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SUMMARY:Diffeomorphism-based feature learning using Poincaré inequalities
  - Clémentine Prieur (Université Grenoble Alpes)
DTSTART:20250508T133000Z
DTEND:20250508T140000Z
UID:TALK230488@talks.cam.ac.uk
DESCRIPTION:We propose a gradient-enhanced algorithm for high-dimensional 
 scalar or vectorial function approximation. The algorithm proceeds in two 
 steps: firstly\, we reduce the input dimension by learning the relevant in
 put features from gradient evaluations\, and secondly\, we regress the fun
 ction output against the pre-learned features. To ensure theoretical guara
 ntees\, we construct the feature map as the first components of a diffeomo
 rphism\, which we learn by minimizing an error bound obtained using Poinca
 r&eacute\; Inequality applied either in the input space or in the feature 
 space. This leads to two different strategies\, which we compare both theo
 retically and numerically and relate to existing methods in the literature
 . In addition\, we propose a dimension augmentation trick to increase the 
 approximation power of feature detection. In practice\, we construct the d
 iffeomorphism using coupling flows\, a particular class of invertible neur
 al networks. Numerical experiments on various high-dimensional functions s
 how that the proposed algorithm outperforms state-of-the-art competitors\,
  especially with small datasets.
LOCATION:Seminar Room 1\, Newton Institute
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