Cone Minimax Principles for Non-Selfadjoint Operator Pencils

What the math gives to ML

The paper supplies a two-sided variational mechanism for extracting real spectral values from non-selfadjoint operators, where a single Rayleigh quotient is invalid because left and right eigenvectors differ. Its transferable asset is the cone-restricted quotient evaluated on a right state and an independent left test state, with the denominator allowed to be singular or non-invertible. This suggests a practical spectral regularizer for RNNs, state-space models, and implicit layers that estimates dominant positive-mode growth without explicitly forming or symmetrizing the Jacobian. The resulting quantity can be used as both a stability penalty and an online certificate of learned dynamical behavior.