M2 Mathematics, Vision, Learning

The students are expected to have basic knowledge of Python.

The course aims to introduce students to Deep Learning through the development of practical projects. We expect that by the end of the course, the students will be able to implement and develop new methods in different domains:

• history of deep learning and its relation to cognitive science;
• feedforward networks, regularisation and optimization;
• representation learning & siamese networks;
• GAN & transfer learning;
• recurrent networks and LSTM for Natural Language Processing;
• object detection;
• self-supervised methods;
• deep reinforcement learning.

With the increase of computational power and amounts of available data, but also with the development of novel training algorithms and new whole approaches, many breakthroughs occurred over the few last years in Deep Learning for object and spoken language recognition, text generation, and robotics. This class will cover the fundamental aspects and the recent developments in deep learning in different domains: Computer Vision, Natural Language Processing, and Deep Reinforcement Learning.

• Each section of the course is divided into 1h30′ lecture and 1h30′ lab. The labs will allow the students to start developing the mini-projects on which the evaluation is based, and receive feedback.
• Evaluation: the evaluation of the course will be based on 3 individual mini-projects on object recognition, natural language processing, and reinforcement learning.

Deep Learning. Ian Goodfellow, Yoshua Bengio, and Aaron Courville, MIT Press, 2016. A Selective Overview of Deep Learning. Jianqing Fan, Cong Ma, Yiqiao Zhong. arXiv 2019.

• Master 1 de Mathématiques, les bases en optimisation et apprentissage statistique.
• Notions de base en Analyse, statistique et apprentissage machine, en programmation en python.

Nous commencerons par formaliser différents modèles de réseaux et par décrire des algorithmes de back-propagation utilisés pour leur minimisation. Le cœur du contenu mathématique du cours consistera ensuite en la présentation de résultats récents sur :

• l'optimisation non-convexe ;
• les propriétés du paysage de la fonction objectif ;
• la stabilité des minimiseurs (notamment dans le cas de réseaux linéaires structurés); l'interprétabilité des réseaux;
• l'expressivité des réseaux, leur complexité de Rademacher et la régularisation avec le dropout ;
• des propriétés des Generative Adversarial Networks (GANs).
• des propriétés de robustesse décisionnelle des réseaux profonds (incertitude, stabilité).

Ces résultats mathématiques seront complétés par la présentation moins mathématisée de différentes architectures et propriétés de réseaux utilisés en pratique.

L’objectif principal de ce cours est de présenter des résultats représentatifs de la recherche actuelle sur les justifications mathématiques des algorithmes d’apprentissage profond; puis de faire le lien avec la mise en pratique de ces algorithmes.

10 séances. Validation : – 1 examen final (90% de la note) – 1 travail à la maison avec implémentation d’algorithme (10% de la note) – Pour le rattrapage du cours, nous prévoyons de faire un examen de rattrapage dont la note remplacera les notes précédentes.

• Bolte, Sabach, Teboulle, "Proximal alternating linearized minimization for nonconvex and nonsmooth problems", Math. Prog. Vol 146, no 1-2, pp 59-594, 2014. - Baldi, Hornik, "Neural networks and principal component analysis: Learning from examples witho.

Basics of linear algebra, calculus and Fourier transform.

Topics:

• Time-Frequency Analysis ;
• Denoising (old/bad recordings) ;
• Audio signal modification (pitch shifting, slowing down,...) ;
• Audio Synthesis ;
• Speech or Music recognition ;
• Estimation of intsantaneous frequencyfréquence fondamentale ;
• Psycho-acoustic ;
• Audio Filtering ;
• LPC : Linear Prediction Coding.

Initiation to several signal processing techniques specific to audio processing.

• Only courses
• Validation: Oral and written report on an academic paper.

Solid understanding of mathematical methods, including linear algebra, probability, integral transforms and differential equations.

This course will focus on discrete models, that is, cases where the random variables of the graphical models are discrete. After an introduction to the basics of graphical models, the course will then focus on problems in representation, inference, and learning of graphical models. We will cover classical as well as state of the art algorithms used for these problems. Several applications in machine learning and computer vision will be studied.

Probabilistic graphical models provide a powerful paradigm to jointly exploit probability theory and graph theory for solving complex real-world problems. They form an indispensable component in several research areas, such as statistics, machine learning, computer vision, where a graph expresses the conditional (probabilistic) dependence among random variables.

• 8 lectures of 3 hours ;
• Quizzes and projet during the course.

Admission to MVA sufficient

• Variational Methods and Partial Differential Equations ;
• Numerical Methods, Algorithmics, and Industrial applications ;
• Curve and Surface Segmentation by Elastic Deformable Models, Active Contours, Deformable Surfaces, Balloon Model ;
• Finite Differences, finite elements, level sets, front competition Active Region, Shape Prior ;
• Minimal Paths and Geodesics ;
• Eikonal Equation, front propagation and Fast Marching ;
• Various metrics: 2D, 3D, surface, anisotropic, space+radius ;
• Geodesic remeshing of domains and surfaces ;
• Applications: surface segmentation, vessel segmentation, virtual endoscopy, extraction of tubular and tree structure… ;
• Testing and implementation of algorithms in Matlab.

A large overview of methods and algorithms of deformable models for image segmentation, illustrated by concrete applications.

• About half on deformable models and half on geodesic methods ;
• 10 sessions of 3 hours, including 3 or 4 with 2 hours on laptop ;
• Validation by Project

• The "Introduction to Deep Learning" course by Vincent Lepetit (taking place during the 1st semester)
• Notions in machine learning, Bayesian statistics, analysis, differential calculus
• Basic knowledge of Python and PyTorch

We will first emphasize the gap between practice and classical theory (e.g., number of parameters), and reconcile them thanks to recent theoretical advances. After a review of recent architectures, we will study visualization techniques, and check that undesired biases present in the dataset (e.g., sensitivity to gender when matching CVs to job offers) are not reproduced. We will then investigate practical issues when training neural networks, in particular data quantity (small or big data), application to reinforcement learning and physical problems, and automatic hyper-parameter tuning.

This course aims at providing insights and tools to address these practical aspects, based on mathematical concepts.

Related books: "Deep Learning" by I. Goodfellow, Y. Bengio and A. Courville.

Examples of references: - "Do Deep Nets Really Need to be Deep?"; L. J. Ba, R. Caruana; NIPS 2014 - "Graph Attention Networks"; P. Velickovic, G. Cucurull, A. Casanova, A. Romero, P. Lio, Y. Bengio; ICLR 2018 - "Women also Snowboard: Overcoming Bias in Captioning Models"; L. A. Hendricks, K. Burns, K. Saenko, T Darrell, A Rohrbach; FAT-ML 2018 - "Scaling description of generalization with number of parameters in deep learning"; M. Geiger, A. Jacot, S. Spigler, F. Gabriel, L. Sagun, S. d'Ascoli, G. Biroli, C. Hongler.

Pré-requis scientifiques : géométrie, algèbre linéaire, probabilités. Pré-requis techniques (utiles pour le projet) : programmation (C, C++, Python ou Matlab).

Thèmes abordés :

• Systèmes de perception 3D
• Traitements et opérateurs
• Recalage
• Segmentation de nuages de points
• Reconstruction de courbes et surfaces
• Modélisation par primitives
• Rendu de nuages de points et maillages

Ce cours donne un panorama des concepts et techniques d'acquisition, de traitement et de visualisation des nuages de points 3D, et de leurs fondements mathématiques et algorithmiques.

• 8 séances de 4h (2h cours, 2h TP informatique).
• Les TP se font sur les ordinateurs des étudiants, avec des logiciels libres à installer.
• 1 séminaire de recherche de 3h
• 1 journée de présentation des projets d'élèves.

Projet basé sur un article de recherche. Déroulement du projet : 1/ Choix d’un article de recherche parmi des propositions ; 2/ Implémentation et tests du ou des algorithmes décrit(s) dans l’article ; 3/ Selon les cas, analyse de l’algorithme, de ses résultats, proposition de variante(s) ; 4/ Remise d’un document expliquant la méthode, les résultats ; et du code réalisé.

Mode de rattrapage : Un étudiant ayant échoué à l’épreuve d’évaluation par projet, se verra la possibilité de choisir un autre projet dans une nouvelle liste d’articles proposée par les enseignants.

Images de profondeur, dir. J. Gallice, 2001, Hermès Science. Modélisation 3D automatique, F. Goulette, 1998, Presses de l'Ecole des Mines. Traitement de nuages de points denses et modélisation 3D d'environnements par système mobile LiDAR / Caméra, J.-E. Deschaud, 2010, thèse de doctorat MINES ParisTech. Rendu Par Points, Christophe Schlick, Patrick Reuter et Tamy Boubekeur, Informatique Graphique et Rendu, Hermès Publishing, 2007 Point-based graphics, M. Gross and H. Pfister editors, 2007, Morgan Kaufmann. Computer Graphics: Principle and Practice Physically-based

• Python programming
• Basics of convex analysis (convex function, convex set)
• Basics of differential calculus (computation of gradient)
• Basics of optimization (gradient descent, linear programming)

It starts by covering the basics of data representation and processing, including linear filtering and Wavelets.
The core of the course is first order optimization methods (gradient descent, stochastic optimization and proximal splitting) with an emphasis on performance guarantees and their applications to inverse problems in imaging and supervised learning using linear models.
The last part of course covers more advanced problems related to the high dimensional setting, using in particular sparsity-inducing regularizers such as the Lasso and compressed sensing methods.

This course reviews fundamental mathematical and numerical method for imaging sciences and machine learning.

Optimal transport (OT) is a fundamental mathematical theory at the interface between optimization, partial differential equations and probability. It has recently emerged as an important tool to tackle a surprisingly large range of problems in data sciences, such as shape registration in medical imaging, structured prediction problems in supervised learning and training deep generative networks. This course will interleave the description of the mathematical theory with the recent developments of scalable numerical solvers. This will highlight the importance of recent advances in regularized approaches for OT which allow one to tackle high dimensional learning problems. The course will feature numerical sessions using Python.

The course is complemented by Python numerical homeworks extracted from the web site www.numerical-tours.com.
The course is validated by a project (an article to read, some computer implementation, a short written report and an oral presentation).

• Gabriel Peyré and Marco Cuturi, Computational Optimal Transport, https://optimaltransport.github.io (course notes, slides, codes). - Gabriel Peyré, The Numerical Tours of Data Sciences, www.numerical-tours.com (for the homework and the projects). - Fili.

Training in algorithms / machine learning. Interest for biophysics / biology / medicine.

(1) Introduction: understanding protein functions at the atomic level (2) Protein structure prediction with AlphaFold2 and transformers (3) Molecular kinematics, inverse problems, loop sampling (4) Boltzmann samplers for sequences and structures (5) Computer practical (6) High-dimensional sampling: from the volume of polytopes to densities of states in statistical physics (7) Spatial partitions and applications

Proteins underlie all biological functions, yet, understanding their mechanisms at the atomic scale remains a fundamental open problem. The difficulties are inherent to complex dynamics in very high dimensional spaces. Indeed, with circa 5000 atoms and xyz coordinates per atom, a polypeptide chain of median size lives in a configuration space of dimension 15,000. While AlphaFold2 has been a game changer by providing plausible structures of selected (well folded) regions of proteins, it by no means provide insights on dynamics. In this context, the goal of this class is twofold. First, to cast the main problems related to protein dynamics into a rigorous mathematical / algorithmic framework. Second, to present some of the major ongoing developments, which feature a stimulating interplay between theoretical biophysics, geometry, topology, and machine learning. To get acquainted with real data, one course will be devoted to a computer practical providing background on standard molecular manipulations, and illustrating selected methods studied in class.

