In this paper, we study the simultaneous approximation to functions in Cm[0, 1] by neural networks with a squashing function and the complexity related to the simultaneous approximation using a Bernstein polynomial and the modulus of continuity. Our proofs are constructive.

For proving linear independence of real numbers, Hermite [18] considered simultaneous approximation to these numbers by algebraic numbers. The point of view introduced by Siegel in 1929 [34] is dual (duality in the sense of convex bodies): he considers simultaneous approximation by means of independent linear forms. We define the height of a linear form L = a0X0 + · · · + amXm with complex coef...

The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for optimization problems where it is di cult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly e cient simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on ...

The Quantum Fisher Information matrix (QFIM) is a central metric in promising algorithms, such as Natural Gradient Descent and Variational Imaginary Time Evolution. Computing the full QFIM for model withdparameters, however, computationally expensive generally requires<mml:math xmlns:mml="http://www.w3.org/1998...