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While implementing Batch Normalization for a particular layer 'L' with 'n' hidden neurons/units in a Neural Network, we first normalize the Activation values of that layer using their respective Mean and Standard Deviation, and then apply the Scaling and Offset factor as shown:

X-norm = (X - mu)/sd
X' = (Y * X-norm) + B

where
mu = mean of X and it is a (n,1) vector
sd = standard deviation of X and it is also a (n,1) vector
X = Activation values of layer 'L' with dimension (n,m) if mini-batch size = m
X-norm = normalized X with dimension (n,m)
Y = Gamma / Scaling factor
B = Beta / Offset factor

Now my question is, what are the dimensions of Gamma and Beta ? Are they (n,1) vectors or are they (n,m) matrices ? My intuition says that since they somewhat are analogous to the Mean and Standard Deviation, they should be (n,1) vectors.

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Gamma and Beta are just scalars for each layer, making the mean and variance of the layer unnecessarily being 0 and 1.

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