The courses consists of 6 lectures (cours magistral) of 3 hours each; plus one lecture consisting of a computer practical.

Basic linear algebra, calculus, probability theory.

Topics:

• speech features & signal processing ;
• hidden markov & finite state modeling ;
• probabilistic parsing ;
• continuous embeddings ;
• deep learning for language-related tasks (DNNs, RNNs) ;
• linguistics and psycholinguistics ;
• comparing human and machine performance.

Speech and natural language processing is a subfield of artificial intelligence used in an increasing number of applications; yet, while some aspects are on par with human performances, others are lagging behind. This course will present the full stack of speech and language technology, from automatic speech recognition to parsing and semantic processing. The course will present, at each level, the key principles, algorithms and mathematical principles behind the state of the art, and confront them with what is know about human speech and language processing. Students will acquire detailed knowledge of the scientific issues and computational techniques in automatic speech and language processing and will have hands on experience in implementing and evaluating the important algorithms.

• The courses consist in 9 three-hours blocks, followed by an oral project presentation ;
• During the courses, we will use on-line quizzes (on the smartphone/computer) to probe comprehension and trigger discussion ;
• The validation is continuous: there is no final exam, but a combination of quizzes during the lessons (20%) and two practical assignments (TDs), (40% each).

The recommended, but not obligatory textbook for the course is D. Jurafsky & J. Martin – Speech and Language Processing, 3rd (online) edition for already available chapters [J&M3], 2nd edition otherwise [J&M2]. Readings for each of the sessions will be provided by the instructors.

• Probabilités, statistiques ;
• Notions en apprentissage et traitement du signal.

• 9 séances de cours de 3h ;
• 3 séances de TP de 3h ;
• Soutenances.

Module Opening

• An undergraduate course in probability.
• It is recommended to have followed either the course of P. Latouche and N. Chopin on "Probabilistic graphical models" or the course of S. Allassonière on "Computational statistics" during the first semester.
• Practicals will be in Python and R. A basic knowledge of both languages is required, students should be able to read and write simple programs and load libraries.

1/ Decision theory:

• Describe frameworks for modelling uncertainty and making decisions ;
• Introduce minimax and Bayes rules.

2/ Bayesian principles:

• Formalize expected utility, discuss interpretations ;
• Show how most tasks of the MLer fit into the framework (supervised and unsupervised learning, active learning, model choice, etc.)
• Practical session 1.

3/ Bayesian computation for ML:

• ML-specific Monte Carlo approaches: variational principles, advanced MCMC ;
• Practical session 2.

4/ Bayesian nonparametrics:

• Popular BNP models: Gaussian, Dirichlet, Pitman-Yor, Gibbs-type, Stick-breaking, Indian Buffet processes, etc ;
• Practical session 3.

5/ Bayesian methods for deep learning:

• Bayesian deep neural networks (BNN) ;
• Dropout as a Bayesian approximation ;
• Bayesian Generative Adversarial Networks ;
• Practical session 4.

By the end of the course, the students should:

• have a high-level view of the main approaches to making decisions under uncertainty ;
• be able to detect when being Bayesian helps and why ;
• be able to design and run a Bayesian ML pipeline for standard supervised or unsupervised learning ;
• have a global view of the current limitations of Bayesian approaches and the research landscape ;
• be able to understand the abstract of most Bayesian ML papers.

• 8×3 hours of lectures and practice TPs ;
• 4 hours of « student seminars » for the evaluation ;
• All classes and material will be in English. Students may write their final report either in French or English.
• Evaluation is project-based, each project revolving around a research paper. Students form groups (the number of students by project will depend on the number of students in the class). Each group reads and reports on a research paper from a list. We strongly encourage a dash of creativity: students should identify a weak point, shortcoming or limitation of the paper, and try to push in that direction. This can mean extending a proof, implementing another feature, investigating different experiments, etc. Deliverables are a small report and a short oral presentation in front of the class, in the form of a student seminar, which will take place during the last lecture.

• Parmigiani, G. and Inoue, L. 2009. Decision theory: principles and approaches. Wiley. - Robert, C. 2007. The Bayesian choice. Springer. - Murphy, K. 2012. Machine learning: a probabilistic perspective. MIT Press. - Ghosal, S., & Van der Vaart, A. W. 2017. Fundamentals of nonparametric Bayesian inference. Cambridge University Press.

Basics of signal processing.

• Audio Indexing (machine Listening): audio signal analysis for content-based information retrieval (automatic music genre recognition, automatic musical instrument identification, tempo or downbeat estimation,…) ;
• Audio Transformations (3D rendering, sound effects, sound modifications): Physical and perceptual approaches (binaural/transaural techniques, head-related transfer functions, wave field synthesis,..). Digital sound effects (flanger, phaser, distortion, artificial reverberation,..). Timbral, scale and pitch modifications ;
• Audio Source Separation: Audio demixing, linear and convolutive mixing models, underdetermined models, sparse models, DUET ;
• High resolution audio spectral analysis: Sinusoidal models, beyond Fourier analysis, spectral MUSIC, ESPRIT.

The aim of this course is to span several domains of audio signal analysis including audio indexing (or machine listening), high-resolution audio spectral analysis, audio source separation, and audio transformations (3D sound rendering, sound effects and sound modifications).

• 13,5 h theoretical lectures ;
• 10,5 h practical sessions (TP) in Matlab (or Python if preferred) ;
• Lectures are planned to be in French but slides will be in English.
• Validation: validation is done through papers reading/analysis with written report and oral presentation.

Y. Grenier, R. Badeau, G. Richard « Polycopiés de cours sur le traitement du signal audio (in French) », Télécom ParisTech. M. Mueller, D. Ellis, A. Klapuri, G. Richard, Signal Processing for Music Analysis", IEEE Journ. on Selected Topics in Sig. Proc., October 2011.

• Applied Mathematics (Linear Algebra, Numerical Analysis, Differential Calculus, Fourier Analysis) Programming (Python, Matlab) ;
• The basic concepts of image processing, optimization and deep learning are useful but will be introduced in the course.

The miniaturisation of sensors and the evolution of computational capabilities has led to the ubiquitous presence of images. However, the increasing demand for image-based content also requires sophisticated post-processing (filtering, restoration etc.), in order to ensure good quality results. At the heart of these post-processings are image models, which allow us to establish powerful and efficient algorithms. Deep learning is the latest addition to a long list of such image models.

We will explore many applications such as denoising, super-resolution, deblurring, texture synthesis and natural image generation. In each case we will present the strengths and limitations of the different techniques studied. In particular, we will present a critical analysis of the methods and show some of the pitfalls in which they sometimes fall.

The aim of this course is to present recent techniques based on deep learning for the quality of images, and to compare them to pre-existing methods.

• 7 sessions of 3 hours each (course + practical session) ;
• 2 review and project preparation sessions ;
• 1 project presentation session
• Evaluation is based on the students' individual reports on practical sessions and on a longer project, and on the final project presentation session.

• Zhang et al (2018). FFDNet. doi:10.1109/TIP.2018.2839891 - Kim et al (2016). Deeply-Recursive Convolutional Network for Image Super-Resolution. doi:10.1109/CVPR.2016.181 - Carvalho et al (2018). Deep Depth from Defocus. arXiv:1809.01567 - Ryu et al (201.

Basic graduate level notions of linear algebra and optimization. Basic programming in C, C++ or java.

• Camera geometry, panorama construction ;
• Calibration, projection matrix ;
• Interest points, including SIFT, matching ;
• Essential and fundamental matrices, RANSAC algorithm ;
• Disparity maps with local methods and filtering ;
• Disparity maps with global methods, graph cuts ;
• Multiple view stereo.

Explore the theoretical foundations of 3D computer vision from multiple views, with emphasis on binocular stereo, and show the practical limitations in the algorithmic state of the art.

• 6 in-class lectures of 3 hours (electronic slides made available to students).
• 5 home assignments with C++ source code to complete and written report.
• Written examination (2.5h)

Hartley, Richard, and Andrew Zisserman. Multiple view geometry in computer vision. Cambridge university press, 2003. Szeliski, Richard. Computer vision: algorithms and applications. Springer Science & Business Media, 2010.

Probability, Linear Algebra, Basic Statistics, Programming (eg C, Python, R). Some training in Statistical Physics may be a bonus but it is absolutely not a prerequisite.

Twelve 2-hour lectures (no exercice classes) covering the following points:

1. Interacting Particles Systems (IPS)
2. Agent-Based Models (ABMs)
3. Analysis & Inference in IPS and ABMs
4. Extrema, Rare Events and Heavy-Tail Processes

Interactions are an intergal part of many systems, be they natural, social, articial and/or virtual. Their modelling and analysis has long posed challenges to the sciences { one may think of the three-body problem in classical mechanics, chaos theory in dynamical systems, feedback loops in climate science, particle systems in statistical physics, confounding variables in statistics, cities and transport systems in quantitative geography, markets in economics, opinion dynamics in social and political science... With the unprecedented availability of data and the advent of new theoretical and computational methods, several approaches in the contemporary mathematical sciences are relevant to tackle such systems: stochastic modelling, simulations, machine learning, to name but a few. This course will provide an introduction to the general question of modelling systems of interactions, covering notions such as complexity, emergence and self-organized criticality, as well as simulation tools known as agent-based models (ABMs). These models provide ways of designing and running in silico controlled experiments of complex real systems. They also provide means of testing statistical and analytical methods: in particular, we will examine methods to learn the structure and content of interactions and causal relationships using ABMs. We will also look at the occurrence, in stochastic processes, ABMs and other algorithms, of extreme and rare events arising from interactions.

There are no formal prerequisites to this course, but undergraduate courses in probability or statistics will help.

The course will both emphasize the principles and concepts underlying the different goals of clinical research (prediction and causation) and develop on specific statistical methods that can be used to plan studies and analyze data in this context.

It will focus on notions and methods that are not covered by other courses of the master (e.g. design, survival analysis, causal inference), that will be tackled both from the theoretical and applied point-of-view.

Methods will be illustrated on several practical examples.

The course aims at introducing both concepts and methods used in clinical (or medical) research. It is integrated to the health science theme of the master program.

• 7 lectures (3 hours), each comprising formal lectures and practical illustrations
• Final group home project presentation (3 hours)
• validation: final exam (60%), home project and presentation (40%).

• Harrell FE. Regression Modeling Strategies. Springer-Verlag, 2014. - Herna?n M, Brumback B, Robins J. Marginal structural models to estimate the joint causal effect of nonrandomized treatments. Journal of the American Statistical Association 2001; 96:44.

Un minimum de pré-requis en probabilité et statistique est nécessaire, typiquement vecteurs gaussiens et estimation paramétrique.

