Exploiting Errors for Efficiency: A Survey from Circuits to Algorithms

When a computational task tolerates a relaxation of its specification or when an algorithm tolerates the effects of noise in its execution, hardware, programming languages, and system software can trade deviations from correct behavior for lower resource usage. We present, for the first time, a synthesis of research results on computing systems that only make as many errors as their users can tolerate, from across the disciplines of computer aided design of circuits, digital system design, computer architecture, programming languages, operating systems, and information theory. Rather than over-provisioning resources at each layer to avoid errors, it can be more efficient to exploit the masking of errors occurring at one layer which can prevent them from propagating to a higher layer. We survey tradeoffs for individual layers of computing systems from the circuit level to the operating system level and illustrate the potential benefits of end-to-end approaches using two illustrative examples. To tie together the survey, we present a consistent formalization of terminology, across the layers, which does not significantly deviate from the terminology traditionally used by research communities in their layer of focus.Comment: 35 page

Non-negative Matrix Factorization with Linear Constraints for Single-Channel Speech Enhancement

This paper investigates a non-negative matrix factorization (NMF)-based approach to the semi-supervised single-channel speech enhancement problem where only non-stationary additive noise signals are given. The proposed method relies on sinusoidal model of speech production which is integrated inside NMF framework using linear constraints on dictionary atoms. This method is further developed to regularize harmonic amplitudes. Simple multiplicative algorithms are presented. The experimental evaluation was made on TIMIT corpus mixed with various types of noise. It has been shown that the proposed method outperforms some of the state-of-the-art noise suppression techniques in terms of signal-to-noise ratio

On Sommerfeld precursor in a Lorentz medium

A one-dimensional electromagnetic problem of Sommerfeld precursor evolution, resulting from a finite rise-time signal excitation in a dispersive Lorentz medium is considered. The effect of the initial signal rate of growth as well as of the medium dumping on the precursor shape and its magnitude is discussed. The analysis applied is based on an approach employing uniform asymptotic expansions. In addition, new approximate formulas are given for the location of the distant saddle points which affect local frequency and dumping of the precursor. The results obtained are illustrated numerically and compared with the results known from the literature.Comment: 19 pages, 8 figure

Information-Theoretic Limits for the Matrix Tensor Product

This paper studies a high-dimensional inference problem involving the matrix tensor product of random matrices. This problem generalizes a number of contemporary data science problems including the spiked matrix models used in sparse principal component analysis and covariance estimation and the stochastic block model used in network analysis. The main results are single-letter formulas (i.e., analytical expressions that can be approximated numerically) for the mutual information and the minimum mean-squared error (MMSE) in the Bayes optimal setting where the distributions of all random quantities are known. We provide non-asymptotic bounds and show that our formulas describe exactly the leading order terms in the mutual information and MMSE in the high-dimensional regime where the number of rows $n$ and number of columns $d$ scale with $d = O(n^\alpha)$ for some $\alpha < 1/20$. On the technical side, this paper introduces some new techniques for the analysis of high-dimensional matrix-valued signals. Specific contributions include a novel extension of the adaptive interpolation method that uses order-preserving positive semidefinite interpolation paths, and a variance inequality between the overlap and the free energy that is based on continuous-time I-MMSE relations

Collider phenomenology of Hidden Valley mediators of spin 0 or 1/2 with semivisible jets

Many models of Beyond the Standard Model physics contain particles that are charged under both Standard Model and Hidden Valley gauge groups, yet very little effort has been put into establishing their experimental signatures. We provide a general overview of the collider phenomenology of spin 0 or 1/2 mediators with non-trivial gauge numbers under both the Standard Model and a single new confining group. Due to the possibility of many unconventional signatures, the focus is on direct production with semivisible jets. For the mediators to be able to decay, a global $U(1)$ symmetry must be broken. This is best done by introducing a set of operators explicitly violating this symmetry. We find that there is only a finite number of such renormalizable operators and that the phenomenology can be classified into five distinct categories. We show that large regions of the parameter space are already excluded, while others are unconstrained by current search strategies. We also discuss how searches could be modified to better probe these unconstrained regions by exploiting special properties of semivisible jets.Comment: 40 pages, 11 figures, published versio

Measurement of dynamic interferometer baseline perturbations by means of wavelength-scanning interferometry

A novel approach for measuring fast oscillations of an absolute value of interferometer optical path difference (OPD) has been developed. The principles of frequency-scanning interferometry are utilized for registration of the interferometer spectral function, from which the OPD is calculated. The proposed approach enables one to capture the absolute baseline variations at frequencies much higher than the spectral acquisition rate. Despite the conventional approaches, associating a single baseline indication to the registered spectrum, in the proposed method a specially developed demodulation procedure is applied to the spectrum. This provides an ability to capture the baseline variations which took place during the spectrum acquisition. An analytical model describing the limitations on the parameters of the possibly registered baseline variations are formulated. The experimental verification of the proposed approach and the developed model has been performed.Comment: 11 pages, 4 figure

Is "Compressed Sensing" compressive? Can it beat the Nyquist Sampling Approach?

