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Quadratically constrained quadratic programs (QCQPs) are a highly expressive class of nonconvex optimization problems. While QCQPs are NP-hard in general, they admit a natural convex relaxation via the standard (Shor) semidefinite program…
The range of stimulated Raman scattering (SRS) frequencies covers a domain which at the low end abuts half the laser frequency, omega_0 / 2, according to the simplest SRS theories, corresponding to scatter from electron densities near 1/4…
We propose a framework to understand the unprecedented performance and robustness of deep neural networks using field theory. Correlations between the weights within the same layer can be described by symmetries in that layer, and networks…
We show that the $N$-particle Sutherland model with inverse-square and harmonic interactions exhibits orthogonality catastrophe. For a fixed value of the harmonic coupling, the overlap of the $N$-body ground state wave functions with two…
This paper describes one objective function for learning semantically coherent feature embeddings in multi-output classification problems, i.e., when the response variables have dimension higher than one. In particular, we consider the…
We analyze the topological properties of the set of functions that can be implemented by neural networks of a fixed size. Surprisingly, this set has many undesirable properties. It is highly non-convex, except possibly for a few exotic…
Planted dense cycles are a type of latent structure that appears in many applications, such as small-world networks in social sciences and sequence assembly in computational biology. We consider a model where a dense cycle with expected…
We introduce Parseval networks, a form of deep neural networks in which the Lipschitz constant of linear, convolutional and aggregation layers is constrained to be smaller than 1. Parseval networks are empirically and theoretically…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
Neural networks, a central tool in machine learning, have demonstrated remarkable, high fidelity performance on image recognition and classification tasks. These successes evince an ability to accurately represent high dimensional…
In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in three-dimensional sensor networks. As in other large-scale complex systems, many global parameters of sensor networks undergo phase…
Many hierarchically modular systems are structured in a way that resembles an hourglass. This "hourglass effect" means that the system generates many outputs from many inputs through a relatively small number of intermediate modules that…
We advocate a new approach of addressing hidden structure problems and finding efficient quantum algorithms. We introduce and investigate the Hidden Symmetry Subgroup Problem (HSSP), which is a generalization of the well-studied Hidden…
Surface plasma waves (SPWs) have been extensively studied in the past two decades with a promise for many applications. However, the effort has so far been met with limited success. It is widely believed that a major caveat lies with the…
Extremely large aperture arrays (ELAAs) and millimeter-wave (mmWave) technologies are essential for achieving high data rates in future wireless communication systems. To perform precise beamforming, these systems require accurate channel…
There have been many attempts to identify high-dimensional network features via multivariate approaches. Specifically, when the number of voxels or nodes, denoted as p, are substantially larger than the number of images, denoted as n, it…
Interference field in wireless networks is often modeled by a homogeneous Poisson Point Process (PPP). While it is realistic in modeling the inherent node irregularity and provides meaningful first-order results, it falls short in modeling…
Approximation of high-dimensional functions is a problem in many scientific fields that is only feasible if advantageous structural properties, such as sparsity in a given basis, can be exploited. A relevant tool for analysing sparse…
In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…
We study the gravitational wave (GW) signature in the doublet left-right symmetric model (DLRSM) resulting from the strong first-order phase transition (SFOPT) associated with $SU(2)_R\times U(1)_{B-L}$-breaking. For different values of the…