Multilayer feedforward networks are universal approximators
Neural Networks
Approximation capabilities of multilayer feedforward networks
Neural Networks
Universal approximation using radial-basis-function networks
Neural Computation
Journal of Computational and Applied Mathematics
Advances in Applied Mathematics
Multilayer neural networks and Bayes decision theory
Neural Networks
Simultaneous Lp-approximation order for neural networks
Neural Networks
Minimization of error functionals over perceptron networks
Neural Computation
Bayesian decision theory on three-layer neural networks
Neurocomputing
Bayesian learning of neural networks adapted to changes of prior probabilities
ICANN'05 Proceedings of the 15th international conference on Artificial neural networks: formal models and their applications - Volume Part II
Discriminant analysis by a neural network with mahalanobis distance
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part II
Multi-category Bayesian Decision by Neural Networks
ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part I
A new algorithm for learning mahalanobis discriminant functions by a neural network
ICONIP'11 Proceedings of the 18th international conference on Neural Information Processing - Volume Part II
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part V
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We have constructed one-hidden-layer neural networks capable of approximating polynomials and their derivatives simultaneously. Generally, optimizing neural network parameters to be trained at later steps of the BP training is more difficult than optimizing those to be trained at the first step. Taking into account this fact, we suppressed the number of parameters of the former type. We measure degree of approximation in both the uniform norm on compact sets and the Lp-norm on the whole space with respect to probability measures.