On introduit dans ce cours des techniques d'analyse stochastique et statistique utiles en particulier pour résoudre des problèmes inverses et d'imagerie. Dans un problème d'imagerie typique (en échographie par exemple), on souhaite imager un milieu, qui peut être le corps humain en imagerie médicale ou la croûte terrestre en imagerie sismique. On dispose d'un ensemble de sources qui émettent des ondes et d'un ensemble de récepteurs qui enregistrent les ondes réfléchies par le milieu. Il s'agit de traiter les données enregistrées pour reconstruire le milieu, en construire une image. Malheureusement, d'une part ces problèmes sont mal posés, dans le sens où les seules données expérimentales ne suffisent pas à déterminer le milieu. Il est donc nécessaire d'ajouter des contraintes ou des a priori qui permettent de régulariser le problème et de réduire l'espace de recherche. D'autre part, les données expérimentales sont entachées de bruit, qui peut être du bruit de source, du bruit de mesure, ou du bruit de milieu. Il se trouve que des idées originales pour traiter ces problèmes sont apparues récemment. Ces idées sont basées sur des outils probabilistes qu'on développera dans ce cours.

Proposer différentes techniques d’analyse stochastique et statistique utiles pour résoudre des problèmes inverses et d’imagerie multi-capteurs (type échographie ultrasonore ou imagerie sismique).

L'UE se compose de 8 cours de 3 heures chacun (cours au tableau) de janvier à mars, plus un cours pour les exposés des étudiants. L'évaluation consiste en un projet réalisé seul ou en binôme, avec remise d'un rapport écrit et d'un code (ou d'un notebook jupyter) et présentation d'un exposé lors du 9ème cours. Le rattrapage éventuel consiste en un nouveau projet (éventuellement lié au projet original) avec remise d'un rapport écrit et d'un code (ou d'un notebook jupyter).

Des notes de cours (en anglais) sont distribuées : 1/ Quelques résultats sur l'équation des ondes : fonction et identités de Green. Expérience de retournement temporel des ondes. 2/ Problèmes inverses mal posés : analyse bayésienne et régularisation. Imagerie par moindres carrés. 3/ Propriétés spectrales des processus aléatoires stationnaires. Imagerie par corrélations croisées. 4/ Propriétés des processus gaussiens. Caractérisation du bruit de speckle. 5/ Théorie des matrices aléatoires. Détection, localisation et identification de réflecteurs. Voir aussi : [1] H. Ammari, J

Probabilités et statistiques (niveau M1), bases du Machine Learning.

Throughout this course, we will debate how this balance can be achieved. This will be done through unpacking the main pillars of AI, both from a CS perspective and from a legal/ policy perspective. In recent years, many countries, private companies, standard bodies, and international organizations, have been calling for governing AI through principles. Those principles include for example fairness, accountability, transparency and human agency. The literature about each one of those components is on the rise both in the CS/ ML domains, and in the social sciences. In each session, we will dive into one of the components, discuss from a theoretical perspective what are the considerations that each domain is adding to the equation, and demonstrate how practically, using real life case studies, we can bridge the gap and merge them into a solution that addresses both.

This course will examine the mutual relationship between law, computer science and public policy. With the wide spread of artificial intelligence, the link between these domains is becoming more and more ambiguous. On one hand, the noticeable benefits that AI algorithms are bringing to our life are leading to a hype of AI, and both policy makers and engineers are seeing automation as a feasible solution for many longstanding societal issues. On the other hand, the gap between the disciplines is growing, misunderstanding of technical terms and concepts is leading lawyers and policy makers to oppose to the deployment of the technology in certain domains, or pressuring them to pass regulation that could hinder innovation. And the lack in understanding the complex socio-political context in which algorithms are operating in, as well as the laws and policies governing this domain, is leading computer scientists to develop solutions that are not compliant and can exacerbate existing biases.

• 5 séances de 2.5h ;
• Numerus clausus : cours limité à 30 places ;
• validation : participation / contrôle continu / projet.

Linear algebra, basic programming with Python

This class provides foundational background for geometry in machine learning. This will be of interest to students who also attend the following lectures:

1st semester: – Medical image analysis – Computational optimal transport – Topological data analysis – Deep learning

2nd semester: – Geometry and shapes spaces – Kernel methods for machine learning – 3D point clouds – Deep learning for medical imaging – Graphs in machine learning – Generative models for imaging – Inverse problems and imaging – Deformable models and geodesic methods – Information and statistical physics – Numerical PDEs for image analysis.

Machine learning sits at the intersection between modelling, software engineering and statistics: data scientists write programs that must satisfy domain-specific constraints, scale up to real data and can be trained with guarantees. In this context, geometry is a convenient tool to encode expert knowledge. Clever distances between data samples allow our methods to enforce fundamental properties while keeping a simple mathematical form. This is especially relevant when dealing with structured data such as anatomical images, protein conformations or physical simulations.

The purpose of this class is to provide a unifying geometric perspective on common machine learning models. By the end, students will be able to answer the following questions: – Should I represent my data samples using vectors, graphs or histograms? – How impactful is the choice of a Euclidean norm vs. a cross entropy? – Can I relate kernels, graphs, manifolds, optimal transport and transformer networks to each other?

• 7 sessions (2-hour lecture + 1-hour workshop) ;
• validation: Project report and presentation (15 points) + quizz (5 points).

1 Free and open-source software – 1.1 Introduction – 1.2 Licensing – 1.3 Economical model of FS projects – 1.4 Case studies

2 Reproducible research – 2.1 Introduction – 2.2 Publishing reproducible research. The editorial process. – 2.3 Legal aspects – 2.4 Writing a reproducible scientific article

This is a course on free software (FS) and reproducible research including how to write and publish reproducible research, the legal aspects of the code, article, and data, and eventually the good practices to write free software and perform reproducible research. Group discussions, debates, and individual dissertations are part of the activities of the course. The plan of the course covers the minimum knowledge that any PhD candidate or master’s student on computational sciences should reach to perform reliable research. The MVA course Projet de recherche reproductible can be considered as a practical follow-up for those students who want perform an actual project on reproducible research.

The course spans a total of 24h, according the this plan: • 6 sessions of master classes, 2h each. • 3 sessions of TP, 3h each. At each session the students will work on the final project and each group will make a partial presentation. • 1 session of 3h where each group will present the final presentation of the project, along with group discussion.

1. Introduction: applications in system monitoring (anomaly detection), environmental sciences. Univariate basic theory (Fisher and Tipett, maximum domains of attrac- tion)
2. Regular variation, vague convergence, M0 convergence (Hult and Lindskog (2006); Resnick (2008)).
3. Multivariate extremes: max-id distributions, reduction to the standard case by marginal standardization, simple max-stable distributions, angular measure (Resnick (2008)).
4. Tutorial session.
5. Statistical learning theory for rare events: conditioning trick, McDiarmid’s Bernstein type inequality, inequalities of VC type. Applications in multivariate extreme value theory (Lhaut et al. (2022); Goix et al. (2015)).
6. Tutorial session:
7. Introduction to statistical learning algorithm for extreme data: Anomaly detection via angular MV-set estimation (Thomas et al. (2017)) and dimension reduction (Goix et al. (2016); Chiapino et al. (2020)), introduction to graphical models and causal inference for extremes (Engelke

With the ubiquity of sensors, Big Data are now increasingly available in a wide variety of domains of human activity (science, industry, health, environment, commerce, security, ...) and rare/extreme phenomena are becoming observable in a significant manner. Before, such events were mainly ’out-of-sample’ and Extreme Value Theory (EVT), the field of probability and statistics concerned with tails of distributions, tackled their study through (parametric) modelling essentially. With the need for analyzing extreme observations, carrying often the critical information to design solutions to applications (e.g. health monitoring of complex infrastructures) for which worst-case scenarios crucially matter, the most recent years have seen an increasing interest of the EVT research community towards novel machine learning algorithms and statistical learning theory, resonating with a continuing effort of the statistical community to address larger-dimensional problems with computationally feasib

Structures de données informatiques, programmation Python, Algèbre Linéaire niveau L3, Calcul différentiel niveau L3, Probabilités niveau L3, Statistiques niveau L3

L’objectif de ce module est de comprendre ce que les approches d’apprentissage profond peuvent apporter à des problématiques de traitement du signal à travers plusieurs cas d’usage industriels comme par exemple, l’identification d’émetteurs radar, la détection de signaux pour la radio cognitive, la reconnaissance de locuteurs, la reconstruction de signaux audio altérés, ou la maintenance prédictive.

Pour chaque cas d’usage, nous étudierons, discuterons et mettrons en place lors de travaux pratiques des traitements « classiques » et les revisiterons selon une approche par « apprentissage ». Pour chaque cas d’usage étudié, nous prendrons le temps d’introduire le contexte opérationnel et de modéliser la physique du problème afin de donner une culture des différents domaines d’application. Dans la partie théorique du cours nous introduirons des concepts et outils de traitement du signal (représentations temps-fréquence et temps- échelle, filtrage) et d’apprentissage machine (approches supervisées et non-supervisées, grandes classes d’algorithmes de classification et de partitionnement de données, optimisation, descente de gradient, bases de l’apprentissage profond et grandes architectures de réseaux de neurones). A travers ces allers-retours entre théorique et pratique nous essayerons de répondre à la question « qu’est-ce qui fait la profondeur de l’apprentissage profond ? ».

Module 1 du track "Industrie et Ingénierie"

Bases de traitement d'image

Module 6 du parcours "industrie et Ingénierie" Thèmes abordés : Fonctionnement des caméras, chaine de traitement des images, photographie computationnelle, débruitage, qualité image, intelligence artificielle dans les traitement et l’évaluation de la qualité des images.

En 2022, on estime à plus de 5 milliards le nombre de photos prises par jour. Les caméras sont partout et ont atteints des niveaux de sophistications inégalées, notamment dans les smartphones. Ce cours est une introduction complète au fonctionnement des caméras et à leur écosytème industriel. Depuis l’entrée de la lumière à travers la lentille jusqu’à la production d’un fichier image, ce cours décrira les systèmes actuels et les défis techniques rencontrés pour atteindre de bonnes performances. Nous verrons comment la miniaturisation des caméras a conduit au développement de techniques de photographie computationnelle utilisant de l’algorithmie analytique ou de l’intelligence artificielle, quelles sont les techniques mises en œuvre pour ces traitements (débruitage, high dynamic range, superrésolution) ainsi que pour l’évaluation de la qualité des images produites.

