M2 Mathematics, Vision, Learning

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The Master 2 MVA (Mathematics, Vision, Learning), created by the mathematics department of the ENS Paris-Saclay, is a unique master in France since its creation in 1996. In cooperation with several academic partners, it trains a large number of university and "grandes ecoles" students each year in Research, Development and Innovation for public and private organizations and companies in the field of mathematics applied to data, image and signal processing.
The huge growth in the use of digital data in all fields of science, technology and society requires the training of high-level mathematical researchers mastering the acquisition and processing of digital data on the one hand, and their automatic interpretation on the other. These two aspects are strictly complementary and are reflected in the three terms characterizing the MVA program.

Course Prerequisites

Admission: On a case-by-case basis, for holders of an M1 in mathematics, informatics or physics, or for 3rd-year engineering school students (potentially admitted for dual programmes, according to agreements).

  • Understand and proficiently use high-level mathematical tools and methods.

  • Understand and mathematically model a problem in order to resolve it.

  • Analyse data and implement digital simulations.

  • Analyse a research paper with a view to summarising it and using it.

  • Be proficient in the use of digital tools and major programming languages.

  • Explain and write, clearly and rigorously, a theory and mathematical results.

Post-graduate profile

Upon completing the MVA Master's degree, graduates have acquired a solid theoretical and practical grounding in the field of data analysis in the broad sense.

Career prospects

Career paths available include doctoral studies, R&D in large organisations and major groups, areas of innovation (start-ups), in almost all sectors of activity.
Students are prepared for these prospects through:
-the teaching modules (the contents of the teaching are illustrated via case studies of real applications)
-the lab-companies forum held each year in November, inviting students to meet potential employers (public or private) in a direct and informal setting.

Covid-19 context (start of the academic year 2020-2021 for this training)

Training offering exclusively via distance-learning until December 2020 for international students detained outside France.

More information


Centre de mathématiques et de leurs applications.

Fédération de Mathématiques (CentraleSupélec),.


ECTS au choix à valider.

Subjects ECTS Lecture directed study practical class Lecture/directed study Lecture/practical class directed study/practical class distance-learning course Project Supervised studies
Topological data analysis for imaging and machine learning 5 12 12 3
Théorie des matrices aléatoires et apprentissage 5 24 6
Sub-pixel Image Processing 5 20 16
Remote sensing data: from sensor to large-scale geospatial data exploitation 5 31.5 7
Reinforcement Learning 5 16 4.5
Problèmes inverses et imagerie : approches statistiques et stochastiques 5 24
Probabilistic graphical models 5 27
Predictions of individual sequences 5 18
Parcimonie et analyse de données massives en astrophysique 5 24
Object Recognition and Computer Vision 5 30
Nuages de points et modélisation 3D 5 12 12
Modélisation en neurosciences et ailleurs 5 20
Méthodes stochastiques pour l'analyse d'images 5 18 9
Méthodes mathématiques pour les neurosciences 5 24 16
L'apprentissage par réseaux de neurones profonds 5 24
Kernel Methods for machine learning 5 23
Introduction to statistical learning 5 16 6
Introduction to Medical Image Analysis 5 24
Introduction à l'imagerie numérique 5 21 6
Imagerie fonctionnelle cérébrale et interface cerveau machine 5 24
Image denoising : the human machine competition 5 20 10 10
Graphs in Machine Learning 5 16 6
Géométrie et espaces de formes 5 20 9
Foundations of distributed and large scale computing optimization 5 24
Fondements Théoriques du deep learning 5 25 5
Discrete inference and learning 5 24
Deformable Models and Geodesic Methods for Image Analysis 5 21 9
Deep Learning in Practice 5 12 12
Deep Learning 5 18 3 6
Convex optimization and applications in machine learning 5 21
Computational statistics 5 20 10
Computational optimal transport 5 18
Biostatistics 5 24
Bayesian machine learning 5 16 8
Audio Signal Processing - Time-Frequency Analysis 5 20
Audio signal Analysis, Indexing and Transformations 5 14 10
Approches géométriques en apprentissage statistique: l'exemple des données longitudinales 5 21
Apprentissage Profond pour la Restauration et la Synthese d'Images 5 12 9 6
Algorithms for speech and natural language processing 5 20
Advanced Learning for Text and Graph 5 14 14
3D Computer Vision 5 18

Stage obligatoire.

Subjects ECTS Lecture directed study practical class Lecture/directed study Lecture/practical class directed study/practical class distance-learning course Project Supervised studies
Stage 20
Modalités de candidatures
Application period
From 01/04/2021 to 01/07/2021
Compulsory supporting documents
  • Letter of recommendation or internship evaluation.

  • Curriculum EU (description of the units of education followed) of the last two years.

  • Motivation letter.

  • All transcripts of the years / semesters validated since the high school diploma at the date of application.

  • Curriculum Vitae.

  • Copy of identity document.

Additional supporting documents
  • Certificate of English level (compulsory for non-English speakers).

  • Choice sheet of M2 (obligatory for the candidates registered in M1 at the University Paris-Saclay) to download on https://www.universite-paris-saclay.fr/en/admission/apply-master-programmes.

  • VAP file (obligatory for all persons requesting a valuation of the assets to enter the diploma).

  • Copy of the last diploma.

Course manager(s)
Nicolas VAYATIS - vayatis@cmla.ens-cachan.fr
Administrative office
DER Maths SECRETARIAT MVA - secretariat-mva@ens-paris-saclay.fr