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Batch Normalization (BN) improves both convergence and generalization in training neural networks. This work understands these phenomena theoretically. We analyze BN by using a basic block of neural networks, consisting of a kernel layer, a…
We study processes with unstable particles in intermediate time-like states. It is shown that the amplitudes squared of such processes factor exactly in the framework of the model of unstable particles with continuous masses. Decay widths…
Batch Normalization (BN) is extensively employed in various network architectures by performing standardization within mini-batches. A full understanding of the process has been a central target in the deep learning communities. Unlike…
We discuss the sources of uncertainty in calculations of the partial widths of the Higgs boson within the Standard Model. The uncertainties come from two sources: the truncation of perturbation theory and the uncertainties in input…
We consider Standard Model Higgs boson production in association with a W boson in hadron collisions. We supplement the fully exclusive perturbative computation of QCD radiative effects up to next-to-next-to-leading order (NNLO) with the…
We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models.…
Understanding the source of the superior generalization ability of NNs remains one of the most important problems in ML research. There have been a series of theoretical works trying to derive non-vacuous bounds for NNs. Recently, the…
It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it…
In this article, we focus on two toy models : the Curie-Weiss model and the system of $N$ particles in linear interactions in a double well confining potential. Both models, which have been extensively studied, describe a large system of…
The linear noise approximation (LNA) describes the random fluctuations from the mean-field concentrations of a chemical reaction network due to intrinsic noise. It is also used as a test probe to determine the accuracy of reduced…
The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the long-time limit the current mathematical…
Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that…
Full-waveform inversion (FWI) is an accurate imaging approach for modeling velocity structure by minimizing the misfit between recorded and predicted seismic waveforms. However, the strong non-linearity of FWI resulting from fitting…
A generalized version of the rotating-wave approximation for the single-mode spin-boson Hamiltonian is presented. It is shown that performing a simple change of basis prior to eliminating the off-resonant terms results in a significantly…
The measurements of the properties of the Higgs boson still leave room for a non minimal scalar sector. Extensions of the Standard Model typically involve multiple neutral Higgs fields which can interfere among themselves. We show that…
Pair production of W gauge bosons is an important process at the LHC entering many experimental analyses, both as background in new-physics searches or Higgs measurements and as signal in precision studies and tests of the Standard Model.…
(Abridged) In the presence of a light WIMP (< 30 MeV), there are degeneracies among the nature of the WIMP, its couplings to standard model particles, its mass m_chi, and the number of equivalent neutrinos beyond the standard model, Delta…
Although wettability is a macroscopic manifestation of molecular-level forces, such as van der Waals (vdW) forces, the impact of nanoconfinement on material properties in reduced film thickness remains unexplored in predicting film…
The processes of production and subsequent decay of W- and Z-bosons in $e^+ e^-$ collisions are considered in a recently proposed modified perturbation theory (PT), based on a direct expansion of probabilities instead of amplitudes. In such…
Full waveform inversion (FWI) is a powerful tool for reconstructing material fields based on sparsely measured data obtained by wave propagation. For specific problems, discretizing the material field with a neural network (NN) improves the…