Recovery of sparse vectors and low-rank matrices from a small number of linear measurements is well-known to be possible under various model assumptions on the measurements. The key requirement on the measurement matrices is typically ...

Ptychography is an imaging technique that involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. ...

In this paper, we focus on the approximation of smooth functions f : [−π,π] → ℂ, up to an unresolvable global phase ambiguity, from a finite set of Short Time Fourier Transform (STFT) magnitude (i.e., ...

We propose a two-step approach for reconstructing a signal x ∈ ℂd from subsampled discrete short-time Fourier transform magnitude (spectogram) measurements: first, we use an aliased Wigner distribution deconvolution approach to solve for a portion ...

In this work we develop stochastic control methods for the study of large deviation principles (LDP) for certain interacting particle systems. Although such methods have been well studied for analyzing large deviation properties of small ...

In this short note, we consider the worst case noise robustness of any phase retrieval algorithm which aims to reconstruct all nonvanishing vectors x ∈ ℂd (up to a single global phase multiple) from the ...

We use a method of rotations to study the Lp boundedness, for 1 < p < ∞, of Fourier multipliers which arise as the projection of martingale transforms with respect to symmetric α-stable processes, 0 ...

We prove that a large class of operators, which arise as the projections of martingale transforms of stochastic integrals with respect to Brownian motion, as well as other closely related operators, are in fact Calderón-Zygmund ...

We propose a geometric scattering-based graph neural network (GNN) for approximating solutions of the NP-hard maximum clique (MC) problem. We construct a loss function with two terms, one which encourages the network to find highly ...

Signed and directed networks are ubiquitous in real-world applications. However, there has been relatively little work proposing spectral graph neural networks (GNNs) for such networks. Here we introduce a signed directed Laplacian matrix, which we ...

Although existing deep learning models perform remarkably well at predicting physicochemical properties and binding affinities, the generation of new molecules with optimized properties remains challenging. Inherently, most GNNs perform poorly in whole-graph representation due to ...

We propose a method for noise reduction, the task of producing a clean audio signal from a recording corrupted by additive noise. Many common approaches to this problem are based upon applying non-negative matrix factorization ...

We present a machine learning model for the analysis of randomly generated discrete signals, modeled as the points of an inhomogeneous, compound Poisson point process. Like the wavelet scattering transform introduced by Mallat, our construction ...

Graph Neural Networks (GNNs) extend the success of neural networks to graph-structured data by accounting for their intrinsic geometry. While extensive research has been done on developing GNN models with superior performance according to a ...

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 the observation that ...

We present an algorithm which is closely related to direct phase retrieval methods that have been shown to work well empirically [1], [2] and prove that it is guaranteed to recover (up to a global ...

The prevalence of graph-based data has spurred the rapid development of graph neural networks (GNNs) and related machine learning algorithms. Yet, despite the many datasets naturally modeled as directed graphs, including citation, website, and traffic ...

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to ...

Convolutional neural networks (CNNs) are revolutionizing imaging science for two- and three-dimensional images over Euclidean domains. However, many data sets are intrinsically non-Euclidean and are better modeled through other mathematical structures, such as graphs or ...

The manifold scattering transform is a multiscalefeature extractor for data defined on a Riemannianmanifold. The initial work on this model focusedprimarily on its theoretical stability and invarianceproperties but did not provide methods forits numerical implementation ...

Graph neural networks (GNNs) have attracted much attention due to their ability to leverage the intrinsic geometries of the underlying data. Although many different types of GNN models have been developed, with many benchmarking procedures ...