use biased estimate of std in layernorm as in the original paper #119
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The original paper computes a biased estimate of sample standard deviation. However, by default,
torch.Tensor.std()uses an unbiased estimate Ref. Therefore, it is necessary to usetorch.Tensor.std(-1,unbiased=False). Moreover, the classnn.LayerNorm()uses biased estimate as well. Though it does not make much difference for large dim, following the definition given in the cited paper is more appropriate.For PyTorch>=2.0, use
torch.Tensor.std(-1,correction=0).