Constraining Absolute Neutrino Masses via Detection of Galactic Supernova Neutrinos at JUNO

A high-statistics measurement of the neutrinos from a galactic core-collapse supernova is extremely important for understanding the explosion mechanism, and studying the intrinsic properties of neutrinos themselves. In this paper, we explore the possibility to constrain the absolute scale of neutrino masses $m^{}_\nu$ via the detection of galactic supernova neutrinos at the Jiangmen Underground Neutrino Observatory (JUNO) with a 20 kiloton liquid-scintillator detector. In assumption of a nearly-degenerate neutrino mass spectrum and a normal mass ordering, the upper bound on the absolute neutrino mass is found to be $m^{}_\nu < (0.83 \pm 0.24)~{\rm eV}$ at the 95% confidence level for a typical galactic supernova at a distance of 10 kpc, where the mean value and standard deviation are shown to account for statistical fluctuations. For comparison, we find that the bound in the Super-Kamiokande experiment is $m^{}_\nu < (0.94 \pm 0.28)~{\rm eV}$ at the same confidence level. However, the upper bound will be relaxed when the model parameters characterizing the time structure of supernova neutrino fluxes are not exactly known, and when the neutrino mass ordering is inverted.Comment: 22 pages, 6 figures, more discussions on systematic uncertainties, matches the published versio

Accelerating Message Passing for MAP with Benders Decomposition

We introduce a novel mechanism to tighten the local polytope relaxation for MAP inference in Markov random fields with low state space variables. We consider a surjection of the variables to a set of hyper-variables and apply the local polytope relaxation over these hyper-variables. The state space of each individual hyper-variable is constructed to be enumerable while the vector product of pairs is not easily enumerable making message passing inference intractable. To circumvent the difficulty of enumerating the vector product of state spaces of hyper-variables we introduce a novel Benders decomposition approach. This produces an upper envelope describing the message constructed from affine functions of the individual variables that compose the hyper-variable receiving the message. The envelope is tight at the minimizers which are shared by the true message. Benders rows are constructed to be Pareto optimal and are generated using an efficient procedure targeted for binary problems

Covariance Estimation in High Dimensions via Kronecker Product Expansions

This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an i.i.d. Gaussian random sample, we establish high dimensional rates of convergence to the true covariance as both the number of samples and the number of variables go to infinity. For covariance matrices of low separation rank, our results establish that PRLS has significantly faster convergence than the standard sample covariance matrix (SCM) estimator. The convergence rate captures a fundamental tradeoff between estimation error and approximation error, thus providing a scalable covariance estimation framework in terms of separation rank, similar to low rank approximation of covariance matrices. The MSE convergence rates generalize the high dimensional rates recently obtained for the ML Flip-flop algorithm for Kronecker product covariance estimation. We show that a class of block Toeplitz covariance matrices is approximatable by low separation rank and give bounds on the minimal separation rank $r$ that ensures a given level of bias. Simulations are presented to validate the theoretical bounds. As a real world application, we illustrate the utility of the proposed Kronecker covariance estimator for spatio-temporal linear least squares prediction of multivariate wind speed measurements.Comment: 47 pages, accepted to IEEE Transactions on Signal Processin

Quasi-hyperbolic momentum and Adam for deep learning

Momentum-based acceleration of stochastic gradient descent (SGD) is widely used in deep learning. We propose the quasi-hyperbolic momentum algorithm (QHM) as an extremely simple alteration of momentum SGD, averaging a plain SGD step with a momentum step. We describe numerous connections to and identities with other algorithms, and we characterize the set of two-state optimization algorithms that QHM can recover. Finally, we propose a QH variant of Adam called QHAdam, and we empirically demonstrate that our algorithms lead to significantly improved training in a variety of settings, including a new state-of-the-art result on WMT16 EN-DE. We hope that these empirical results, combined with the conceptual and practical simplicity of QHM and QHAdam, will spur interest from both practitioners and researchers. Code is immediately available.Comment: Published as a conference paper at ICLR 2019. This version corrects one typological error in the published tex

Generalization Error in Deep Learning

Deep learning models have lately shown great performance in various fields such as computer vision, speech recognition, speech translation, and natural language processing. However, alongside their state-of-the-art performance, it is still generally unclear what is the source of their generalization ability. Thus, an important question is what makes deep neural networks able to generalize well from the training set to new data. In this article, we provide an overview of the existing theory and bounds for the characterization of the generalization error of deep neural networks, combining both classical and more recent theoretical and empirical results

