Group Invariance and Stability to Deformations of Deep Convolutional Representations

Abstract : In this paper, we study deep signal representations that are invariant to groups of transformations and stable to the action of diffeomorphisms without losing signal information. This is achieved by generalizing the multilayer kernel introduced in the context of convolutional kernel networks and by studying the geometry of the corresponding reproducing kernel Hilbert space. We show that the signal representation is stable, and that models from this functional space, such as a large class of convolutional neural networks with homogeneous activation functions, may enjoy the same stability.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.inria.fr/hal-01536004
Contributeur : Alberto Bietti <>
Soumis le : vendredi 9 juin 2017 - 20:10:31
Dernière modification le : jeudi 15 juin 2017 - 09:08:51

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  • HAL Id : hal-01536004, version 1
  • ARXIV : 1706.03078

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Alberto Bietti, Julien Mairal. Group Invariance and Stability to Deformations of Deep Convolutional Representations. 2017. <hal-01536004>

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