Deep learning has achieved a great success in many areas, from computer vision to natural language processing, to game playing, and much more. Yet, what deep learning is really doing is still an open question. There are a lot of works in this direction. For example, [6] tried to explain deep learning by group renormalization, and [5] tried to explain deep learning from the view of functional ap...

We compute explicit bounds in the Gaussian approximation of functionals of infinite Rademacher sequences. Our tools involve Stein’s method, as well as the use of appropriate discrete Malliavin operators. Although our approach does not require the classical use of exchangeable pairs, we employ a chaos expansion in order to construct an explicit exchangeable pair vector for any random variable wh...

We analyze the feasibility of extremely rapid estimation of correlation energy from the HF-SCF charge distribution in w Ž . x closed-shell molecules. In Kristyan’s previous work Chem. Phys. 224 1997 33-51 a simple linear relationship using atomic correlations was developed in order to calculate correlation energy of molecules. This method has been further refined in this Letter. The proposed me...

Abstract: We investigate four diatomic molecules containing transition metals using two variants of hybrid functionals. We compare global hybrid functionals that only partially counteract self-interaction to local hybrid functionals that are designed to be formally free from one-electron self-interaction. As d-orbitals are prone to be particularly strongly influenced by self-interaction errors,...

Stable direct and indirect decentralized adaptive radial basis neural network controllers are presented for a class of interconnected nonlinear systems. The feedback and adaptation mechanisms for each subsystem depend only upon local measurements to provide asymptotic tracking of a reference trajectory. Due to the functional approximation capabilities of radial basis neural networks, the dynami...

Ground state geometries have been computed using Density Functional Theory (DFT) at B3LYP/6-31G(d,p) level of theory. The excitation energies and spectroscopic parameters have been computed using Long range Corrected (LC) hybrid functional by Time Dependent Density Functional Theory (TDDFT) with LC-BLYP level of theory. The Polarizable Continuum Model (PC...

The development of new exchange-correlation functionals within density functional theory means that increasingly accurate information is accessible at moderate computational cost. Recently, a newly developed self-consistent hybrid functional has been proposed (Skone et al., Phys. Rev. B 89:195112, 2014), which allows for a reliable and accurate calculation of material properties using a fully a...