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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:20260604T120000
DTEND;TZID=Europe/Paris:20260604T130000
DTSTAMP:20260727T223021
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:20260611T120000
DTEND;TZID=Europe/Paris:20260611T130000
DTSTAMP:20260727T223021
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:20260618T120000
DTEND;TZID=Europe/Paris:20260618T130000
DTSTAMP:20260727T223021
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:20260727T223021
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:20260727T223021
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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