equations (ODEs) driven by path differentiable vector fields. Path differentiable functions constitute a proper subclass of Lipschitz fun…
Semialgebraic Representation of Monotone Deep Equilibrium Models and Applications to Certification
Tong Chen, Jean-Bernard Lasserre, Victor Magron +1
Deep equilibrium models are based on implicitly defined functional relations and have shown competitive performance compared with the traditional deep networks. Monotone operator e…
A Sublevel Moment-SOS Hierarchy for Polynomial Optimization
Tong Chen, Jean-Bernard Lasserre, Victor Magron +1
We introduce a sublevel Moment-SOS hierarchy where each SDP relaxation can be viewed as an intermediate (or interpolation) between the d-th and (d+1)-th order SDP relaxations of th…
Sequential convergence of AdaGrad algorithm for smooth convex optimization
Cheik Traoré, Edouard Pauwels
We prove that the iterates produced by, either the scalar step size variant, or the coordinatewise variant of AdaGrad algorithm, are convergent sequences when applied to convex obj…
A Hölderian backtracking method for min-max and min-min problems
Jérôme Bolte, Lilian Glaudin, Edouard Pauwels +1
We present a new algorithm to solve min-max or min-min problems out of the convex world. We use rigidity assumptions, ubiquitous in learning, making our method applicable to many o…
A mathematical model for automatic differentiation in machine learning
Jerome Bolte, Edouard Pauwels
Automatic differentiation, as implemented today, does not have a simple mathematical model adapted to the needs of modern machine learning. In this work we articulate the relations…