Module du track I&I

Connaissance en algèbre linéaire, probabilités & statistiques, optimisation, programmation python

1. Introduction aux systèmes de mesure : images et diagraphies (sismique, électromagnétique, ultrasonique, mécanique…)
2. Compression, Super-résolution
3. Mesures de qualité et ranking
4. Alignement des données
5. Amélioration de contraste, Inpainting
6. Classification, Segmentation, Inversion

Ce cours est une introduction aux techniques d’apprentissage statistiques appliquées aux géosciences, avec des applications dans le domaine de l’énergie. Les mesures géophysiques sont acquises avec des capteurs de haute technologie, dans des conditions extrêmes. Elles permettent de décrire et d’analyser le sous-sol pour prendre des décisions critiques. Ces mesures sont de différents types – images, signaux – et sont basées sur une grande variété de physiques (électromagnétique, ultrasonique, mécanique…). Ceci permet d’apporter des informations complémentaires aux experts en interprétation. Ce cours décrit des exemples de taches automatisées avec de l’intelligence artificielle (IA) et de l’apprentissage statistique et couvre l’ensemble de la chaine de traitement de données, de l’acquisition jusqu’à l’interprétation. Il se compose de contenus théoriques et pratiques sur des méthodes traditionnelles, des méthodes conventionnelles d’apprentissage statistiques et des méthodes deep learnin

Module du track I&I

Recherche Opérationnelle, programmation Python, Réseaux

Thèmes abordés : Études des problèmes d’optimisation réseaux, formulations, méthodes et algorithmes pour dimensionner, planifier, orchestrer les réseaux d’aujourd’hui et les futurs réseaux.

L’aide à la décision est un domaine essentiel pour planifier et gérer les réseaux. L’objectif de ce module est d’apporter des connaissances sur les méthodes d’optimisation mathématiques et leur utilisation pour traiter les problématiques de conception et gestion des réseaux. Ces méthodes sont d’autant plus cruciales que les défis algorithmiques vont exploser dans les prochaines années, avec l’arrivée des réseaux virtualisés et autonomes.

La première partie de ce module sera dédiée à des séances de (re)mise à niveau en recherche opérationnelle, en particulier en optimisation combinatoire et théorie des graphes, ainsi que dans le domaine des réseaux telecoms. Les méthodes de résolution exactes les plus pertinentes seront exposées théoriquement puis expliquées sur les exemples les plus répandus dans la littérature du domaine. De plus, plusieurs exemples d’application des modèles étudiés seront développés sur des exemples très concrets, inspirés de problèmes réels tels que les problèmes de network design, de planification de capacités, de routage de flots (Traffic Engineering) et de placement de composants réseaux. Les TPs permettront de tester et analyser les formulations mathématiques en les programmant et en les résolvant à l’aide de solveurs sur étagère, et de concevoir et tester des algorithmes heuristiques. La seconde partie du module concernera les problèmes d’optimisation liés aux récentes évolutions des réseaux.

Module du track I&I

There are no real prerequisites, the course is more or less self-contained

More precisely, the goal is to construct and analyse algorithms that discover, and then treat, data one after the other one rather than directly with the whole batch. Typical examples are stopping times (prophets, secretary), online matching, k-servers, etc. I will cover the main techniques used (related to linear optimisation, stochastic approximation, tree reductions..) and will provide as many open questions as possible.

The objectives are to understand and master how to sequentially take that may have a strong impact on the future (typically depletion of budget). This course will be at the junction of mathematics, theoretical computer science and economics.

This is a "blackboard research course". All classes are going to be taught solely on the blackboard

• Undegraduate-level linear algebra.
• It is recommended to have followed the first-semester course of A. d'Aspremont "Convex optimization and applications in machine learning".
• Tutorial (TP) sessions will be in Python. Basic knowledge of the language and of general programming concepts (functions, loops, recursivity, data structures, ...) are expected.

1- Introduction: 3h lecture 2- Motion planning for robotics: 2h lecture, 1h TP 3- Inverse problems for robot control: 2h lecture, 1h TP 4- Optimal control and trajectory optimization: 2h lecture, 1h TP 5- Perception and estimation: 3h lecture 6- Reinforcement learning for robotics: 2h lecture, 1h TP 7- Legged locomotion: 2h lecture, 1h TP 8- Responsible robotics: 3h lecture 9- Final exam: 4h student seminar (Project/report presentations)

A large part of the recent progress in robotics has sided with advances in machine learning, optimization and computer vision. The objective of this lecture is to introduce the general conceptual tools behind these advances and show how they have enabled robots to perceive the world and perform tasks ranging, beyond factory automation, to highly-dynamic saltos or mountain hikes. The course covers modeling and simulation of robotic systems, motion planning, inverse problems for motion control, optimal control, and reinforcement learning. It also includes practical exercises with state-of-the-art robotics libraries, and a broader reflection on our responsibilities when it comes to doing research and innovation in robotics.

None

Session 1: AI governance intro Session 2: sectoral example Session 3: transversal laws, the EU AI Act and beyond Session 4: foundational models

The goal of this short course is to familiarize the students with the different ethical, legal, and policy related considerations in machine learning.

AI’s unprecedented capabilities can foster productive dialogue, empowering individuals and societies to enhance accountability. It can also enhance inclusion and representation, supporting a thriving civic space. However, if left unchecked, AI also poses a massive threat to democratic society. For one, AI tends to perpetuate and even exacerbate inequalities due to a lack of diversity. Without adequate safeguards, AI also presents privacy and surveillance concerns, especially when personal data falls into the wrong hands. There is a worrying lack of transparency with regards to the data and algorithms being used by AI platforms and how they are being utilized to make decisions over sensitive issues in the everyday life. This makes it difficult to attribute responsibility should things go awry.

Module Opening

Les bases d'un M1 de mathématiques appliquées en probabilités, statistiques et optimisation.

Les principaux modèles considérés sont: les modèles bayésiens, les modèles gaussiens, les modèles de mélanges de gaussiennes (GMM), les modèles par patchs, les modèles d'entropie maximale. Les outils considérés sont: l'optimisation et les opérateurs proximaux, l'échantillonnage par MCMC ou Langevin, le transport optimal, les réseaux de neurones, ...

L'objectif de ce cours est de donner un large panorama des modèles probabilistes et des outils utilisés dans le domaine de la restauration ou de l'édition d'images numériques.

9 séances de 3h + examen écrit.

Notions en modélisation et en machine learning et/ou deep learning, Programmation en python (librairies numpy, pandas, scikit, pytorch ou tensorflow)

L’objectif de ce cours est de relier la technologie qui bouleverse toutes les sciences et tous les secteurs (l’intelligence artificielle) aux enjeux majeurs pour l’humanité que sont le changement climatique et l’impact de l’activité humaine sur l’environnement. Il abordera de façon complémentaires les sujets de l’impact de l’IA elle-même sur l’environnement, la façon d’utiliser l’IA pour mesurer ces impacts, ou enfin d’activement réduire les effets de l’Homme sur la planète.

CM1 (3h) : Impacts environnementaux de l’intelligence artificielle TP1 (3h) : Étude de cas: évaluation environnementale d’un système d’IA CM2 (3h) : L’exploitation des données climatiques et environnementales TP2 (3h) : Cas d’application d’algorithmes d’apprentissage machine à des données d’infrason en région polaire CM3 (3h) : Tour d’horizon des approches d’apprentissage machine au service de la réduction de notre empreinte environnementale. TP3 (3h) : Etude de cas: exploitation de données de capteurs par techniques d’IA (domaine du grand cycle de l’eau).

Module Opening

Good knowledge and practice of Linear algebra.

The course starts with a basic primer on convex analysis followed by a quick overview of convex duality theory. The second half of the course is focused on algorithms, including first-order and interior point methods, together with bounds on their complexity. The course ends with illustrations of these techniques in various applications.

The objective of this course is to learn to recognize, transform and solve a broad class of convex optimization problems arising in various fields such as machine learning, finance or signal processing.

• 6 cours de 3 heures
• Validation : Examen

• Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press. - Introductory Lectures on Convex Optimization, Y. Nesterov, Springer. - Lectures on Modern Convex Optimization, A. Nemirovski and A. Ben-Tal, SIAM.

Integral calculus, elements of statistics, numerical computation, linear algebra, optimisation, Python.

• Notions de base de physique : Équations de Maxwell (régime quasistatique, loi de Biot et Savart)., Modèles de source.
• Problème direct et inverse en M/EEG : Problème direct (résolution par éléments finis), Débruitage des signaux M/EEG, Problème inverse (MUSIC, Beamforming, Imaging), Validation.
• Analyse statistique de données fonctionnelles : Modèle linéaire, modèles à effets mixtes, Test d’hypothèses, tests non paramétriques, comparaisons multiples, Inférence de modèles de connectivité, apprentissage de réseaux et apprentissage de covariance.
• Vers des interfaces cerveau-ordinateur : Communiquer via l’activité du cerveau, Extraction et classification de caractéristiques pertinentes, sélection de modèle, Rôle du feedback.

This lecture deals with brain functional imaging and its application to create brain computer interfaces using two non-invasive techniques used to estimate brain activity: 1) M/EEG which measures the electro-magnetic field created by cortical currents, 2) functional MRI which measures a signal (BOLD) linked to energy consumption in the brain.

• Cours de 8 séances
• Le mode de validation contient un contrôle écrit ET un TD.
• Le mode de rattrapage est un commentaire critique d’article.

• We provide some lecture notes covering most of the course content.
• Russell A. Poldrack, Jeanette A. Mumford, Thomas E. Nichols. Handbook of Functional MRI Data Analysis.
• Brette and Destexhe eds. Handbook of Neural Activity Measurement. Cambridge University Press 2012.

Une bonne connaissance du calcul différentiel en dimension finie et dans les espaces de Banach. Une certaine familiarité avec les variétés différentielles pourra être utile.

Nous montrerons que la construction et l’étude de ces métriques, le calcul effectif des géodésiques dans ces espaces de formes et la compréhension des cartes exponentielles locales sont des questions d’une grande importance théorique et pratique. Nous verrons que ce point de vue géométrique unifie un grand nombre de questions importantes très concrètes : appariements denses à partir de points marqués ou de nuages de points, appariements de variétés, appariements difféomorphiques d’images dans le cas de grandes déformations, métamorphoses automatiques entre images et ouvre des voies nouvelles pour la construction de modèles probabilistes de formes.

Si le cours s’attachera principalement à expliquer les outils et les concepts qui sont assez nouveaux dans le cadre du traitement d’images et les algorithmes associés, nous proposerons plusieurs illustrations dans le cadre médical pour l’analyse de la variabilité anatomique.

Ce cours a pour objectif de proposer une exposition introductive d’un point de vue géométrique sur les modèles déformables qui consiste à construire des métriques riemanniennes sur des espaces d’objets (n-uplets de points, courbes, régions binaires, surfaces, champ de tenseurs, images en niveau de gris, mesures etc) considérés comme des variétés de dimension finie ou infinie à partir de l’étude des déformations infinitésimales naturelles agissant sur ces objets.

Le cours alternera 9 séances de cours et 3 séances de TP.

L. Younes, Shapes and Diffeomorphisms, Springer 2010.

Each year all MVA lecturers will be invited to propose articles which deserve a reproducible edition. These projects might be co-supervised by researchers from Centre Borelli or other research centers. Specifically, the students are expected to: • Fully understand a proposed article, write a pseudo-code, and review its bibliography. • Design a demo interface to illustrate as better as possible the article. This implies a selection of parameters and their default values, as well as choosing good and bad examples to show. • Write a reproducible version of the article and compare both. • In the final stage of the course, each group of students will review the article prepared by another group.

This is an MVA course about writing a reproducible edition of a scientific work. It could be considered the practical follow up of the MVA course Fondamentaux de la recherche reproductible et du logiciel libre, although both courses are independent. It consists on a tutored project which includes reading in detail a scientific article, the implementation of the method, publication of a complete scientific report associated to the source code, and the creation of an online demonstrator in the IPOL journal system.

