אירועים והרצאות בפקולטה למדעי המחשב ע"ש הנרי ומרילין טאוב

Approximating high-dimensional functionals with low-dimensional models is a central issue of machine learning, image processing, physics and mathematics. Deep convolutional networks are able to approximate such functionals over a wide range of applications. This talk shows that these computational architectures take advantage of scale separation, symmetries and sparse representations. We introduce simplified architectures which can be analyzed mathematically. Scale separations is performed with wavelets and scale interactions are captured through phase coherence. We show applications to image classificaiton and generation as well as regression of quantum molecular energies and modelization of turbulence flows. Short Bio.: ========== Stéphane Mallat is a French applied mathematician, Professor at College de France and Ecole Normale Superieure. He has made some fundamental contributions to the development of wavelet theory in the late 1980s and early 1990s. He has also done work in applied mathematics, signal processing, music synthesis and image segmentation. With Yves Meyer, he developed the Multiresolution Analysis (MRA) construction for compactly supported wavelets, which made the implementation of wavelets practical for engineering applications by demonstrating the equivalence of wavelet bases and conjugate mirror filters used in discrete, multirate filter banks in signal processing. He also developed (with Sifen Zhong) the Wavelet transform modulus maxima method for image characterization, a method that uses the local maxima of the wavelet coefficients at various scales to reconstruct images. He introduced the scattering transform that constructs invariance for object recognition purposes. Mallat is the author of A Wavelet Tour of Signal Processing (ISBN 012466606X), a text widely used in applied mathematics and engineering courses. He has held teaching positions at New York University, Massachusetts Institute of Technology, École polytechnique and at the Ecole normale supérieure. He is currently Professor of Data Science at College de France. ========================== Refreshments will be served from 14:15 Lecture starts at 14:30