Neutrinos and Future Concordance Cosmologies

We review the free parameters in the concordance cosmology, and those which might be added to this set as the quality of astrophysical data improves. Most concordance parameters encode information about otherwise unexplored aspects of high energy physics, up to the GUT scale via the "inflationary sector," and possibly even the Planck scale in the case of dark energy. We explain how neutrino properties may be constrained by future astrophysical measurements. Conversely, future neutrino physics experiments which directly measure these parameters will remove uncertainty from fits to astrophysical data, and improve our ability to determine the global properties of our universe.Comment: Proceedings of paper given at Neutrino 2008 meeting (by RE

A Fast Scalable Heuristic for Bin Packing

In this paper we present a fast scalable heuristic for bin packing that partitions the given problem into identical sub-problems of constant size and solves these constant size sub-problems by considering only a constant number of bin configurations with bounded unused space. We present some empirical evidence to support the scalability of our heuristic and its tighter empirical analysis of hard instances due to improved lower bound on the necessary wastage in an optimal solution.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1902.0342

Harmless interpolation of noisy data in regression

A continuing mystery in understanding the empirical success of deep neural networks is their ability to achieve zero training error and generalize well, even when the training data is noisy and there are more parameters than data points. We investigate this overparameterized regime in linear regression, where all solutions that minimize training error interpolate the data, including noise. We characterize the fundamental generalization (mean-squared) error of any interpolating solution in the presence of noise, and show that this error decays to zero with the number of features. Thus, overparameterization can be explicitly beneficial in ensuring harmless interpolation of noise. We discuss two root causes for poor generalization that are complementary in nature -- signal "bleeding" into a large number of alias features, and overfitting of noise by parsimonious feature selectors. For the sparse linear model with noise, we provide a hybrid interpolating scheme that mitigates both these issues and achieves order-optimal MSE over all possible interpolating solutions.Comment: 52 pages, expanded version of the paper presented at ITA in San Diego in Feb 2019, ISIT in Paris in July 2019, at Simons in July, and as a plenary at ITW in Visby in August 201

Chanel No5 (fb^-1): The Sweet Fragrance of SUSY

We present compounding evidence of supersymmetry (SUSY) production at the LHC, in the form of correlations between the nominal 5\fb ATLAS and CMS results for the 7 TeV 2011 run and detailed Monte Carlo collider-detector simulation of a concrete supersymmetric model named No-Scale F-SU(5). Restricting analysis to those event selections which yield a signal significance S/sqrt(B+1) greater than 2, we find by application of the \chi^2 statistic that strong correlations exist among the individual search strategies and also between the current best fit to the SUSY mass scale and that achieved using historical 1\fb data sets. Coupled with an appropriately large increase in the "depth" of the \chi^2 well with increasing luminosity, we suggest that these features indicate the presence of a non-random structure to the data - a light fragrance perhaps evocative of some fuller coming fruition. Those searches having signal significances below 2 are assembled into a lower exclusion bound on the gaugino mass, which is shown to be consistent with the prior best fit. Assuming the forthcoming delivery of an additional tranche of integrated luminosity at 8 TeV during 2012 that measures on the order 15\fb, we project a sufficiency of actionable data to conclusively judge the merits of our proposal.Comment: 8 Pages, 2 Figures, 1 Tabl

Analysis of multivariate Gegenbauer approximation in the hypercube

In this paper, we are concerned with multivariate Gegenbauer approximation of functions defined in the $d$-dimensional hypercube. Two new and sharper bounds for the coefficients of multivariate Gegenbauer expansion of analytic functions are presented based on two different extensions of the Bernstein ellipse. We then establish an explicit error bound for the multivariate Gegenbauer approximation associated with an $\ell^q$ ball index set in the uniform norm. We also consider the multivariate approximation of functions with finite regularity and derive the associated error bound on the full grid in the uniform norm. As an application, we extend our arguments to obtain some new tight bounds for the coefficients of tensorized Legendre expansions in the context of polynomial approximation of parameterized PDEs.Comment: Adv. Comput. Math., to appea