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X-WR-CALNAME:Département de mathématiques et applications
X-ORIGINAL-URL:https://www.math.ens.psl.eu
X-WR-CALDESC:évènements pour Département de mathématiques et applications
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TZID:Europe/Paris
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DTSTART:20260329T010000
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DTSTART:20261025T010000
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260602T120000
DTEND;TZID=Europe/Paris:20260602T130000
DTSTAMP:20260721T184029
CREATED:20260601T101208Z
LAST-MODIFIED:20260601T101650Z
UID:21779-1780401600-1780405200@www.math.ens.psl.eu
SUMMARY:ENS-Data Science colloquium - Rebecca Willett : How do simple rotations affect the implicit bias of Adam?
DESCRIPTION:Adaptive gradient methods such as Adam and Adagrad are widely used in = machine learning\, yet their effect on the generalization of learned = models =E2=80=93 relative to methods like gradient descent =E2=80=93 = remains poorly understood. Prior work on binary classification suggests = that Adam exhibits a =E2=80=9Crichness bias\,=E2=80=9D which can help it = learn nonlinear decision boundaries closer to the Bayes-optimal decision = boundary relative to gradient descent. However\, the coordinate-wise = preconditioning scheme employed by Adam renders the overall method = sensitive to orthogonal transformations of feature space. We show that = this sensitivity can manifest as a reversal of Adam=E2=80=99s = competitive advantage: even small rotations of the underlying data = distribution can make Adam forfeit its richness bias and converge to a = linear decision boundary that is farther from the Bayes-optimal decision = boundary than the one learned by gradient descent. To alleviate this = issue\, we show that a recently proposed reparameterization method =E2=80=93= which applies an orthogonal transformation to the optimization = objective =E2=80=93 endows any first-order method with equivariance to = data rotations\, and we empirically demonstrate its ability to restore = Adam=E2=80=99s bias towards rich decision boundaries. This is joint work = with Adela DePavia and Vasileios Charisopoulos. \n\n\n\n  \n\n\n\nThese seminars are being made possible through the support of the CFM-ENS Chair « Modèles et Sciences des Données ». \n\n\n\nThe organizers: Giulio Biroli\, Alex Cayco Gajic\, Bruno Loureiro\, Stéphane Mallat\, Gabriel Peyré.
URL:https://www.math.ens.psl.eu/evenement/ens-data-science-colloquium-rebecca-willett-how-do-simple-rotations-affect-the-implicit-bias-of-adam/
LOCATION:Amphi Jean Jaurès\, 29 rue d'Ulm\, PARIS\, 75005\, France
CATEGORIES:ENS-Data Science colloquium
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260604T120000
DTEND;TZID=Europe/Paris:20260604T130000
DTSTAMP:20260721T184029
CREATED:20260601T103907Z
LAST-MODIFIED:20260601T103907Z
UID:21783-1780574400-1780578000@www.math.ens.psl.eu
SUMMARY:Learning Monge Maps with Constrained Drifting Models
DESCRIPTION:The estimation of optimal transport maps (a.k.a. Monge maps) is a central problem in optimal transport literature. Recent observations reveal that the flow map of the Wasserstein gradient flow of the relative entropy closely approximates—though does not exactly equal—the Monge map between a given source distribution and a Gaussian target. In this work\, we demonstrate how the evolution equation governing this flow map can be corrected to form a constrained gradient flow that provably converges to the true Monge map.When the maps are parametrized as gradients of convex models (e.g. ICNN)\, we show that the resulting optimization scheme can be interpreted as a L²-natural gradient descent in the parameter space\, and that this approach is further connected to the recently introduced drifting generative models. On toy experiments\, we empirically illustrate the clear advantage of using that L²-natural gradient instead of the Euclidean for estimating Monge maps in this framework. \n\n\n\nJoint work with  T. Dumont and F.-X. Vialard\, https://arxiv.org/pdf/2603.25182
