4 papers · 1 filter
Subdifferentiation with symmetry
Cédric Josz
Given an objective function that is invariant under an action of a Lie group, we study how its subgradients relate to the orbits of the action. Our main finding is that they satisf…
Reachability of gradient descent
Cédric Josz, Wenqing Ouyang
We show that gradient descent can converge to any local minimum of a smooth semi-algebraic function. This holds if the step sizes are nonsummable and sufficiently small. The same r…
Lyapunov stability of the Euler method
Cédric Josz
We extend the Lyapunov stability criterion to Euler discretizations of differential inclusions. It relies on a pair of Lyapunov functions, one in continuous time and one in discret…
On the geometry of flat minima
Cédric Josz
What does it mean to be flat? We propose to define it by measuring the maximal variation around a point, or from a dual perspective, the distance to neighboring level sets. After d…