I have chosen a text of my preferred author and thinker Dr. Eliyahu Goldratt about "Engines of Disharmony". The text is publicly available on the website of Goldratt Consulting [1] in Pdf format. The text represents the foreword of the Japanese version of Eli's book "The Choice". I downloaded the Pdf file and transformed the text into a plain ASCII text. For the analysis, I only used the first four pages of the original document.

This paper first answers the question "why do the two most powerful techniques Dropout and Batch Normalization (BN) often lead to a worse performance when they are combined together?" in both theoretical and statistical aspects. Theoretically, we find that Dropout would shift the variance of a specific neural unit when we transfer the state of that network from train to test. However, BN would maintain its statistical variance, which is accumulated from the entire learning procedure, in the test phase. The inconsistency of that variance (we name this scheme as "variance shift") causes the unstable numerical behavior in inference that leads to more erroneous predictions finally, when applying Dropout before BN. Thorough experiments on DenseNet, ResNet, ResNeXt and Wide ResNet confirm our findings. According to the uncovered mechanism, we next explore several strategies that modifies Dropout and try to overcome the limitations of their combination by avoiding the variance shift risks.