URL:https://www.math.ens.psl.eu/evenement/learning-monge-maps-with-constrained-drifting-models/
LOCATION:Salle W
CATEGORIES:CSD seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260609T093000
DTEND;TZID=Europe/Paris:20260609T123000
DTSTAMP:20260721T184029
CREATED:20251018T115549Z
LAST-MODIFIED:20260601T072422Z
UID:20146-1780997400-1781008200@www.math.ens.psl.eu
SUMMARY:Hélène Mathis - Modélisation d'écoulements diphasiques compressibles
DESCRIPTION:Première partie : \n\n\n\nLa modélisation et la simulation d’écoulements diphasiques constituent un sujet de recherche important\, notamment pour leurs applications en sûreté nucléaire.Dans certains scenarii d’accidents interviennent des écoulements très hétérogènes\, constitués d’eau liquide et de bulles d’air et/ou de vapeur.Afin de modéliser de tels écoulements\, on privilégie des modèles moyennés\, donnant une description macroscopique des écoulements\, la description à l’échelle des interfaces eau-gaz étant hors portée.Cependant connaître les propriétés de l’interface\, en particulier l’évolution de l’aire interfaciale et de la tension de surface\, demeure important.Dans cette première partie\, nous nous intéresserons à la dérivation de modèles d’écoulements diphasiques avec tension de surface et seront confrontées deux approches : une première approche par homogénéisation\, la seconde par principe d’Hamilton. \n\n\n\nDeuxième partie : \n\n\n\nLa plupart des modèles d’écoulements diphasiques compressibles\, comme ceux vus en première partie\, entrent dans la classe des systèmes hyperboliques de relaxation.Dans cette partie\, nous nous intéresserons au comportement des solutions de ces systèmes en fonction du temps caractéristique associé à la relaxation.Pour cela\, nous nous concentrerons sur une classe de modèles munis d’une structure entropique\, permettant d’utiliser une méthode d’entropie relative pour analyser le comportement asymptotique des solutions. On présentera ce résultat de stabilité pour des écoulements diphasiques barotropes ou non\, illustré de simulations numériques.
URL:https://www.math.ens.psl.eu/evenement/helene-mathis/
LOCATION:Salle W – ENS PSL\, 45 rue d'Ulm\, Paris\, 75005\, France
CATEGORIES:Séminaire Analyse non linéaire et EDP
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260611T120000
DTEND;TZID=Europe/Paris:20260611T130000
DTSTAMP:20260721T184029
CREATED:20260608T085937Z
LAST-MODIFIED:20260608T085959Z
UID:21794-1781179200-1781182800@www.math.ens.psl.eu
SUMMARY:Constant Bourdrez et Hanna Benarroch
DESCRIPTION:Constant Bourdrez : « Learning To Sample From Diffusion Models Via Inverse Reinforcement Learning«  \n\n\n\nHanna Benarroch : « Certified Per-instance Unlearning using Individual Sensitivity Bounds« 
URL:https://www.math.ens.psl.eu/evenement/constant-bourdrez-et-hanna-benarroch/
LOCATION:Salle W
CATEGORIES:CSD seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260615T104500
DTEND;TZID=Europe/Paris:20260615T114500
DTSTAMP:20260721T184029
CREATED:20260608T091630Z
LAST-MODIFIED:20260608T091724Z
UID:21800-1781520300-1781523900@www.math.ens.psl.eu
SUMMARY:Convexity in Whitney Problems
DESCRIPTION:Suppose E is a compact subset of R^n\, and we are given a function f\, mapping E to the real numbers. How can we tell if the function lies on a smooth convex function? Can we construct an almost optimal\, smooth\, convex interpolant of the function? These are examples of Whitney-type extension and trace problems; while theoretical\, they are driven by practical questions of interpolation of data\, where convexity is a natural constraint. I will begin with an answer to these questions by presenting work of mine proving there is a Finiteness Principle for the non-linear space of strongly convex functions in $C^{1\,1}(\mathbb{R}^n)$. This work is the first attempt to understand the constrained interpolation problem for convex functions in $C^{1\,1}(\mathbb{R}^n)$. We will spend time discussing useful techniques and tools from analysis as well as important open problems in the field.
