Explicit Separators for Consecutive Levels of Parrilo's Sum-of-Squares Hierarchy over the Copositive Cone

What the math gives to ML

The paper provides a constructive hierarchy of increasingly powerful sum-of-squares certificates for nonnegativity on the nonnegative orthant, together with an exact threshold method for finding robust separators between consecutive levels. Its transferable mechanism is the use of nested certificates, dual witnesses, and a monotone shift threshold to detect when a Lyapunov inequality becomes certifiable. A neural-network implementation can use low-order SOS certificates as adaptive stability monitors or regularizers, increasing the certificate level only when a weaker level fails.