• Designed and deployed an LLM-based brand-identification pipeline

• Systematically evaluate the model's hierarchy by truncating the backbone at varying depths, to identify the exact point where task-relevant performance peaks or plateaus for emotion recognition.
• Correlate layer-wise activations with classical neuroscientific biomarkers (Alpha/Beta power, spatial topography) to reveal whether certain layers specialize in simple rhythms while others focus on complex clinical patterns.
• Design a mechanism to fuse the layers identified as "experts" at specific features, to test whether a weighted fusion of diverse layers outperforms the standard approach of using only the final layer.

[1] Wang, Jiquan, et al. "CBraMod: A criss-cross brain foundation model for EEG decoding." arXiv:2412.07236 (2024).
[2] Zhou, Yuchen, et al. "CSBrain: A cross-scale spatiotemporal brain foundation model for EEG decoding." arXiv:2506.23075 (2025).
Supervised by Tuan-Kiet Doan (tuan.doan@ip-paris.fr)

• Mathematically model data and physical processes, and be able to extract relevant information and knowledge through statistical tools.
• Develop a learning model from data, with honest testing that takes computational limitations into account.

• Build new non-parametric estimators in situations not covered in class.
• Critique techniques used with respect to their complexity and intrinsic performance.

• Explain the fundamental concepts of statistical learning and relate them to the essential choices (representation, modeling, optimization, evaluation) to be made when facing a given problem.
• Explain the models and the learning algorithms dedicated to them, the reasoning behind their construction, and compare them with each other.
• Implement methods (neural or not) on supervised classification or regression tasks; in particular, evaluate them.

• Calculate the gradient of the loss of a generalized linear model.
• Manipulate convex inequalities in order to prove the convergence of an algorithm.
• Identify the properties of an optimization problem in order to choose an appropriate resolution method.
• Reformulate an optimization problem using Lagrangian duality.
• Implement an optimization algorithm using a closed form gradient or automatic differentiation.

• Explain the difficulties associated with processing textual language data and the related tasks.
• Explain methods of numerical representation of text, and basic methods of text processing for classical tasks.
• Describe the elements leading to the successful use of neural models for the representation and processing of written language.
• Implement methods (traditional and early neural approaches) on a range of simple tasks, using Python and specialized libraries (NLTK, Gensim, Scikit-learn).

• Explain the theory underlying the main architectures and learning paradigms of deep learning.
• Program these architectures in Python using the PyTorch deep learning framework.
• Apply these architectures to typical computer vision, NLP, or audio problems such as classification, regression, or generation.

• Basic understanding of modern database systems, their function, and implementation, and be able to model databases.
• Formulate queries over databases using SQL, create and update databases using SQL, understand the concepts of query processing and optimization.

• Model complex systems using graphs.
• Apply learning techniques on graphs.
• Interpret the results obtained.

• Compute the conditional expectation of a random variable given a sigma-algebra.
• Describe and compute the conditional distribution of a random variable given a sigma-algebra or another random variable.
• Recognize and use a sufficient statistic to estimate a parameter.
• Define, recognize and study a martingale, in particular its asymptotic behavior.

• Characterize a Markov chain and its kernel.
• Compute conditional expectations and probabilities of future events or statistics given the past by exploiting the Markov property, including when this future occurs at random times.

• Understand phenomena related to high dimension.
• Master fundamental probabilistic tools for the analysis of learning algorithms.
• Implement central mathematical techniques in preparation for a Master 2 in statistics and data science.

• Build a quadrature method of any order.
• Define basic and importance sampling Monte Carlo methods.
• Choose an ODE method adapted to the problem at stake.
• Compare the numerical methods both from their theoretical properties and their experimental performance.
• Prove convergence by splitting the global error into consistence and stability errors.

• Model physical phenomena or noisy time signals using stochastic differential equations.
• Evaluate functionals of solutions of stochastic differential equations.
• Simulate solutions of stochastic differential equations.

• Define a probabilistic model of a discrete-event phenomenon.
• Define a probabilistic model of a system with a spatial component.
• Evaluate the performance of the previously modeled systems.

• Describe the processing cycle of a web page, the HTTP protocol, its handling by a browser, its internal representation (the DOM), and its presentation to the user.
• Develop programs that interface with this ecosystem: on the server and in a browser.
• Use the basic libraries of web programming.
• Search for new libraries specialized for particular application domains, interpret their documentation, context, and feasibility for a given problem.

• Solve linear systems and determine the LU decomposition of matrices.
• Determine the eigenvalues and eigenvectors of symmetric matrices.
• Model and solve linear optimization problems using the simplex algorithm. Express the dual problem of a linear optimization problem and use the existing links between the primal and dual problems.
• Design and apply gradient methods to solve nonlinear optimization problems with or without constraints, in one or several dimensions.
• Identify points of the considered domain satisfying necessary or sufficient conditions for local optimality or, in the convex case, for global optimality.

• Identify useful/relevant resources and their veracity in order to build their analysis.
• Sort and use these resources to complement the different tools presented in class.
• Analyze and interpret the observations resulting from the analysis tools.
• Produce and justify strategic recommendations for one of the market players.

• Interpret the main indicators of finance and accounting.
• Analyze a balance sheet, investments and depreciation of a company.
• Explain inventory and how salaries work.
• Assess inflation and corporate debt.
• Explain corporate income tax.

• Understand and situate the "human factor" within complex socio-technical systems.
• Describe and explain the main cognitive processes of humans.
• Identify the benefits of taking humans into account in design processes, and describe and critique the main strategies for doing so.
• Identify the main ethical issues related to behavior measurement and the integration of users in design.
• Identify the courses that further explore these themes (TSE, SES, HC).

• Define the main concepts of sociology such as identity, community, social capital, norm, privacy, public sphere, and social structures.
• Identify and name social dynamics within social networks and their impact on organizations.
• Analyze personal use of technology with critical distance.
• Use sociological concepts to demystify Internet-related myths.
• Justify professional decisions based on a deep understanding of the mechanisms of social appropriation of technologies.

An introduction to contemporary philosophy themes renewed by empirical findings from biology and psychology, examining both the underlying research and the questions it raises. No prior knowledge required; the course aims to equip students with concepts to understand modern debates. Topics covered this year:

• Identity in peril: from the Ship of Theseus to schizophrenia.
• Is morality a product of natural Evolution? From cooperation among vampires to Frans de Waal's monkeys.
• How is submission produced? From Stanley Milgram's experiments to the Panopticon.
• Why are we afraid of inferiority? From Tocqueville to the rankings of the Grandes Écoles.
• Is death an ephemeral invention of life? From August Weismann to transhumanism.