Related papers: Phase transition of \emph{descending} phase retrie…
In this letter, we apply the artificial neural network in a supervised manner to map out the quantum phase diagram of disordered topological superconductor in class DIII. Given the disorder that keeps the discrete symmetries of the ensemble…
We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase…
The phase retrieval problem has garnered significant attention since the development of the PhaseLift algorithm, which is a convex program that operates in a lifted space of matrices. Because of the substantial computational cost due to…
We study harmonic map regression, a nonparametric estimator for manifold-valued responses, that penalizes the empirical Fr\'echet risk by the Dirichlet energy. By connecting penalized regression to the theory of harmonic maps, the estimator…
We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still…
We develop a flexible feature selection framework based on deep neural networks that approximately controls the false discovery rate (FDR), a measure of Type-I error. The method applies to architectures whose first layer is fully connected.…
We consider a popular nonsmooth formulation of the real phase retrieval problem. We show that under standard statistical assumptions, a simple subgradient method converges linearly when initialized within a constant relative distance of an…
Deep learning has been immensely successful at a variety of tasks, ranging from classification to AI. Learning corresponds to fitting training data, which is implemented by descending a very high-dimensional loss function. Understanding…
Phase reconstruction, which estimates phase from a given amplitude spectrogram, is an active research field in acoustical signal processing with many applications including audio synthesis. To take advantage of rich knowledge from data,…
In this paper, we propose a new global analysis framework for a class of low-rank matrix recovery problems on the Riemannian manifold. We analyze the global behavior for the Riemannian optimization with random initialization. We use the…
Our general subject is the emergence of phases, and phase transitions, in large networks subjected to a few variable constraints. Our main result is the analysis, in the model using edge and triangle subdensities for constraints, of a sharp…
Phase retrieval (PR) concerns the recovery of complex phases from complex magnitudes. We identify the connection between the difficulty level and the number and variety of symmetries in PR problems. We focus on the most difficult far-field…
In this work, we address a foundational question in the theoretical analysis of the Deep Ritz Method (DRM) under the over-parameteriztion regime: Given a target precision level, how can one determine the appropriate number of training…
This paper shows how data-driven deep generative models can be utilized to solve challenging phase retrieval problems, in which one wants to reconstruct a signal from only few intensity measurements. Classical iterative algorithms are known…
Probabilistic sampling methods have become very popular to solve single-shot path planning problems. Rapidly-exploring Random Trees (RRTs) in particular have been shown to be very efficient in solving high dimensional problems. Even though…
We study a random matrix model for the statistical properties of the purity of a bipartite quantum system at a finite (fictitious) temperature. This enables us to write the generating function for the cumulants, for both balanced and…
This paper discusses the critical decision process of extracting or selecting the features in a supervised learning context. It is often confusing to find a suitable method to reduce dimensionality. There are pros and cons to deciding…
We consider the problem of finding a low rank symmetric matrix satisfying a system of linear equations, as appears in phase retrieval. In particular, we solve the gauge dual formulation, but use a fast approximation of the spectral…
We calculate analytically the phase boundary for a nonequilibrium phase transition in a one-dimensional array of coupled, overdamped parametric harmonic oscillators in the limit of strong and weak spatial coupling. Our results show that the…
In the last five decades, iterative phase retrieval methods draw large amount of interest across the research community as a non-interferometric approach to recover quantitative phase distributions from one (or more) intensity measurement.…