Reply to "Comments on 'Using Neural Networks to Predict Dye Concentrations in Multiple-Dye Mixtures'"

We appreciate Dr. Vangheluwe’s comments on neural nets and the importance of verification and validation of models generated with the back propagation method. If the number of degrees of freedom is larger than the amount of independent experimental data, then the model may memorize the training data and not learn. This is a real danger with neural networks. The number of degrees of freedom is actually related to the number of hidden nodes, which should be kept