A Spectral Phase Admissibility Certificate for Complex Linear Maps

The paper imports the Kontsevich Segal Witten criterion from quantum gravity into machine learning to evaluate complex linear maps Standard techniques analyze magnitude or positive definiteness whereas this method exclusively limits the collective phase of a spectrum The researchers create three distinct differentiable certificates comprising a determinant sector a subset product envelope and the full criterion The subset envelope prevents all exterior power eigenvalues from touching the negative real axis This constraint precisely matches the accept or reject choices of an exponential minor enumeration while reducing processing expenses drastically The team provides a differentiable enforcement application via a Schur parameterization The document also identifies crucial boundaries regarding where this system works The constraint cannot balance deep linear propagation since restricting the phase budget damages eigenvector conditioning Furthermore the technique remains completely blind to magnitude based targets like normalizing flow likelihoods Thus researchers must restrict this tool specifically to models that process the argument of a spectral product