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This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly…
This paper presents a generalization of the random dot product model for networks whose edge weights are drawn from a parametrized probability distribution. We focus on the case of integer weight edges and show that many previously studied…
We consider communication-efficient weighted and unweighted (uniform) random sampling from distributed data streams presented as a sequence of mini-batches of items. This is a natural model for distributed streaming computation, and our…
Structures play a significant role in the field of signal processing. As a representative of structural data, low rank matrix along with its restricted isometry property (RIP) has been an important research topic in compressive signal…
We describe a simple and general neural network weight compression approach, in which the network parameters (weights and biases) are represented in a "latent" space, amounting to a reparameterization. This space is equipped with a learned…
We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…
Compression is a standard procedure for making convolutional neural networks (CNNs) adhere to some specific computing resource constraints. However, searching for a compressed architecture typically involves a series of time-consuming…
Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…
Recently, it has been shown that compressed sensing (CS) has the potential to lower energy consumption in wireless electrocardiogram (ECG) systems. By reducing the number of acquired measurements, the communication burden is decreased and…
This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With the knowledge of the probability for each atom of the…
We consider the problem of recovering a single or multiple frequency-sparse signals, which share the same frequency components, from a subset of regularly spaced samples. The problem is referred to as continuous compressed sensing (CCS) in…
Echo State Networks (ESNs) are a class of single layer recurrent neural networks that have enjoyed recent attention. In this paper we prove that a suitable ESN, trained on a series of measurements of an invertible dynamical system, induces…
Reservoir computing (RC) represents a class of state-space models (SSMs) characterized by a fixed state transition mechanism (the reservoir) and a flexible readout layer that maps from the state space. It is a paradigm of computational…
This paper proposes a novel and interpretable recurrent neural-network structure using the echo-state network (ESN) paradigm for time-series prediction. While the traditional ESNs perform well for dynamical systems prediction, it needs a…
We develop a framework that we call compressive rate estimation. We assume that the composite channel gain matrix (i.e. the matrix of all channel gains between all network nodes) is compressible which means it can be approximated by a…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
A proposition that connects randomness and compression is put forward via Gibbs entropy over set of measurement vectors associated with a compression process. The proposition states that a lossy compression process is equivalent to {\it…
Well-controlled quantum devices with their increasing system size face a new roadblock hindering further development of quantum technologies: The effort of quantum tomography---the characterization of processes and states within a quantum…
Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or…
Constrained counting and sampling are two fundamental problems in Computer Science with numerous applications, including network reliability, privacy, probabilistic reasoning, and constrained-random verification. In constrained counting,…