Abstract:

Bernstein Polynomials were one of the first mathematical polynomials that were used for approximation. Moreover, Neural networks were used for almost applicable targets. In this paper, we introduce the Bernstein neural network as a mathematical operator that combines the concepts of neural networks and Bernstein polynomials. It is used to approximate measurable functions by representing them as a weighted sum of Bernstein polynomials. Moreover, a special activation function that is derived from Bernstein Polynomials is defined and used to approximate functions. Furthermore, we estimate the degree of approximation with equivalent bounds to modulus of smoothness. Finally, we estimate the degree of approximation using comparable limitations to the modulus of smoothness.