It is well known that IN is simply 1-batch of BN. It is true in training phase, but not in inference.

In inference phase, BN uses popular mini-batch statistic for mean and standard variation, while IN uses them unchanged from training time, as noted in AdaIN paper below.

Reference: arxiv.org/abs/1703.06868

Rank is the number of linearly independent rows or columns in a matrix. Following matrix is a 2-rank matrix(not 3) as 3rd row can be made by composition of 1st and 2nd row.

Reference: https://blog.naver.com/dhkdwnddml/220313237499