The course is made of 7 sessions of 3h hours each. The sessions are mainly practical, for the students to work on their projects. Some of the session will be preceded by a short master class on the topics 2 of the course.

The students are expected to have a background in statistics and computer programming.

• Introduction to medical imaging ;
• Classification ;
• Detection ;
• Segmentation ;
• Registration ;
• Denoising and reconstruction ;
• Generative models (autoencoders, GANs) ;
• Validation, interpretation and reproducibility.

Medical imaging technologies provide unparalleled means to study structure and function of the human body in vivo. Interpretation of medical images is difficult due to the need to take into account three-dimensional, time-varying information from multiple types of medical images. Artificial intelligence (AI) holds great promises for assisting in the interpretation and medical imaging is one of the areas where AI is expected to lead to the most important successes. In the past years, deep learning technologies have led to impressive advances in medical image processing and interpretation. This course covers both theoretical and practical aspects of deep learning for medical imaging. It covers the main tasks involved in medical image analysis (classification, segmentation, registration, generative models…) for which state-of-the-art deep learning techniques are presented, alongside some more traditional image processing and machine learning approaches.

• 9 X 3h (either 3h lecture or 1h30 lecture/1h30 lab)
• validation: article presentation and project

Admission to MVA. Programming skills in Python (and/or C++) are recommended.

Topological Data Analysis (TDA) is a sound family of techniques that is gaining an increasing importance for the interactive analysis and visualization of data in imaging and machine learning applications. Given the increasing size and complexity of current data sets, these approaches aim at helping users understand the complexity of their data by providing insights about its topological and geometric structure.

The soundness, efficiency and robustness of TDA made it increasingly popular in the last few years in a variety of 2D and 3D imaging applications, for various feature extraction tasks. In higher dimensions, these techniques have recently found various applications in unsupervised (clustering) and supervised machine learning.

The purpose of this course is to introduce the main concepts of the recent field of Topological Data Analysis and illustrate their use in imaging (scientific visualization) and machine learning applications, both from a mathematical and practical point of view.

• 6 lectures of 2 hours ;
• 6 practical sessions of 2 hours ;
• 1 final research seminar (3 hours).

[1] H. Edelsbrunner, J. Harer, "Computational Topology: An Introduction", American Mathematical Society, 2010. [2] J. Milnor. "Morse Theory", Princeton University Press, 1963. [3] A. Fomenko and T. Kunii, "Topological modeling for visualization", Springer 1997. [4] J. Tierny, "Topological Data Analysis for Scientific Visualization", Springer, 2018. [5] S. Oudot, "Persistence Theory: From Quiver Representations to Data Analysis". AMS Mathematical Surveys and Monographs, volume 209, 2015. [6] F. Chazal, B. Michel, "An introduction to Topological Data Analysis: fundamental and practical aspects.

Intégration et transformation de Fourier, espaces L^p et l^p. Probabilités (vecteur aléatoire, vecteur gaussien). Notions de base en calcul différentiel et géométrie différentielle plane.

Des notions sur les distributions ne sont pas indispensables mais sont un plus.

Plan du cours :

1. Formation et représentation des images numériques.

• Projection perspective, diffraction, numérisation, échantillonnage. Théorème de Shannon, aliasing.

2. Interpolation et transformations géométriques.

• Interpolation de Shannon et transformée de Fourier discrète, décomposition periodic+smooth.
• Interpolations directes et indirectes, splines, interprétation spectrale.
• Translations sous-pixelliques, zoom, rotation, extrapolation de spectre.
• Aliasing et super-résolution.

3. Interprétation de la phase de la transformée de Fourier.

• Images à phase aléatoire, champs gaussiens et synthèse de textures.
• Cohérence de phase et mesure de netteté.
• Application à la déconvolution aveugle.

4. Pixel infinitésimal et opérateurs différentiels.

• Consistance des schémas aux différences finies.
• Variation totale de Shannon.

L'objectif du cours est de comprendre en détail, sous plusieurs angles différents, le lien entre les images numériques, par nature discrètes, et la réalité continue qu'elles représentent.

8 séances "cours + TP". Examen

L. Moisan, "Modeling and Image Processing" (available on the course web page). L. Moisan, "Periodic plus smooth image decomposition", Journal of Mathematical Imaging and Vision, vol 39:2, pp. 161-179, 2011 (available on the course web page). R. Abergel, L. Moisan, The Shannon Total Variation'', Journal of Mathematical Imaging and Vision, 2017. A. Leclaire, L. Moisan, No-reference image quality assessment and blind deblurring with sharpness metrics exploiting Fourier phase information'', Journal of Mathematical Imaging and Vision, 2015.

Linear algebra, multivariable calculus, Fourier analysis, image processing, programming in python.

The following subjects are covered during the course: 1/ Modeling of optical and SAR (Synthetic Aperture Radar) acquisition systems and radiometric and geometric corrections; 2/ Recovering 3D information from optical and SAR sensors (stereo-vision and multi-stereo, point matching, sub-pixel accuracy, interferometry), 3/ Time series creation and analysis (change detection, multi-temporal change analysis, either on single modality or combining heterogeneous sensors). The required mathematical tools are introduced along the way. Namely, variational calculus, discrete and continuous optimization, approximation theory and spectral analysis, mathematical morphology, statistical modeling and inference.

If there is one source of big data today, it is the continuous stream of high-resolution images from Earth observation satellites. A good understanding of these systems and instruments allows to fully take advantage of this source of information. This course is a well balanced mix of mathematical modeling of these systems and practical works handling remote sensing images retrieved either from space agencies or private providers to solve real-scale imaging problems.

• 9x (3h30 per session).
• Reports and source code of practical sessions.
• Project on a remote sensing subject (report, code and oral presentation).
• The courses will be closely linked to practical work sessions (during the course or to do on your own) giving you a straightforward expertise to handle these data. Usage of a personal laptop is encouraged for practical sessions.
• Evaluation is done through practical works and a project done all along the period. The projects are dedicated to current issues raised by the newly launched or upcoming sensors and rely on machine learning and/or image processing methods.

• Tupin et al. (2014). Remote Sensing Imagery. John Wiley & Sons.
• Nicolas (2017), Les Bases de l’Imagerie Satellitaire, Notes de cours Telecom ParisTech.
• CNES, ONERA, IGN (2008), Imagerie Spatiale Des principes d’acquisition au traitement des images.

Pré-requis : Eléments de statistiques et probabilités, niveau L3/M1

In particular, the following topics will be covered (not necessarily in this order):

• maximum likelihood and Bayesian estimation ;
• linear and logistic regression ;
• clustering: k-means vs mixture models, the EM algorithm ;
• graphical models: definitions, exact and approximate inference algorithm (sum-product) ;
• Gaussian processes.

The course will provide an overview of probabilistic machine learning (that is, learning approaches derived some form of probabilistic modelling) with particular emphasis on graphical models (probabilistic models where dependences are represented by a graph).

• 9 classes of 3 hours each ;
• All classes and materials will be in English. All interactions, homeworks, exams may be done in French or English.

Validation:

• 3 homeworks with simple implementations of algorithms (Matlab, R, Python ou autre) ;
• 1 final exam ;
• Reading a research paper and write a small report (less than 4 pages).

Chris Bishop. Pattern Recognition and Machine Learning. Springer, 2006

Probability theory and convex optimisation notions.

In online learning, data are acquired and treated on the fly; feedbacks are received and algorithms uploaded on the fly. This field has received a lot of attention recently because of the possible applications coming from internet. They include choosing which ads to display, repeated auctions, spam detection, experts/algorithm aggregation (and boosting), etc.

The objectives of the course (in English) is to introduce and study the main concepts (regret, calibration, etc.) of online learning, construct algorithms and show connection with game theory.

We will also cover the bandit setting (cf the course of Reinforcement learning) and its generalization, the partial monitoring

6 séances de 3h + examen.

Prediction, learning, and games Nicolò Cesa-Bianchi and Gábor Lugosi Cambridge University Press, 2006.

Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems S. Bubeck and N. Cesa-Bianchi, . In Foundations and Trends in Machine Learning, Vol 5: No 1, 1-122, 2012.

Approachability, Regret and Calibration: Implications and equivalences. V. Perchet, Journal of Dynamics and Games, 1:181-254, 2014.

Lattimore, T., & Szepesvári, C. (2020). Bandit algorithms. Cambridge University Press.

The prerequisites to the course are a good knowledge of differential calculus and probability theory from the viewpoint of measure theory.

• Introduction to dynamical systems: orbits and phase portraits, invariant manifolds, center manifold in finite dimension.
• Introduction to bifurcation theory: dimension 1 (saddle-node, transcritical, pitchfork), dimension 2 (Hopf), center manifold, normal form, equivariant bifurcations.
• Applications: single spiking neuron dynamics, Turing mechanism for cortical pattern formation, geometric visual hallucinations.
• Mesoscopic models of visual cortical areas: anatomical structure of the visual cortex (V1), functional architecture of V1, neural fields models.
• Neuronal models: aspatial Hodgkin-Huxley model, simplified models, synaptic models, spatial models.
• Importance of noise: Brownian motion, stochastic differential equations, application to neurons.

We present mathematical tools that are central to modeling in neuroscience. The prerequisites to the course are a good knowledge of differential calculus and probability theory from the viewpoint of measure theory. The thrust of the lectures is to show the applicability to neuroscience of the mathematical concepts without giving up mathematical rigor. The concepts presented in the lectures will be illustrated by exercise sessions.

8 séances de 5h. Examen pour la première session, rattrapage sous forme de lecture d’article.

Kandel, Eric R., Principles of neural science, 2013. Byrne, John H., Ruth Heidelberger, et Melvin Neal Waxham, From molecules to networks: an introduction to cellular and molecular neuroscience, 2014. Gerstner, Wulfram, Werner M. Kistler, Richard Naud, et Liam Paninski. Neuronal dynamics: from single neurons to networks and models of cognition, 2014. Koch, Christof. Biophysics of Computation: Information Processing in Single Neurons. 2004. Bressloff, Paul C. Waves in Neural Media, 2014. Eugène Izhikevich, Dynamical systems in neuroscience: the geometry of excitability and bursting, 2006. G

• Basic knowledge of linear algebra, probability, statistics, and a good knowledge of linear models in machine learning are required.
• Basic knowledge of Hilbertian and Fourier analysis is useful.
• Having followed a course on optimization is also useful, but not mandatory.
• Practical coding skills are useful for the data challenge.

We will start with a presentation of the theory of positive definite kernels and reproducing kernel Hilbert spaces, which will allow us to introduce several kernel methods including kernel principal component analysis and support vector machines. Then we will come back to the problem of defining the kernel. We will present the main results about Mercer kernels and semigroup kernels, as well as a few examples of kernel for strings and graphs, taken from applications in computational biology, text processing and image analysis. Finally we will touch upon topics of active research, such as large-scale kernel methods and deep kernel machines.

The goal of this course is to present the mathematical foundations of kernel methods, as well as the main approaches that have emerged so far in kernel design.

