Which of the following statements are true?

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a$.$ The mean output of a batch normalization layer is alaways $0.$

b$.$ For batch normalization a running mean of the mean batch activation $$ and standard deviation $$ has to be stored during the training phase.

c$.$ The mean output of a layer normalization layer is always $0,$ if no learnable parameters $$ and $$ are applied.

d$.$ For layer normalization a running mean of the mean batch activation $$ and standard deviation $$ has to be stored during the training phase.

e$.$ If the batch size is $1,$ batch normalization is equal to layer normalization