LayerNorm and RMSNorm

Shows exactly which centering and bias operations RMSNorm removes from LayerNorm while retaining feature-wise rescaling.

LayerNorm centers x by its mean and scales by standard deviation before gain and bias, while RMSNorm skips centering and scales x by its root mean square before gain.

LayerNorm removes feature offset and scale, while RMSNorm removes only scale and performs fewer statistics.

Normalization by a feature-group scale is common to both; mean subtraction is the decisive structural difference.

The RMSNorm paper argues that re-scaling invariance can be retained without LayerNorm's re-centering operation.