Kernel methods are a class of algorithms well suited for such problems. Indeed they extend the applicability of many statistical methods initially designed for vectors to any type of data, without the need for explicit vectorization. The price to pay is the need to define a so-called positive definite kernel function between the objects.

The final note will be an average of a homework (20%), a data challenge (40%), and a final written exam (40%). You can work on the project alone or with up to two friends. Data challenge is now online. Instructions will be given in class to access it.

N. Aronszajn, "Theory of reproducing kernels", Transactions of the American Mathematical Society, 68:337-404, 1950. C. Berg, J.P.R. Christensen et P. Ressel, "Harmonic analysis on semi-groups", Springer, 1994. N. Cristianini and J. Shawe-Taylor, "Kernel Methods for Pattern Analysis", Cambridge University Press, 2004. B. Schölkopf et A. Smola, "Learning with kernels", MIT Press, 2002. B. Schölkopf, K. Tsuda et J.-P. Vert, "Kernel methods in computational biology", MIT Press, 2004. V. Vapnik, "Statistical Learning Theory", Wiley, 1998.

Bases de probabilité, de statistique et d'analyse de Fourier (Cours de L3 suffisant) ; bases de traitement du signal.

Le cours présentera les grands principes de la formation et de l’acquisition des images numériques (capteurs, échantillonnage, quantification, dynamique, bruit), les ingrédients principaux de la structure des images (radiométrie, couleur, géométrie, texture, artefacts d’acquisition), tout en s’attachant à donner une connaissance des outils les plus classiques de l’amélioration ou de l’analyse des images.

Le cours sera aussi souvent que possible illustré par des exemples d’applications issus des domaines de la photographie numérique grand public, de l’imagerie médicale ou de l’imagerie aérienne.

Le premier objectif de ce cours est de familiariser les étudiants avec les images numériques.

Le deuxième objectif est de confronter dans une approche thématique divers outils mathématiques approfondis par ailleurs dans le master (Ondelettes, EDP, approches variationnelles, approches stochastiques, etc.).

• 7 séances de cours (3h)
• 2 séances de TP (3h)
• rendez-vous individuels pour le suivi des projets.
• Validation par projet : rapport, remise d’un code informatique (langage au choix) et soutenance individuelle.

1-Introduction: perception visuelle, théorie de la gestalt, définition de la vision ; 2-La nature discrète des images: échantillonnage, théorie de Shannon, théorie d’Attneave ; 3-Principes de statistique conduisant à la détection d’objets modélisables ; 4-Théorie a contrario: notion de modèle de fond, de NFA, modélisation gaussienne du fond et de la forme à détecter ; 5-Une problématique générique: détection d’anomalies dans les images, différentes théories, apport de l’a contrario ; 6-Comparaison sur des exemples les théories classiques de la détection d’anomalies en imagerie hyperspectrale ; 7-Détection dans les séries temporelles ; 8-Applications à l’imagerie satellitaire récurrente, détection de nuages, détection et catégorisation temporelle des changements.

Le but du cours est d’entraîner les élèves à une discipline qui semble être une des applications les plus fréquentes de l’analyse d’images, de vidéo et de séries temporelles, la détection.

7 à 9 séances de trois heures décomposées en théorie + une analyse de cas. Les étudiants devront rendre régulièrement des exercices élucidant les points techniques du cours, faire des rapports expérimentaux (basés sur des articles IPOL avec démo en ligne), et ils devront aussi mener au moins une analyse approfondie d’un article de détection.

• Bases de théorie des probabilités (notions de théorie de la mesure, de convergences de mesures de probas).
• Bases d'algèbre linéaire (spectre de matrices, notamment symmétriques/hermitiennes).
• Bases (rappelées en cours) d'analyse notamment complexe (notion d'analyticité, intégration complexe).

1/ Compréhension des comportements spectraux de grandes matrices aléatoires (théorème de Marcenko-Pastur, loi du demi-cercle, modèles dits "spike"), de l'apprentissage et l'utilisation des outils théoriques (transformée de Stieltjes, méthodes gaussiennes) et de leur application à l'inférence statistiques de modèles matriciels (estimation de fonctionnelles du spectre, de formes quadratiques, etc.). 2/ Exploiter ces outils pour démontrer une nette rupture à la fois intuitive, pratique et théorique de l'apprentissage statistique en grandes dimensions: il est notamment démontré que nombre de méthodes, apprises par ailleurs au cours du MVA (SVM, méthodes par noyaux et par graphes), voient leurs intuitions et leurs performances s'effondrer lorsque des données de (pas toujours si) grandes tailles sont prises en compte. Les applications concrètes visées concernent entre autres: clustering spectral, méthodes à noyaux, détection de communautés sur des graphe et classification supervisée.

Le cours introduit les rudiments théoriques de la théorie des matrices aléatoires puis son application à l'apprentissage automatisé. Le cours est divisé en deux parties.

Le cours est essentiellement magistral et dispensé au tableau (sauf dernier cours "séminaire" sur l'utilisation moderne de la théorie en apprentissage). Plusieurs DM (devoirs maison, assez simples) ponctuent la première partie pour se familiariser avec l'utilisation des outils. Deux TPs (travaux pratiques sur ordinateur, Matlab ou Python) concluent la première partie (TP Inférence statistique) ainsi qu'une application de la deuxième (TP Détection de communautés sur des graphes).

L'évaluation finale s'effectue par DS (devoir sur table), la note finale étant une moyenne des notes du DS, des TPs et des DMs (ceux n'ayant pas rendu une partie des DMs, TPs n'étant alors évalués que sur le DS).

Polycopié du cours: https://romaincouillet.hebfree.org/docs/courses/rmt/poly.pdf.

• Première partie de R. Couillet, M. Debbah, "Random Matrix Methods for Wireless Communications", Cambridge University Press, 2001. https://romaincouillet.hebfree.org/docs/book_outline.pdf.
• Autres références sur demande.

Basic linear algebra, analysis and probability

Topics :

• Instance-level recognition: camera geometry, local-invariant features, correspondence, efficient visual search
• Category-level recognition: bags of features, sparse coding and dictionary learning
• Neural networks, optimization methods
• Convolutional neural networks for visual recognition
• Motion and human actions
• 3D object recognition
• Weakly-supervised learning for visual recognition

Automated object recognition - and more generally scene analysis - from photographs and videos is the great challenge of computer vision. The objective of this course is to provide a coherent introductory overview of the image, object and scene models, as well as the methods and algorithms, used today to address this challenge.

Organization of courses : 10 lectures of 3 hours each. All materials and lectures will be in English. Reports from assignments and the final project can be done in French or English.

Validation : There will be three programming assignments representing 50% of the grade and a research-oriented final project (including report and presentation) representing 50% of the grade.

D.A. Forsyth and J. Ponce, "Computer Vision: A Modern Approach'', Prentice-Hall, 2nd edition, 2011 J. Ponce, M. Hebert, C. Schmid, and A. Zisserman, "Toward Category-Level Object Recognition'', Lecture Notes in Computer Science 4170, Springer-Verlag, 2007. R. Szeliski, "Computer Vision: Algorithms and Applications", Springer, 2010, Available online: http://szeliski.org/Book/.

Undergraduate courses in Analysis and Probability.

Topics :

• Typology of learning problems
• Statistical models and main algorithms for classification, scoring, ...
• Performance criteria and inference principles
• Convex risk minimization
• Complexity measures
• Aggregation and ensemble methods
• Main theorems

The course presents the mathematical foundations for supervised learning.

Organization :

• 8 theoretical sessions
• 4 practical sessions

Validation :

• Part 1 : partial exam (mandatory)
• Part 2 : final exam or paper review project (report+oral presentation)
• Re-take : written exam or project (proposed only for students who attended Part 1 and Part 2).

S. Boucheron, O. Bousquet, and G. Lugosi. Theory of Classification: a Survey of Recent Advances. ESAIM: Probability and Statistics, 9:323375, 2005.

L. Devroye, L. Györfi, G. Lugosi, A Probabilistic Theory of Pattern Recognition, Springer, New York, 1996.

• Medical Image Modalities and
• Image Filtering andLow Level Operations
• Image Classification
• Segmentation with Deformable Contours and Surfaces
• Parametric and Deformable Registration of Images.

The course is an introduction to medical image analysis, ranging from generic image analysis such as image registration and image segmentation to more advanced techniques in statistical and mechanical modeling for computational anatomy and physiology.

• 8 courses ;
• Validation: Projects + article presentation + quizz (mini exam).

We assume that the students are familiar with the notions introduced in a "Introduction to Probability theory" course. We also assume that they know the conditional expectation and Markov Chains in finite time and finite space.

The course will start with the stochastic gradient algorithm, its theoretical properties and numerical bottlenecks. After a brief introduction to Bayesian inference we will discuss the numerical challenges when computing bayesian estimators. This will lead us to the EM algorithm and its stochastic versions, and more generally to Majorize – Minimize algorithms.

Stochastic approximations will be detailed to better understand the convergence conditions of the previous algorithms.

The second part of the course will be devoted to random variable simulation methods. Starting from the rejection method, we will then present some classical Markov Chain Monte Carlo samplers (Metropolis Hastings and Gibbs algorithms). We will then discuss recent advances in MCMC : Adaptive MCMC, adaptive parallel tempering and Approximated Bayesian Computing methods.

This course will detail statistical computational methods and bayesian inference. This course propose to introduce several stochastic optimisation algorithms and sampling methods. The goal is to understand the theory and the numerical implementations issues related to these algorithms.

• This course will be decomposed into 20 h of lectures and 20h of training and lab work sessions.
• Validation : 2/3 = homework following each training session (4) and 1/3 = Oral presentation of one scientific paper ; Team work (2), no report.

For references on probabilities, you can look at Jean-François Legall's course which is available online. You will find the basics of measurement theory, probabilities and Markov chains. Non-uniform random variate generation, Luc Devroye (available online) The bayesian Choice, Christian Robert Méthodes de Monte Carlo par Chaines de Markov, Christian Robert Stochastic approximations with decreasing gain: Convergence and Asymptotic theory, Bernard Delyon.

Each session will comprise two hours of lecture followed by two hours of programming sessions.

The ALTEGRAD course aims at providing an overview of state-of-the-art ML and AI methods for text and graph data with a significant focus on applications.

• 7 séances de 4 heures ;
• Grading for the course will be based on a final data challenge plus lab based evaluation.

• Theoretical tools: linear algebra, basic probabilities, reinforcement learning ;
• Programming tools: familiarity with python.

Lecture 1 : MDP and Dynamic Programming
Lecture 2 : The first algorithms of Reinforcement Learning
Lecture 3 : The Actors : Policy Iteration and Gradient
Lecture 4 : The Critics : RL with functiun Approximation
Lecture 5 : Scaling up RL : Towards Deep RL and Continuous MDPS
Lecture 6 : Exploration-Exploitation in RL
Lecture 7 : Average-reward Reinforcement Learning and Instance Optimal Algorithms
Lecture 8 : Bandit Methods for Pure Exploration and Planning in RL

This class aims at providing a comprehensive and modern introduction to reinforcement learning concepts and algorithms. It endeavors to provide a solid formal basis on foundational notions of reinforcement learning.

8 lectures + 1 written exam

Elementary probability theory (discrete and continuous) Fourier analysis, differential calculus.

