4 papers
The Stability Landscape in Wave-Packet Scattering: Geometric Rigidity and Sharp Sobolev Thresholds
Max Getter, S. Ivan Trapasso
A central challenge in modern harmonic analysis is to quantify the balance between the approximation power of finely resolved multiscale representations and their robustness to non…
Energy Propagation in Scattering Convolution Networks Can Be Arbitrarily Slow
Hartmut Führ, Max Getter
We analyze energy decay for deep convolutional neural networks employed as feature extractors, including Mallat's wavelet scattering transform. For time-frequency scattering transf…
Digital implementations of deep feature extractors are intrinsically informative
Max Getter
Rapid information (energy) propagation in deep feature extractors is crucial to balance computational complexity versus expressiveness as a representation of the input. We prove an…
Cheeger Bounds for Stable Phase Retrieval in Reproducing Kernel Hilbert Spaces
Hartmut Führ, Max Getter
Phase retrieval seeks to reconstruct a signal from phaseless intensity measurements and, in applications where measurements contain errors, demands stable reconstruction. We study…