URL:https://www.math.ens.psl.eu/evenement/convexity-in-whitney-problems/
LOCATION:Salle W (ENS)
CATEGORIES:Séminaire de l'équipe Analyse
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260618T120000
DTEND;TZID=Europe/Paris:20260618T130000
DTSTAMP:20260721T184029
CREATED:20260615T085406Z
LAST-MODIFIED:20260615T085406Z
UID:21813-1781784000-1781787600@www.math.ens.psl.eu
SUMMARY:Special session on coding agents with Emmanuel Sérié\, Olivier Cappé\, Gabriel Peyré
DESCRIPTION:Emmanuel Sérié: Harness over harnesses — demo of cosmon orchestrating Claude Code agents (noogram.org) \n\n\n\nOlivier Cappé: demo of Antigravity for doing useful things \n\n\n\nGabriel Peyré: demo of Codex for making video games and doing math
URL:https://www.math.ens.psl.eu/evenement/special-session-on-coding-agents-with-emmanuel-serie-olivier-cappe-gabriel-peyre/
LOCATION:Salle W
CATEGORIES:CSD seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260624T093000
DTEND;TZID=Europe/Paris:20260624T103000
DTSTAMP:20260721T184029
CREATED:20260622T111017Z
LAST-MODIFIED:20260622T111236Z
UID:21857-1782293400-1782297000@www.math.ens.psl.eu
SUMMARY:Information-estimation geometry: a scale space view of prior probability models
DESCRIPTION:Solving most image processing tasks\, such as denoising\, deblurring\, inpainting\, etc\, require explicitly or implicitly a prior probability model of natural images. Classically\, both learning (by maximizing likelihood) and using (via Bayes’ rule) such prior models are intractable due to the curse of dimensionality. Diffusion models take a different approach\, where the prior density is replaced by a family of score vector fields across noise levels. They have led to impressive success in generative modeling\, but the learned density is not explicit nor is it readily usable as a prior for solving inverse problems. In this talk\, I will show how to bridge this gap by adopting a scale-space representation of the prior density itself. This leads to a procedure for learning normalized density functions from data.  The resulting prior can be used in inverse problems to efficiently access the normalized posterior density\, its mean\, and draw posterior samples. Further\, the scale space gives access to geometric properties of the learned probability distribution that have both information- and estimation-theoretic interpretations. I will show how this can be used to test the common hypothesis that natural images lie on a low-dimensional manifold and define a perceptual distance function between images that predicts human judgments.
URL:https://www.math.ens.psl.eu/evenement/information-estimation-geometry-a-scale-space-view-of-prior-probability-models/
LOCATION:Salle W
CATEGORIES:CSD seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260624T120000
DTEND;TZID=Europe/Paris:20260624T130000
DTSTAMP:20260721T184029
CREATED:20260622T111645Z
LAST-MODIFIED:20260622T111645Z
UID:21860-1782302400-1782306000@www.math.ens.psl.eu
SUMMARY:Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning
DESCRIPTION:Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi)\, a stylized limit of gradient-based training in which hierarchical feature learning becomes an explicit iterative spectral procedure. In this limit\, the dynamics at each layer decouple: given the current representation\, the next layer selects directions with maximal accessible low-degree correlation to the label. This yields a tractable surrogate mechanism for deep learning\, together with a natural kernel-space interpretation. Neural LoFi provides a mathematically explicit framework for studying multi-layer feature learning beyond the lazy regime. It predicts how representations are selected layer by layer\, explains how emergence of concepts arises with given sample complexity\,and gives a concrete mechanism by which depth progressively constructs new features from old ones through low-degree compositionality. We complement the theory with mechanistic experiments on fully connected and convolutional architectures\, showing that Neural LoFi improves over lazy random-feature baselines\, recovers meaningful structured filters\, and predicts representations aligned with early gradient-descent feature discovery with real datasets.
URL:https://www.math.ens.psl.eu/evenement/deep-learning-as-neural-low-degree-filtering-a-spectral-theory-of-hierarchical-feature-learning/
LOCATION:Salle W
CATEGORIES:CSD seminar
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