This course addresses one of the fundamental problems of signal and image processing, the separation of noise and signal. This was already the key problem of Shannon’s foundational Mathematical Theory of Communication.

This course organized by three image processing specialists and deep learning practitioners stands at this crucial crossroad. We will explain the classical theories, the neural devices and demonstrate what perspectives and cross-fertilization this comparison yields. Both theories process image patches.

The course will be designed to understand in depth patch structure and the structure of the global ensemble of patches.

1-Explore the structure of images at « patch » level. (Patches are small image extracts that are processed in computational neural networks and in recent image processing. The current dimension that start being well understood is about 8×8=64 to 60×60=3600).

2-Apply it to a fundamental problem requiring an understanding of this structure: image denoising.

3-Compare image processing designed by humans to image processing learned by deep neural networks.

• Each session will imply a combination of course, online experiments with IPOL
• The course consist of theoretical lectures and practical workshops. Two types of practical workshops • IPOL workshops: testing image denoising methods on the IPOL platform (Image Processing On Line, www.ipol.im). No programming is required. • Deep-learning workshops: guided workshops were we will experiment training and using CNNs for denoising. These require some basic Python programming.

Validation :

1. Simple mathematical exercises on the subject of the course + experimental report on image processing experiments made on line (no programming will be required). Both delivered each week + exercices on Colab Notebooks.
2. A final oral examination (or written if the number of students is too important).

• A. Buades, B. Coll, and J. M. Morel. A review of image denoising algorithms, with a new one. Multiscale Modeling Simulation 2005. • K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian. Image denoising by sparse 3D transform-domain collaborative filtering. IEEE Transactions on image processing , 2007. • D.Zoran and Y.Weiss. Scale invariance and noise in natural images. In Computer,Vision, 2009 IEEE 12th International Conference, 2009. • G. Facciolo, N. Pierazzo, and J.-M. Morel. Conservative Scale Recomposition for Multiscale Denoising SIAM Journal on Imaging Sciences.

Linear algebra, basic statistics, others tools needed will be covered in the lectures.

We will also discuss online decision-making on graphs, suitable for recommender systems or online advertising. Finally, we will always discuss the scalability of all approaches and learn how to address huge graphs in practice. The lectures will show not only how but mostly why things work. The students will learn relevant topics from spectral graph theory, learning theory, bandit theory, necessary mathematical concepts and the concrete graph-based approaches for typical machine learning problems. The practical sessions will provide hands-on experience on interesting applications (e.g., online face recognizer) and state-of-the-art graphs processing tools (e.g., GraphLab).

The graphs come handy whenever we deal with relations between the objects. This course, focused on learning, will present methods involving two main sources of graphs in ML:

1. graphs coming from networks, e.g., social, biological, technology, etc.
2. graphs coming from flat (often vision) data, where a graph serves as a useful nonparametric basis and is an effective data representation for tasks as spectral clustering, manifold or semi-supervised learning.

• The course will feature 11 sessions, 8 lectures and 3 recitations (TD), each of them 2 hours long. There may be a special session with guest lectures. There may be also an extra homework with extra credit.
• The evaluation is be based on reports from TD and from the projects. Several project topics will be proposed but the students will be able to come up with their own and they will be able to work in groups of 2-3 people. The slides and the scribes from the lectures are the best reference and are made to be comprehensive There is no recommended textbook. The material we cover is mostly based on research papers, some of which very recent.

Have basic knowledge of linear algebra and functionnal analysis. Be familiar with Python programming.

• Large scale optimization
• Proximal algorithms
• Majorization-Minimization methods
• Parallel optimization
• Distributed optimization strategies

The objective of this course is to introduce the theoretical background which makes it possible to develop efficient algorithms to successfully address these problems by taking advantage of modern multicore or distributed computing architectures. This course will be mainly focused on nonlinear optimization tools for dealing with convex problems. Proximal tools, splitting techniques and Majorization-Minimization strategies which are now very popular for processing massive datasets will be presented. Illustrations of these methods on various applicative examples will be provided.

• Each section of the course is divided into 1h30' lecture and 1h30' lab. The labs will include Python programming of optimization algorithms and will provide the students the opportunity to apply the methods seen in lecture to applicative examples in the context of datascience.
• Validation: TP reports + exam.

• D. Bertsekas, Nonlinear programming, Athena Scientic, Belmont, Massachussets, 1995. - Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course, Springer, 2004. - S. Boyd and L. Vandenberghe, Convex optimization, Cambridge University Pre.

Le cours nécessite de maîtriser de Python et Pytorch ainsi que des bases d’algèbre linéaire et d’optimisation.

• Understanding Large Language Models
  • What are Large Language Models (LLMs)
  • Overview of applications: natural language processing tasks, code generation, proof generation
  • Challenges and limitations of LLMs
• Working with Text Data
  • Data preprocessing techniques for text data
  • Tokenization and vocabulary building
• Attention Mechanisms
  • Types of attention mechanisms (self-attention, multi-head attention)
  • Efficient implementations
• Implementing a GPT Model from scratch
  • Overview of Generative Pre-trained Transformers (GPT)
  • Architecture of GPT models (normalisation layers, residual connections, positional embedding)
  • Pretraining on Unlabeled Data: scaling laws, evaluation metrics
• Fine Tuning
  • Fine tuning for text classification
  • Fine tuning with human feedback and reward models
• Retrieval Augmented Generation
  • Using retrieval mechanisms to enhance generation tasks
  • Language agents
• LLMs for code generation
  • Code generation tasks (code completion, code summarization, code repair)
  • Learning from code-related feedback
  • Inference algorithms for code
• LLMs and formal code
  • LLMs for mathematics
  • Neural theorem proving
  • Verified code synthesis

L’objectif de ce cours est de présenter les Large Language Models, en insistant particulièrement sur l’architecture Transformers. La première moitié du cours porte sur toutes les notions essentielles pour cette architecture, et l’objectif est de coder en entier un Transformer utilisable, en ayant compris en profondeur et avec des outils mathématiques les mécanismes d’attention. La seconde moitié du cours discute de certaines applications des LLMs dans des cadres formels (code, preuve).

8 séances

Les sujets suivants seront abordés:

– Transport de probabilités en apprentissage profond. Génération et échantillonnage par transport.

– Équation de Fokker Plank donnant l’évolution de la densité de probabilité d’un système dynamique. Équation de Langevin pour l’échantillonnage de probabilités

– Génération de données par score diffusion. Applications à l’image et au son.  Lien avec le débruitage et la formule de Tweety-Myasawa.

– Apprentissage du score avec des réseaux de neurones profonds. Généralisation de l’apprentissage pour la génération de données.

– Interprétation des réseaux. Débruitage et parcimonie dans des bases orthogonales.

– Génération de données conditionnée par une information complémentaire

– Interpolant stochastiques pour la prédiction. Applications à la prédiction de systèmes physiques chaotiques comme la météorologie.

Le cours étudie l’état de l’art de la génération d’images, de sons et de données scientifiques par réseaux de neurones profonds. Cela s’obtient par échantillonnage de  distributions de probabilités, grâce à une équation de transport. Le cours se concentre sur l’équation de score diffusion. Elle transforme un bruit blanc, en effectuant un débruitage progressif pour générer des données (images, sons,…). Cela nécessite d’estimer le score de la densité de probabilité, avec un réseau de neurone profond. Le cours introduit les bases mathématiques, algorithmiques et certaines applications.

Les sujets suivants seront abordés:

– Transport de probabilités en apprentissage profond. Génération et échantillonnage par transport.

– Équation de Fokker Plank donnant l’évolution de la densité de probabilité d’un système dynamique. Équation de Langevin pour l’échantillonnage de probabilités

– Génération de données par score diffusion. Applications à l’image et au son.  Lien avec le débruitage et la formule de Tweety-Myasawa.

– Apprentissage du score avec des réseaux de neurones profonds. Généralisation de l’apprentissage pour la génération de données.

– Interprétation des réseaux. Débruitage et parcimonie dans des bases orthogonales.

– Génération de données conditionnée par une information complémentaire

– Interpolant stochastiques pour la prédiction. Applications à la prédiction de systèmes physiques chaotiques comme la météorologie.

8 séances : une séance de cours est suivie d’une présentation par un chercheur d’un domaine de recherche en lien avec le cours.
Le cours est validé par un projet sur l'un des challenges proposé.

Python with numpy proficiency is required. Some familiarity with scipy, opencv,
scikit-image, pandas, and one of the major neural network frameworks (pytorch, tensorflow,
jax) is recommended. Jupyter will be used for interactive teaching and for evaluation.

1. Overview of technical and chemical imaging; relation to materiality
2. Cross-modal image registration
3. Modeling conditional expectation in multimodal imaging of oil paintings
4. Direct microstructural analysis of paintings
5. Text and image embeddings with pre-trained networks
6. Image-to-image translation with CNNs

Art history and cultural heritage science are undergoing rapid advances due to the
simultaneous advent of new and inexpensive imaging modalities, fast computation, and ubiquitous high-speed internet. We can easily collect gigabytes or terabytes of multimodal imaging data about an artwork such as a painting, offering the ability to dramatically improve our understanding of who made it, how it was made, its state of conservation, and its relation to other artworks. Additionally, cultural heritage institutions are digitizing millions of works and making them freely available, presenting opportunities for researchers to investigate and visualize central art-historical questions such as attribution, style, and iconography in new
ways.
In all cases, extracting the full value from these data requires the extensive use of
sophisticated computational tools. The aims of this course are two-fold: first, to familiarize students with the rich and little-known world of cultural heritage imaging and its many fascinating and challenging problems; and second, to provide an introduction to a selection of the most important recent developments in computer vision and deep learning to solve these
problems.

A considerable portion of each session will involve hands-on work with real data from across the instructor’s 19 years of experience in the field of cultural heritage imaging. Course
readings will include important papers from the computer vision and deep learning fields (KeyNet, MAGSAC++, Neural Style Transfer, U-Net, CLIP, DINOv2, etc.)

• At least one basic course in Statistics, Probability, Differential Calculus, Optimization and Linear Algebra
• Good knowledge about Statistical Learning
• At least one introductory course about Deep Learning
• At least one basic course in Programming (Python and Pytorch)
• Basic concepts of image processing and computer vision
• Knowledge about Medical Imaging is not necessary

• Representation Learning
• Transfer Learning
• Domain Adaptation
• Multi-task Learning
• Knowledge Distillation
• Self-Supervised Learning and Foundation models
• Attention and Transformers
• Disentangled Representations using Generative Models
• Uncertainty, Interpretability and Explainability in Neural Networks

Good and expressive data representations can improve the accuracy of machine learning problems and ease interpretability and transfer. For computer vision and medical imaging tasks, handcrafting good data representations, a.k.a. feature engineering, was traditionally hard. Deep Learning has changed this paradigm by allowing the automatic discovery of discriminative, relevant and well-organized representations (i.e., mappings) from data. This is known as representation learning. The objective of this course is to provide an introduction to representation learning in computer vision and medical imaging applications.

8 lectures divided into 1,5h of theory and 1,5h of practical session + 1 session of exam

first year level knowledge in statistics and probability

Lecture 1
• Review of fundamental concepts in stochastic processes.
• Introduction to standard Brownian motion.
• Properties and path regularity of Brownian motion.

