Related papers: The S-matrix bootstrap with neural optimizers I: z…
The multiple scattering method T-matrix (MSTMM) can be used to solve the electromagnetic response of systems consisting of many compact scatterers, retaining a good level of accuracy while using relatively few degrees of freedom, largely…
We consider the fundamental problem of learning linear predictors (i.e., separable datasets with zero margin) using neural networks with gradient flow or gradient descent. Under the assumption of spherically symmetric data distribution, we…
Recent advances in electron microscopy allowed the generation of high-energy electron wave packets of ultrashort duration. Here we present a non-perturbative S-matrix theory for scattering of ultrashort electron wave packets by atomic…
A generalized scattering amplitude where momenta of incoming-particles and outgoing-particles as well as positions of incoming-particles and outgoing-particles are specified is formulated. Idealistic beams and idealistic measuring…
Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g., sorting, picking closest neighbors, or shortest paths). Although these discrete decisions are easily computed, they break the…
Solution of the discretized Lippmann-Schwinger equation in the spatial frequency domain involves the inversion of a linear operator specified by the scattering potential. To regularize this inevitably ill-conditioned problem, we propose a…
Matrix completion is one of the key problems in signal processing and machine learning, with applications ranging from image pro- cessing and data gathering to classification and recommender sys- tems. Recently, deep neural networks have…
We propose an end-to-end deep learning framework that comprehensively solves the inverse wave scattering problem across all length scales. Our framework consists of the newly introduced wide-band butterfly network coupled with a simple…
Smoothing splines are twice differentiable by construction, so they cannot capture potential discontinuities in the underlying signal. In this work, we consider a special case of the weak rod model of Blake and Zisserman (1987) that allows…
This paper investigates a discontinuous neural network which is used as a model of the mammalian olfactory system and can more generally be applied to solve non-negative sparse approximation problems. By inherently limiting the systems…
We investigate theoretically coherent detection implemented simultaneously on a set of mutually orthogonal spatial modes in the image plane as a method to characterize properties of a composite thermal source below the Rayleigh limit. A…
Neutron and X-ray scattering represent two state-of-the-art materials characterization techniques that measure materials' structural and dynamical properties with high precision. These techniques play critical roles in understanding a wide…
We derive an expression for the relation between two scattering transition amplitudes which reflect the same dynamics, but which differ in the description of their initial and final state vectors. In one version, the incident and scattered…
We carried out a Pad\'e approximant analysis on a compact factor of the $T$-matrix for $NN$ scattering to explore the nonperturbative renormalization prescription in a universal manner. The utilities and virtues for this Pad\'e analysis…
We develop a transfer-matrix formulation of the scattering of electromagnetic waves by a general isotropic medium which makes use of a notion of electromagnetic transfer matrix $\mathbf{M}$ that does not involve slicing of the scattering…
With the aim of constructing a biologically plausible model of machine listening, we study the representation of a multicomponent stationary signal by a wavelet scattering network. First, we show that renormalizing second-order nodes by…
Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments.…
We obtain a nonperturbative, analytical solution to integral equation of scattering theory by assuming the field within the scattering object is a spherical wave with a scattering amplitude equal to that of the far field. This approximation…
Standard gradient descent methods yield point estimates with no measure of confidence. This limitation is acute in overparameterized and low-data regimes, where models have many parameters relative to available data and can easily overfit.…
We focus on the robustness of neural networks for classification. To permit a fair comparison between methods to achieve robustness, we first introduce a standard based on the mensuration of a classifier's degradation. Then, we propose…