Classifications and regressions from data requires to approximate functions in high dimensional spaces. Avoiding the curse of dimensionality raises issues in many branches of mathematics including statistics, probability, harmonic analysis and geometry. Recently, deep convolutional networks have obtained spectacular results for image understanding, audio recognition, natural language analysis and all kind of data analysis problems. We shall review their architecture, and analyze their mathematical properties, with many open questions. These architectures implement non-linear multiscale contractions, and sparse separations, where wavelets play an important role. Applications are shown for image and audio classification as well as quantum energy regressions.
The talk will be followed by a reception in the Huxley Common Room (549) from 18:00.
Further information about Professor Mallat’s work can be found here.