STAGE Chow rank and explainable polynomial models

Date de mise à jour de l’offre

Ecole Polytechnique :

Laboratoire d'informatique de l'École polytechnique (LIX) is a computer science laboratory of École Polytechinque doing research in many areas of computer science and applied mathematics. The internship will take place in the MAX team (http://www.lix.polytechnique.fr/max/max-web/max/max-home.en.html).

Description de la mission

The idea of the project would be to come up with a way to simplify polynomials by replacing them with a “nearby polynomial of low Chow rank in the spirit of the principal component analysis for matrices (https://en.wikipedia.org/wiki/Principal_component_analysis) and apply the developed method to polynomials arising in controller synthesis (from https://arxiv.org/pdf/2208.12804.pdf).
The expected result includes:
1. A partial (for small ranks and dimensions) algorithm for computing low-Chow-rank approximations.
2. Evaluation of the algorithm on the examples.

Profil recherché

solid knowledge of linear algebra and proficiency in Python. Additional background in algebra and/or continuous optimization would be helpful but not required.

Niveau de qualification requis

Bac
  • Employeur
    Ecole Polytechnique
  • Secteur d’activité de la structure
    Enseignement - Formation - Recherche
  • Effectif de la structure
    De 51 à 250 salariés
  • Site internet de la structure
    https://www.lix.polytechnique.fr
  • Type de stage ou contrat
    Stage pour lycéens et étudiants en formation initiale
  • Date prévisionnelle de démarrage
  • Durée du stage ou contrat
    Plus de 2 mois et jusqu'à 4 mois
  • Le stage est-il rémunéré ?
    Oui
  • Niveau de qualification requis

    Bac
  • Lieu du stage
    1 rue Honoré d’Estienne d’Orves
    91120 PALAISEAU
  • Accès et transports
    15 minutes from the Lozere station of RER B