It is well known that the initialization of weights in deep neural networks can have a dramatic impact on learning speed. For example, ensuring the mean squared singular value of a network’s input-output Jacobian isO(1) is essential for avoiding the exponential vanishing or explosion of gradients. The stronger condition that all singular values of the Jacobian concentrate near 1 is a property k...

‎this paper presents two main results that the singular values of the hadamard product of normal matrices $a_i$ are weakly log-majorized by the singular values of the hadamard product of $|a_{i}|$ and the singular values of the sum of normal matrices $a_i$ are weakly log-majorized by the singular values of the sum of $|a_{i}|$‎. ‎some applications to these inequalities are also given‎. ‎in addi...

‎artificial neural networks have the advantages such as learning, ‎adaptation‎, ‎fault-tolerance‎, ‎parallelism and generalization‎. ‎this ‎paper is a scrutiny on the application of diverse learning methods‎ ‎in speed of convergence in neural networks‎. ‎for this aim‎, ‎first we ‎introduce a perceptron method based on artificial neural networks‎ ‎which has been applied for solving a non-singula...

Weighted inequalities with power-type weights for operators of harmonic analysis, such as maximal and singular integral operators, commutators integrals in grand variable exponent Lebesgue spaces are derived. The defined on quasi-metric measure doubling condition (spaces homogeneous type). proof the result regarding Hardy–Littlewood operator is based appropriate sharp weighted norm estimates we...

Abstract We prove weighted boundedness of Calderón–Zygmund and maximal singular operators in generalized Morrey spaces on quasi-metric measure spaces, general non-homogeneous, only under the growth condition measure, for a certain class weights. Weights characteristic are independent each other. Weighted operator is also proved case when lower upper Ahlfors exponents coincide with Our approach ...