Notes and Comments on S. Mallat’s Lectures at Collège de France (2020)
Résumé
The 2020 course by Stéphane Mallat, Professor at the Collège de France, focuses on the question 'Why are convolutional network architectures generic?' From a mathematical perspective, this entails three types of problems: estimation, optimization, and approximation. The courses in 2018 and 2019 addressed the first two, while the third is the theme for this year. Thus, we will ask questions such as: what is the a priori information (regularity, symmetry, sparsity), why convolutions, what types of filters, what is the role of non-linearities, and the connection with neurophysiology in the context of image and sound. The transformation into wavelets and their applications to obtain descriptors as well as convolutional filters are at the heart of the course.
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