It is well known that the addition of noise to the input data of a neural network during training can, in some circumstances, lead to significant improvements in generalization performance. Previous work has shown that such training with noise is equivalent to a form of regularization in which an extra term is added to the error function. However, the regularization term, which involves second derivatives of the error function, is not bounded below, and so can lead to difficulties if used directly in a learning algorithm based on error minimization. In this paper we show that for the purposes of network training, the regularization term can be reduced to a positive semi-definite form that involves only first derivatives of the network mapping. For a sum-of-squares error function, the regularization term belongs to the class of generalized Tikhonov regularizers. Direct minimization of the regularized error function provides a practical alternative to training with noise.

In this paper we present results from the first use of neural networks for real-time control of the high-temperature plasma in a tokamak fusion experiment. The tokamak is currently the principal experimental device for research into the magnetic confinement approach to controlled fusion. In an effort to improve the energy confinement properties of the high-temperature plasma inside tokamaks, recent experiments have focused on the use of noncircular cross-sectional plasma shapes. However, the accurate generation of such plasmas represents a demanding problem involving simultaneous control of several parameters on a time scale as short as a few tens of microseconds. Application of neural networks to this problem requires fast hardware, for which we have developed a fully parallel custom implementation of a multilayer perceptron, based on a hybrid of digital and analogue techniques.