Related papers: Energy Propagation in Scattering Convolution Netwo…
Many practical machine learning tasks employ very deep convolutional neural networks. Such large depths pose formidable computational challenges in training and operating the network. It is therefore important to understand how fast the…
We study an aspect of the following general question: which properties of a signal can be characterized by its scattering transform? We show that the energy contained in high order scattering coefficients is upper bounded by the energy…
Scattering Networks were initially designed to elucidate the behavior of early layers in Convolutional Neural Networks (CNNs) over Euclidean spaces and are grounded in wavelets. In this work, we introduce a scattering transform on an…
The scattering transform is a wavelet-based model of Convolutional Neural Networks originally introduced by S. Mallat. Mallat's analysis shows that this network has desirable stability and invariance guarantees and therefore helps explain…
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 upper bound for the speed of energy propagation in a…
In this paper we address the problem of constructing a feature extractor which combines Mallat's scattering transform framework with time-frequency (Gabor) representations. To do this, we introduce a class of frames, called uniform covering…
The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…
We theoretically and numerically prove that under an electromagnetic plane wave with linear polarization incident normally to cylindrical passive scatterers, a single energy diagram can integrate absorption, scattering, and extinction cross…
Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to…
We present a novel approach to the regression of quantum mechanical energies based on a scattering transform of an intermediate electron density representation. A scattering transform is a deep convolution network computed with a cascade of…
We study wave propagation through a one-dimensional array of subwavelength resonators with periodically time-modulated material parameters. Focusing on a high-contrast regime, we use a scattering framework based on Fourier expansions and…
We analytically study the time-averaged electromagnetic energy stored inside scatterers containing inclusions of arbitrary shapes. Assuming the low density of inclusions, we derive the expression for the energy-transport velocity through…
Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called…
Resonant scattering of electrons with low energies (as compared to the bandwidth) on a single neutral short-range impurity in graphene is analyzed theoretically, taking into account the valley degeneracy. Resonances dramatically increase…
Wave scattering in chaotic systems with a uniform energy loss (absorption) is considered. Within the random matrix approach we calculate exactly the energy correlation functions of different matrix elements of impedance or scattering…
The dream of machine learning in materials science is for a model to learn the underlying physics of an atomic system, allowing it to move beyond interpolation of the training set to the prediction of properties that were not present in the…
A wavelet scattering network computes a translation invariant image representation, which is stable to deformations and preserves high frequency information for classification. It cascades wavelet transform convolutions with non-linear…
We show that the spatial distribution of the energy density of optimally shaped waves inside a scattering medium can be described by considering only a few of the lowest eigenfunctions of the diffusion equation. Taking into account only the…
A general machine learning architecture is introduced that uses wavelet scattering coefficients of an inputted three dimensional signal as features. Solid harmonic wavelet scattering transforms of three dimensional signals were previously…
Convolutional neural networks (CNNs) have been shown to both extract more information than the traditional two-point statistics from cosmological fields, and marginalise over astrophysical effects extremely well. However, CNNs require large…