Approximation Algorithms Using Generalized Translation Networks with One Hidden Layer

Neural networks are widely studied by many researchers because neural networks can be flexibly applied to many physical areas including particle physics, astronomical physics, plasma physics, pattern recognition, very large scale integrated (VLSI) implementation, wireless networks, robotics and so on. In this paper, we investigate approximation algorithms for continuous multivariate target trajectories by using generalized translation networks. To do this, we first approximate continuous multivariate target trajectories by using multivariate Bernstein polynomials. The multivariate Bernstein polynomials are then approximated by using generalized translation networks. Finally, we can approximate the continuous multivariate target trajectories by using the generalized translation networks. Our approach gives not only the degree of approximation, but also the design of the hidden layer. That is, our research deals with the complexity problem, which is more difficult than the density problem. Moreover, the obtained algorithm does not rely on any smoothness of the multivariate target trajectories, but does rely on the the continuity of the multivariate target trajectories only. To support our theory, we demonstrate a numerical example. Neural networks are widely studied by many researchers because neural networks can be flexibly applied to many physical areas including particle physics, astronomical physics, plasma physics, pattern recognition, very large scale integrated (VLSI) implementation, wireless networks, robotics and so on. In this paper, we investigate approximation algorithms for continuous multivariate target trajectories by using generalized translation networks. To do this, we first approximate continuous multivariate target trajectories by using multivariate Bernstein polynomials. The multivariate Bernstein polynomials are then approximated by using generalized translation networks. Finally, we can approximate the continuous multivariate target trajectories by using the generalized translation networks. Our approach gives not only the degree of approximation, but also the design of the hidden layer. That is, our research deals with the complexity problem, which is more difficult than the density problem. Moreover, the obtained algorithm does not rely on any smoothness of the multivariate target trajectories, but does rely on the the continuity of the multivariate target trajectories only. To support our theory, we demonstrate a numerical example.