Lecture 2
• Introduction to continuous-time martingales.
• Quadratic variation and Doob-Meyer decomposition.
• Martingale convergence theorems.

Lecture 3
• Stochastic integrals with respect to continuous martingales.
• Itô isometry and Itô integral properties.

Lecture 4
• Itô’s formula and applications.
• Solutions to stochastic differential equations (SDEs).
• Connections between SDEs and PDEs (Fokker–Planck, Kolmogorov).

Lecture 5
• Girsanov’s theorem and change of measure.
• Radon-Nikodym derivatives between diffusion laws.
• Applications to likelihood ratios and importance sampling.

Lecture 6
• Martingale problem formulation.
• Equivalence between martingale problems and SDEs.
• Weak vs. strong solutions.

Lecture 7
• Introduction to diffusion models in generative modeling.
• Continuous-time perspective on diffusion models.
• Sampling guarantees and theoretical underpinnings.

Lecture 8
• Diffusion-based MCMC methods.
• Unadjusted Langevin Algorithm (ULA): analysis and limitations.
• Overdamped Langevin dynamics and extensions.

Stochastic calculus has become an essential tool for understanding and justifying modern machine learning techniques, such as the Unadjusted Langevin Algorithm and diffusion models. To equip students with the necessary background, this course offers an introduction to stochastic calculus and its applications in machine learning, with a particular focus on sampling and generative modeling.
The course is naturally divided into two parts. The first part will cover the fundamentals of Itô calculus, including diffusion processes and their connections to partial differential equations. The second part will introduce applications of stochastic calculus in the analysis of diffusion-based Markov Chain Monte Carlo (MCMC) methods and generative models.

The course has three main objectives.
The first is to present the foundational concepts of stochastic calculus and Itô calculus. The second is to develop familiarity with stochastic differential equations and diffusion processes. Finally, students should be able to apply these tools to the design and analysis of modern machine learning methods, such as diffusion-based MCMC and generative models.
On successful completion of this course, a student will be able to:
• Apply the fundamental concepts of stochastic calculus and explain their relevance in modern statistics, machine learning, and applied contexts.
• Demonstrate familiarity with diffusion processes and their applications in machine learning.
• Use stochastic calculus to understand and design modern generative models.
• Apply stochastic calculus to design and analyze contemporary sampling methods.

Week 1: Introduction to Explainable AI (XAI)
● Overview of XAI:
○ What is Explainable AI?
○ Importance and challenges of interpretability
○ Real-world applications of XAI (e.g., healthcare, finance, autonomous systems)
○ Introduction to different types of explanations in AI
● LIME & SHAP (post-hoc explanation):
○ Understanding Local Interpretable Model-agnostic Explanations (LIME) [2]
○ Introduction to SHAP (SHapley Additive exPlanations) [3] and Kernel SHAP
● Hands-on Tutorial : Implementing LIME and SHAP on vision tasks (TP on vision)

Week 2 Introduction to Explainable AI (XAI)
● Attribution Methods (CAM & Grad-CAM & Gradient based strategy post-hoc explanation) :
○ Class Activation Mapping (CAM)
○ Gradient-weighted Class Activation Mapping (Grad-CAM)[1]
○ Application to convolutional neural networks (CNNs)
○ Integrated gradient
● Hands-on Tutorial : Using CAM and Grad-CAM to interpret vision models (TP on vision)

Week 3: Variance-based Sensitivity Analysis
● Variance-based Sensitivity Analysis (post-hoc explanation) :
○ Overview of sensitivity analysis methods
○ Mathematical foundations and applications
○ Review of key articles on variance-based methods for XAI [4][5]
● Hands-on Tutorial :Applying variance-based sensitivity analysis on audio models (TP on audio)

Week 4: Counterfactual Explanations
● Understanding Counterfactuals :
○ Definition and theory of counterfactual explanations [6]
○ Application in AI models for decision-making transparency
● Hands-on Tutorial : Counterfactual explanations for audio-based AI systems (TP on audio)

Week 5: Concept Bottleneck Models
● Concept Bottleneck Models :
○ Overview of Concept Bottleneck Models and their role in improving interpretability [8,9]
○ Using intermediate concepts to explain final predictions
● Hands-on Tutorial : Implementing and evaluating Concept Bottleneck Models for vision-based tasks (TP on vision)

Week 6: Concept Activation Vectors (CAVs)
● Concept Activation Vectors :
○ Introduction to CAVs for interpreting deep learning models [10]
○ How CAVs connect human-understandable concepts to neural network activations
● Hands-on Tutorial : Using CAVs to interpret vision-language models (TP on vision-NLP)

Week 7: Prototype Networks
● Prototype Networks :
○ Understanding Prototype Networks and how they improve explainability by leveraging representative prototypes for predictions [11]
● Hands-on Tutorial : Building and testing Prototype Networks for audio-related tasks (TP on audio)

Week 8: Chain of Thought Reasoning
● Chain of Thought Reasoning :
○ How models can simulate human-like reasoning processes through chains of thought [12]
○ Importance of step-by-step explanations in complex decision-making systems
● Hands-on Tutorial : Applying Chain of Thought reasoning in NLP models (TP on NLP)

Week 9: Knowledge Graphs in XAI
● Knowledge Graphs :
○ Introduction to knowledge graphs and their use in enhancing model interpretability [13]
○ Role of knowledge graphs in NLP and AI systems for structured explanations
● Hands-on Tutorial : Integrating knowledge graphs into NLP models (TP on NLP)

Week 10: Final Project and Exam
● Project and Exam:
○ Final exam (1h)
○ Students work on a final project to apply multiple XAI techniques across a multimodal dataset (2h)

This course explores Explainable Artificial Intelligence (XAI), a crucial subfield of machine learning dedicated to enhancing the transparency of complex models. While modern AI systems—particularly Deep Neural Networks (DNNs) and Foundation Models achieve state-of-the-art performance, their black-box nature makes it challenging to understand the reasoning behind their predictions. This lack of interpretability raises concerns about trust, accountability, and the ability to extract meaningful insights from these models.
The course examines two key perspectives in XAI:
1. The argument for using inherently interpretable models in high-stakes domains such as healthcare and finance.
2. The development of post hoc explanation techniques that provide insight into complex models after training.
Students will engage with a variety of state-of-the-art XAI methods across multiple modalities, including computer vision, audio processing, and natural language processing (NLP). Topics covered include attribution techniques, sensitivity analysis, Concept Bottleneck Models, Concept Activation Vectors (CAVs), and Counterfactual Explanations. Through hands-on exercises, students will gain practical experience applying XAI techniques, equipping them to enhance transparency and interpretability across diverse AI applications.

Required Reading and Resources:
1. https://github.com/jacobgil/pytorch-grad-cam
2. Ribeiro, M. T., Singh, S., & Guestrin, C. (2016). « Why should I trust you? » Explaining the predictions of any classifier. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining.
3. Lundberg, S. M., & Lee, S. I. (2017). A unified approach to interpreting model predictions. Advances in Neural Information Processing Systems (NeurIPS).
4. Sobol, Ilya M. « Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. » Mathematics and computers in simulation 55.1-3 (2001): 271-280.
5. Fel, T., Cadène, R., Chalvidal, M., Cord, M., Vigouroux, D., & Serre, T. (2021). Look at the variance! efficient black-box explanations with sobol-based sensitivity analysis. Advances in neural information processing systems, 34, 26005-26014.
6. Mothilal, Ramaravind K., Amit Sharma, and Chenhao Tan. « Explaining machine learning classifiers through diverse counterfactual explanations. » Proceedings of the 2020 conference on fairness, accountability, and transparency. 2020.
7. Agerri, R., & García-Serrano, A. (2021). « Multimodal deep learning: A review of the state of the art. » arXiv:2111.04138.
8. Koh, Pang Wei, et al. « Concept bottleneck models. » International conference on machine learning. PMLR, 2020.
9. Kazmierczak, R., Berthier, E., Frehse, G., & Franchi, G. (2023). CLIP-QDA: An explainable concept bottleneck model. arXiv preprint arXiv:2312.00110.
10. Parekh, J., Khayatan, P., Shukor, M., Newson, A., & Cord, M. (2024). A concept-based explainability framework for large multimodal models. Advances in Neural Information Processing Systems, 37, 135783-135818.
11. Donnelly, Jon, Alina Jade Barnett, and Chaofan Chen. « Deformable protopnet: An interpretable image classifier using deformable prototypes. » Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2022.
12. Saparov, Abulhair, and He He. « Language models are greedy reasoners: A systematic formal analysis of chain-of-thought. » arXiv preprint arXiv:2210.01240 (2022).
13. Tiddi, Ilaria, and Stefan Schlobach. « Knowledge graphs as tools for explainable machine learning: A survey. » Artificial Intelligence 302 (2022): 103627.
14. https://christophm.github.io/interpretable-ml-book/

We will cover:
Core techniques for distributed training
Modern frameworks and scaling strategies
Practical implementations with real-world toolchains
Theoretical underpinnings of large-scale learning
Inference and applications

This course introduces the foundations and practices of training modern Large Language Models (LLMs) at scale. Students will learn how deep learning models are trained across multiple GPUs, nodes, and clusters, and why distributed training is the key to enabling today’s largest AI systems.

Enrollment will be limited to 60 students. 
The course will consist of 8 sessions. The first 7 sessions will each include 2 hours of lectures followed by 2 hours of hands-on lab work. The final session will be dedicated to grading.
1. Foundations of distributed LLM Training
2. Hardware and Software Ecosystem
3. Parallelism I: Fundamental Techniques
4. Parallelism II: Advanced Use Cases
5. Synchronization and Communication Strategies
6. Inference at Scale
7. Data, Evaluation, Metrics, Alignment, Ethics, and RL(HF) 
8. Poster Session and Final Evaluation

La durée du PFE/stage est au minimum de quatre mois, sauf pour les élèves en double diplôme contraints à un stage plus long.

Le PFE/stage peut débuter après la fin des cours et il peut se poursuivre au-delà de la date limite de remise du rapport.

L’étudiant choisit un projet de fin d'étude /stage, de RECHERCHE , ayant reçu l’agrément d’un enseignant du master, qui doit correspondre aux thématiques enseignées. Le PFE / stage doit présenter un enjeu de recherche scientifique réel et le développement applicatif d’un des thèmes développés dans le master. Un répertoire des offres reçues par le secrétariat est mis à la disposition des étudiants.

1 / Rapport : chaque étudiant doit remettre au secrétariat du master un rapport de recherche écrit, le plus complet et le plus illustré possible afin de rendre compte de manière détaillée des travaux de recherche effectués 2 / Soutenance : la présentation orale du travail est très fortement conseillée et compte dans la note de PFE/stage. 3 / Fiche d’évaluation : la fiche d’évaluation doit être complétée par le tuteur de stage et l’enseignant référent à l’issue de la soutenance. 4 / Jury : le jury du master examine l’ensemble des rapports et fiches d’évaluation et se réserve le droit de modifier la note de PFE/stage proposée.

Une note de PFE/stage supérieure à 10/20 est impérative pour obtenir le master.