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Adaptive pattern recognition and neural networks
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A stochastic version of the delta rule
CNLS '89 Proceedings of the ninth annual international conference of the Center for Nonlinear Studies on Self-organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks on Emergent computation
A back-propagation algorithm with optimal use of hidden units
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Neural Computation
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Neural Computation
Noise injection: theoretical prospects
Neural Computation
Randomizing Outputs to Increase Prediction Accuracy
Machine Learning
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Neural Processing Letters
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Neural Processing Letters
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AIKED'09 Proceedings of the 8th WSEAS international conference on Artificial intelligence, knowledge engineering and data bases
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A study of the effect of noise injection on the training of artificial neural networks
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Neural Processing Letters
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Applied Soft Computing
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Artificial Intelligence
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We study the effects of adding noise to the inputs, outputs, weight connections, and weight changes of multilayer feedforward neural networks during backpropagation training. We rigorously derive and analyze the objective functions that are minimized by the noise-affected training processes. We show that input noise and weight noise encourage the neural-network output to be a smooth function of the input or its weights, respectively. In the weak-noise limit, noise added to the output of the neural networks only changes the objective function by a constant. Hence, it cannot improve generalization. Input noise introduces penalty terms in the objective function that are related to, but distinct from, those found in the regularization approaches. Simulations have been performed on a regression and a classification problem to further substantiate our analysis. Input noise is found to be effective in improving the generalization performance for both problems. However, weight noise is found to be effective in improving the generalization performance only for the classification problem. Other forms of noise have practically no effect on generalization.