BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Département de mathématiques et applications - ECPv6.2.2//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
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
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Europe/Paris
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20260329T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20261025T010000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260624T093000
DTEND;TZID=Europe/Paris:20260624T103000
DTSTAMP:20260624T012525
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:20260624T012525
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
END:VEVENT
END:VCALENDAR