Spectral Norm Regularization for Improving the Generalizability of Deep Learning

We investigate the generalizability of deep learning based on the sensitivity to input perturbation. We hypothesize that the high sensitivity to the perturbation of data degrades the performance on it. To reduce the sensitivity to perturbation, we propose a simple and effective regularization method, referred to as spectral norm regularization, which penalizes the high spectral norm of weight matrices in neural networks. We provide supportive evidence for the abovementioned hypothesis by experimentally confirming that the models trained using spectral norm regularization exhibit better generalizability than other baseline methods

Pulse-phase resolved spectroscopy of continuum and reflection in SAX J1808.4-3658

We perform phase-resolved spectroscopy of the accreting millisecond pulsar, SAX J1808.4-3658, during the slow-decay phase of the 2002 outburst. Simple phenomenological fits to RXTE PCA data reveal a pulsation in the iron line at the spin frequency of the neutron star. However, fitting more complex spectral models reveals a degeneracy between iron-line pulsations and changes in the underlying hotspot blackbody temperature with phase. By comparing with the variations in reflection continuum, which are much weaker than the iron line variations, we infer that the iron-line is not pulsed. The observed spectral variations can be explained by variations in blackbody temperature associated with rotational Doppler shifts at the neutron star surface. By allowing blackbody temperature to vary in this way, we also find a larger phase-shift between the pulsations in the Comptonised and blackbody components than has been seen in previous work. The phase-shift between the pulsation in the blackbody temperature and normalisation is consistent with a simple model where the Doppler shift is maximised at the limb of the neutron star, ~90 degrees prior to maximisation of the hot-spot projected area.Comment: 8 pages, 10 figures, 2 tables. Accepted by MNRA

Universal transient behavior in large dynamical systems on networks

We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient response of a system through the evolution in time of the squared norm of the state vector, which is averaged over different realizations of the initial perturbation. We develop a mathematical formalism that computes this quantity for graphs that are locally tree-like. We show that for unidirectional networks the theory simplifies and general analytical results can be derived. For example, we derive analytical expressions for the average squared norm for random directed graphs with a prescribed degree distribution. These analytical results reveal that unidirectional systems exhibit a high degree of universality in the sense that the average squared norm only depends on a single parameter encoding the average interaction strength between the individual constituents. In addition, we derive analytical expressions for the average squared norm for unidirectional systems with fixed diagonal disorder and with bimodal diagonal disorder. We illustrate these results with numerical experiments on large random graphs and on real-world networks.Comment: 19 pages, 7 figures. Substantially enlarged version. Submitted to Physical Review Researc

Linear Prediction of Long-Range Dependent Time Series

We present two approaches for next step linear prediction of long memory time series. The first is based on the truncation of the Wiener-Kolmogorov predictor by restricting the observations to the last $k$ terms, which are the only available values in practice. Part of the mean squared prediction error comes from the truncation, and another part comes from the parametric estimation of the parameters of the predictor. By contrast, the second approach is non-parametric. An AR($k$) model is fitted to the long memory time series and we study the error made with this misspecified model

A new formalism for the estimation of the CP-violation parameters

In this paper, we use the time super-operator formalism in the 2-level Friedrichs model \cite{fried} to obtain a phenomenological model of mesons decay. Our approach provides a fairly good estimation of the CP symmetry violation parameter in the case of K, B and D mesons. We also propose a crucial test aimed at discriminating between the standard approach and the time super-operator approach developed throughout the paper

Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing low-rank matrix approximation. These techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets. This paper presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions. These methods use random sampling to identify a subspace that captures most of the action of a matrix. The input matrix is then compressed—either explicitly or implicitly—to this subspace, and the reduced matrix is manipulated deterministically to obtain the desired low-rank factorization. In many cases, this approach beats its classical competitors in terms of accuracy, robustness, and/or speed. These claims are supported by extensive numerical experiments and a detailed error analysis. The specific benefits of randomized techniques depend on the computational environment. Consider the model problem of finding the k dominant components of the singular value decomposition of an m × n matrix. (i) For a dense input matrix, randomized algorithms require O(mn log(k)) floating-point operations (flops) in contrast to O(mnk) for classical algorithms. (ii) For a sparse input matrix, the flop count matches classical Krylov subspace methods, but the randomized approach is more robust and can easily be reorganized to exploit multiprocessor architectures. (iii) For a matrix that is too large to fit in fast memory, the randomized techniques require only a constant number of passes over the data, as opposed to O(k) passes for classical algorithms. In fact, it is sometimes possible to perform matrix approximation with a single pass over the data

Chandra observations of the recurrent nova CI Aql after its April 2000 outburst

We report the results of two Chandra observations of the recurrent nova CI Aql at 14 and 16 months after its outburst in April 2000, respectively. The X-ray emission is faint in both cases, without any noticeable change in spectrum or intensity. Although the emission is very soft, it is not luminous enough to be due to late-time H-burning. This implies that the luminous supersoft phase ended even before the time predicted by the most recent calculations. The details of the X-ray spectrum, together with the fact that the observed X-ray intensity is brighter than pre-outburst (1992/1993), suggest that the observed X-ray emission is either due to ionization of the circumstellar material or due to the shocks within the wind and/or with the surrounding medium.Comment: 10 pages ApJ style with 5 figures; accepted for publication in Ap