When generating the guage tensor from the message matrix, the operation can be highly ill-conditioned. The message $M$ is a semi positive definite matrix, and we want $M^{0.5}$ and $M^{-0.5}$.
This can be done by eigen decomposition:
$$M = U D U^\dagger, M^{0.5} = U \sqrt{D}, M^{-0.5} = 1 / \sqrt{D} U^\dagger$$
However, there can be zero eigen values, in their paper they claim: "where a pseudoinverse may be required if small eigenvalues are present", and in code they added a small value link
I found that such operation leads to a large numerical error.
When generating the guage tensor from the message matrix, the operation can be highly ill-conditioned. The message$M$ is a semi positive definite matrix, and we want $M^{0.5}$ and $M^{-0.5}$ .
This can be done by eigen decomposition:
However, there can be zero eigen values, in their paper they claim: "where a pseudoinverse may be required if small eigenvalues are present", and in code they added a small value link
I found that such operation leads to a large numerical error.