From Data Distributions to Regularization in Invariant Learning

For unbiased models the regulatizer reducesto the intuitive form that penalizes the mean squared difference between the network output for transformed and untransformed inputs - i.e. the error in satisfying the desired invariance. In general the regularizer includes a term that measures correlations between the error in fitting the data, and the error in satisfying the desired inva.riance. For infinitesimal transformations, the regularizer is equivalent (up to terms linear in the variance of the transformation parameters) to the tangent prop form given by Simard et a1.