CCM Colloquium: Stéphane Mallat

Title: Hamiltonian Estimations by Inverse Renormalisation Group and Convolution Nets

Abstract: Estimating high-dimensional probability distributions and physical Hamiltonians from data is an old outstanding problem. It is typically unstable, especially near phase transitions. We revisit this topic with models resulting from multiscale harmonic analysis and neural networks. We show that renormalisation group calculations in wavelet orthonormal bases amount to precondition the Hamiltonian estimation. Stable Hamiltonian estimations are shown on the phi^4 model and weak lensing Cosmological data. Multiscale models of turbulences are computed, with a deep network whose filters are wavelets. Hamiltonian estimation is also closely related to classification. ResNet accuracy is obtained on ImageNet with wavelet filters, by learning the potential functions that approximate Hamiltonians.