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In this paper we consider germs of k-parameter generic families of analytic 2-dimensional vector fields unfolding a saddle-node of codimension k and we give a complete modulus of analytic classification under orbital equivalence and a…

We present an algorithm for computing a Smith form with multipliers of a regular matrix polynomial over a field. This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant…

Optimizing non-convex functions is of primary importance in the vast majority of machine learning algorithms. Even though many gradient descent based algorithms have been studied, successive convex approximation based algorithms have been…

We study a simple adaptive model in the framework of an N -player normal form game. The model consists of a repeated game where the players only know their own action space and their own payoff scored at each stage, not those of the other…

We develop new adaptive algorithms for variational inequalities with monotone operators, which capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Our algorithms automatically adapt to…

A game theory inspired methodology is proposed for finding a function's saddle points. While explicit descent methods are known to have severe convergence issues, implicit methods are natural in an adversarial setting, as they take the…

Model selection on validation data is an essential step in machine learning. While the mixing of data between training and validation is considered taboo, practitioners often violate it to increase performance. Here, we offer a simple,…

Reinforcement Learning (RL) has emerged as a transformative approach in the domains of automation and robotics, offering powerful solutions to complex problems that conventional methods struggle to address. In scenarios where the problem…

This article is an introduction to some aspects of \'Ecalle's mould calculus, a powerful combinatorial tool which yields surprisingly explicit formulas for the normalising series attached to an analytic germ of singular vector field or of…

In an infinite dimensional Hilbert space we consider a family of commuting analytic vector fields vanishing at the origin and which are nonlinear perturbations of some fundamental linear vector fields. We prove that one can construct by the…

A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to…

We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable…

We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly convex problems converge only to local minimizers, when randomly initialized. We…

Automata learning is a technique that has successfully been applied in verification, with the automaton type varying depending on the application domain. Adaptations of automata learning algorithms for increasingly complex types of automata…

Modeling how a robot interacts with the environment around it is an important prerequisite for designing control and planning algorithms. In fact, the performance of controllers and planners is highly dependent on the quality of the model.…

We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…

We consider the saddle point problem where the objective functions are abstract convex with respect to the class of quadratic functions. We propose primal-dual algorithms using the corresponding abstract proximal operator and investigate…

The development and deployment of Autonomous Vehicles (AVs) on our roads is not only realistic in the near future but can also bring significant benefits. In particular, it can potentially solve several problems relating to vehicles and…

We apply the saddle-point method to derive asymptotic estimates or asymptotic series for the number of partitions of a natural integer into parts chosen from a subset of the positive integers whose associated Dirichlet series satisfies…

A method is presented to exploit adaptive integration algorithms using importance sampling, like VEGAS, for the task of scanning theoretical predictions depending on a multi-dimensional parameter space. Usually, a parameter scan is…