Data compression capability of "Compressed sensing (sampling)" in signal discretization is numerically evaluated and found to be far from the theoretical upper bound defined by signal sparsity. It is shown that, for the cases when ordinary sampling with subsequent data compression is prohibitive, there is at least one more efficient, in terms of data compression capability, and more simple and intuitive alternative to Compressed sensing: random sparse sampling and restoration of image band-limited approximations based on energy compaction capability of transforms. It is also shown that assertions that "Compressed sensing" can beat the Nyquist sampling approach are rooted in misinterpretation of the sampling theory.Comment: 5 pages, 4 figure

Towards Verification of Uncertain Cyber-Physical Systems

Cyber-Physical Systems (CPS) pose new challenges to verification and validation that go beyond the proof of functional correctness based on high-level models. Particular challenges are, in particular for formal methods, its heterogeneity and scalability. For numerical simulation, uncertain behavior can hardly be covered in a comprehensive way which motivates the use of symbolic methods. The paper describes an approach for symbolic simulation-based verification of CPS with uncertainties. We define a symbolic model and representation of uncertain computations: Affine Arithmetic Decision Diagrams. Then we integrate this approach in the SystemC AMS simulator that supports simulation in different models of computation. We demonstrate the approach by analyzing a water-level monitor with uncertainties, self-diagnosis, and error-reactions.Comment: In Proceedings SNR 2017, arXiv:1704.0242

Tensor B-Spline Numerical Methods for PDEs: a High-Performance Alternative to FEM

Tensor B-spline methods are a high-performance alternative to solve partial differential equations (PDEs). This paper gives an overview on the principles of Tensor B-spline methodology, shows their use and analyzes their performance in application examples, and discusses its merits. Tensors preserve the dimensional structure of a discretized PDE, which makes it possible to develop highly efficient computational solvers. B-splines provide high-quality approximations, lead to a sparse structure of the system operator represented by shift-invariant separable kernels in the domain, and are mesh-free by construction. Further, high-order bases can easily be constructed from B-splines. In order to demonstrate the advantageous numerical performance of tensor B-spline methods, we studied the solution of a large-scale heat-equation problem (consisting of roughly 0.8 billion nodes!) on a heterogeneous workstation consisting of multi-core CPU and GPUs. Our experimental results nicely confirm the excellent numerical approximation properties of tensor B-splines, and their unique combination of high computational efficiency and low memory consumption, thereby showing huge improvements over standard finite-element methods (FEM)

Fundamental Limits of Electromagnetic Axion and Hidden-Photon Dark Matter Searches: Part I - The Quantum Limit

We discuss fundamental limits of electromagnetic searches for axion and hidden-photon dark matter. We begin by showing the signal-to-noise advantage of scanned resonant detectors over purely resistive broadband detectors. We discuss why the optimal detector circuit must be driven by the dark-matter signal through a reactance; examples of such detectors include single-pole resonators. We develop a framework to optimize dark matter searches using prior information about the dark matter signal (e.g. astrophysical and direct-detection constraints or preferred search ranges). We define integrated sensitivity as a figure of merit in comparing searches over a wide frequency range and show that the Bode-Fano criterion sets a limit on integrated sensitivity. We show that when resonator thermal noise dominates amplifier noise, substantial sensitivity is available away from the resonator bandwidth. Additionally, we show that the optimized single-pole resonator is close to the Bode-Fano limit, establishing the resonator as a near-ideal method for single-moded dark-matter detection. We optimize time allocation in a scanned resonator using priors and derive quantum limits on resonant search sensitivity. We show that, in contrast to some previous work, resonant searches benefit from quality factors above one million, the characteristic quality factor of the dark-matter signal. We also show that the optimized resonator is superior, in signal-to-noise ratio, to the optimized reactive broadband detector at all frequencies at which a resonator may practically be made. At low frequencies, the application of our optimization may enhance scan rates by a few orders of magnitude. Finally, we discuss prospects for evading the quantum limits using backaction evasion, photon counting, squeezing and other nonclassical approaches, as a prelude to Part II.Comment: Extended discussion on coupling to dark matter signal in Section III, the role of priors in scan time allocation in Section V B, and resonant vs. broadband searches in Appendix