Approximation of smooth functions by neural networks
نویسنده
چکیده
We review some aspects of our recent work on the approximation of functions by neural and generalized translation networks.
منابع مشابه
Approximation bounds for smooth functions in C(Rd) by neural and mixture networks
We consider the approximation of smooth multivariate functions in C(IRd) by feedforward neural networks with a single hidden layer of nonlinear ridge functions. Under certain assumptions on the smoothness of the functions being approximated and on the activation functions in the neural network, we present upper bounds on the degree of approximation achieved over the domain IRd, thereby generali...
متن کاملApproximation Bounds for Smooth Functions in C(IRd) by Neural and Mixture Networks
We consider the approximation of smooth multivariate functions in C(I R d) by feedforward neural networks with a single hidden layer of non-linear ridge functions. Under certain assumptions on the smoothness of the functions being approximated and on the activation functions in the neural network, we present upper bounds on the degree of approximation achieved over the domain IR d , thereby gen...
متن کاملNeural Networks for Optimal Approximation of Smooth and Analytic Functions
We prove that neural networks with a single hidden layer are capable of providing an optimal order of approximation for functions assumed to possess a given number of derivatives, if the activation function evaluated by each principal element satisfies certain technical conditions. Under these conditions, it is also possible to construct networks that provide a geometric order of approximation ...
متن کاملOptimal approximation of piecewise smooth functions using deep ReLU neural networks
We study the necessary and sufficient complexity of ReLU neural networks—in terms of depth and number of weights—which is required for approximating classifier functions in an L-sense. As a model class, we consider the set E(R) of possibly discontinuous piecewise C functions f : [−1/2, 1/2] → R, where the different “smooth regions” of f are separated by C hypersurfaces. For given dimension d ≥ ...
متن کاملVerification of an Evolutionary-based Wavelet Neural Network Model for Nonlinear Function Approximation
Nonlinear function approximation is one of the most important tasks in system analysis and identification. Several models have been presented to achieve an accurate approximation on nonlinear mathematics functions. However, the majority of the models are specific to certain problems and systems. In this paper, an evolutionary-based wavelet neural network model is proposed for structure definiti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998