Possible typo in the tangent-normalization formula in rCM and Causal-rCM

[chijw]

Thank you for the great work and for releasing the code!

I noticed a possible typo in the tangent normalization formula in both rCM and Causal-rCM.

The paper seems to use

and claims that

$$ \left|F_\theta-F_{\theta^-}-\frac{g}{|g|_2^2+c}\right|_2^2=\frac{|g|_2^2}{|g|_2^2+c}\approx 1. $$

However, the left-hand side appears to be

$$ \frac{|g|_2^2}{(|g|_2^2+c)^2}, $$

which is generally not close to 1.

The released code instead seems to use

g = g.double() / (g.double().norm(p=2, dim=(1, 2, 3, 4), keepdim=True) + 0.1)

which gives

$$ \frac{|g|_2^2}{(|g|_2+c)^2}\approx 1 $$

when $|g|_2 \gg c$, and this also seems consistent with the sCM formulation:

Could you confirm whether this is just a typo in the rCM and Causal-rCM papers? Thanks!