@JanoschMenke torch BatchNorm1d doesn’t use unbiased estimator for variance.
And running_mean and running_var only apply when model is in eval mode.
Also, BatchNorm1d module has learnable affine parameters. That you should consider when computing output. But it initializes with 0 and 1 for bias and gamma.
Running averages are changing as you forward the input through the model.
print((beispiel_x -torch.mean(beispiel_x, axis=0))/torch.sqrt(torch.var(beispiel_x, axis=0,unbiased=False)+bn.eps))

>>> 
tensor([[-1.2247, -0.7071,  0.7071,  1.2247,  1.3363],
        [ 0.0000, -0.7071, -1.4142, -1.2247, -1.0690],
        [ 1.2247,  1.4142,  0.7071,  0.0000, -0.2673]])