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While the authors of Batch Normalization (BN) identify and address animportant problem involved in training deep networks-- \textit{InternalCovariate Shift}-- the current solution has certain drawbacks. For instance, BNdepends on batch statistics for layerwise input normalization during trainingwhich makes the estimates of mean and standard deviation of input(distribution) to hidden layers inaccurate due to shifting parameter values(especially during initial training epochs). Another fundamental problem withBN is that it cannot be used with batch-size $ 1 $ during training. We addressthese drawbacks of BN by proposing a non-adaptive normalization technique forremoving covariate shift, that we call \textit{Normalization Propagation}. Ourapproach does not depend on batch statistics, but rather uses adata-independent parametric estimate of mean and standard-deviation in everylayer thus being computationally faster compared with BN. We exploit theobservation that the pre-activation before Rectified Linear Units followGaussian distribution in deep networks, and that once the first and secondorder statistics of any given dataset are normalized, we can forward propagatethis normalization without the need for recalculating the approximatestatistics for hidden layers.

Why Regularized Auto-Encoders learn Sparse Representation?