The autumn school will have 4 courses and 5 invited speakers. Please refer to the planning for definitive hours.

Courses

C1. Rafaël Pinot -- The Marauders Map of adversarial examples: State of knowledge on evasion attacks in machine learning

In this small lecture, we will examine an important security challenge in modern machine learning: adversarial example attacks. State-of-the-art models are highly vulnerable to these attacks, which raises serious security concerns, particularly when such models are deployed in critical AI-driven technologies, such as self-driving cars or fraud detection systems. Beyond their security implications, adversarial attacks also reveal how limited our understanding of these models remains, and how little control we truly have over their behavior. The problem of adversarial examples is far from solved and continues to be an active area of research. We will provide insights to help navigate this field by outlining the current state of knowledge: how adversarial attacks are constructed, what strategies exist to mitigate them, and what open problems remains, especially concerning their impact on learning theory.

C2. Adrien Taylor -- Convex Optimization and First-Order Algorithms for Data Science

This short course introduces key algorithmic principles in first-order and convex optimization, with an emphasis on their relevance to data science and machine learning. It covers both classical foundations and recent developments, aiming to highlight core ideas behind algorithm design and analysis in modern optimization. The class assumes basic familiarity with linear algebra and calculus.

C3. Aymeric Dieuleveut -- Conformal prediction: from a general introduction towards conditional guarantees    

In this introductory lecture, I will give an introduction to the setup of conformal prediction, in particular the setup, algorithmic solutions, and challenges. I will then focus on conditional guarantees: from impossibility theorems in the worst case, towards approximate results in asymptotic or non asymptotic setups. I will conclude by discussing how these techniques can be used in practice today.

C4. Marylou Gabrié -- Transport based generative modeling and applications to sampling   

In this mini-course we will discuss the modeling and sampling of high-dimensional probability distributions in the current context of highly-effective generative models. We will focus in particular on generative models based on transport maps: normalizing flows, diffusion models and flow matchings.

Invited Speakers

 Laëtitia Chapel -- Approximating Optimal Transport plans with Sliced-Wasserstein   

Optimal Transport (OT) has become a key tool for comparing probability distributions, especially through the Wasserstein distance. Used as a loss function, it performs well across tasks such as classification, domain adaptation, and generative modeling. A major advantage of OT is that it produces an optimal coupling revealing explicit correspondences between samples, enabling applications like shape matching, color transfer, or aligning data distributions with priors in generative models.

However, computing transport plans remains computationally expensive. The Sliced-Wasserstein Distance (SWD) offers a faster way to approximate the Wasserstein distance by projecting distributions onto one-dimensional subspaces, where closed-form solutions exist. Importantly, SWD alone does not approximate the transport plan. Recent work introduces a slicing scheme that enables approximation of both the OT distance and the transport plan. After a quick review of OT and of the the vanilla Sliced-Wasserstein distance, I will introduce this new scheme and will demonstrate its practical value across applications, including a sliced OT-based conditional flow matching approach for image generation, where fast computation of transport plans is essential.

Thomas Moreau -- Optimization bilevel et unrolling   

Bi-level optimization has emerged as a principled framework for model selection in settings where the model output is obtained through an optimization problem, common in imaging, inverse problems, and physics-based models.

In this talk, I will introduce the bi-level optimization paradigm and its relevance in machine learning and inverse problems, as well as the concept of unrolling for computing hypergradients.

I will then provide practical insights on recent results, focusing on advances for bi-level solvers such as SOBA, and theoretical and empirical results on unrolled networks.

Throughout, I’ll emphasize the interplay between optimization, learning, and algorithmic structure.

Mathilde Mougeot -- Machine learning and numerical simulations. Interplay between data and physical models.

In recent years, considerable progress has been made in implementing decision support procedures based on machine learning methods through the use of very large databases and learning algorithms. 

In many application areas, the available databases are modest in size, raising the question of whether it is reasonable, in this context, to seek to develop powerful tools based on machine learning techniques.  This presentation describes hybrid models that use knowledge from physics to implement effective machine learning models with an economy of data.

Aurélien Bellet -- Privacy in Machine Learning

Abstract: Machine learning models can inadvertently leak sensitive information about the data used to train them. This talk will begin with an overview of the main classes of privacy attacks targeting machine learning models. I will then introduce privacy-preserving approaches, focusing on the foundations of differential privacy and how it enables training with provable and robust guarantees. Building on this, I will discuss auditing methods to assess and enforce privacy protections in practice. I will conclude by highlighting some open research challenges.

Gabriel Cardoso -- Predictive posterior sampling from non-stationnary Gaussian process priors via Diffusion models with application to climate data.   

Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of non-stationary priors, often necessary for capturing complex spatial patterns, makes sampling from the predictive posterior distribution (PPD) computationally intractable. In this talk, we propose using a two-step approach based on diffusion generative models (DGMs) to mimic PPDs associated with non-stationary GP priors: we replace the GP prior by a DGM surrogate, and leverage recent advances on training-free guidance algorithms for DGMs to sample from the desired posterior distribution. We apply our approach to a rich non-stationary GP prior from which exact posterior sampling is untractable and validate that the issuing distributions are close to their GP counterpart using several statistical metrics. We also demonstrate how one can fine-tune the trained DGMs to target specific parts of the GP prior. Finally we apply the proposed approach to solve inverse problems arising in environmental sciences.