Slice and Partition Rank Criteria for Polynomial Zero-Avoidance

What the math gives to ML

The paper turns support-entropy arguments into finite, checkable certificates: failure of a uniform-marginal distribution on a coefficient support yields an explicit entropy gap rather than merely an asymptotic statement. This is potentially transferable to tensorized neural layers, where the support of allowed interactions controls both parameter count and contraction cost. The most practical adaptation is a certificate-guided design or pruning method for higher-order interaction layers: retain channel-interaction supports whose marginal constraints admit a large dual margin, because their effective tensor rank is provably below the naive alphabet-size bound. The extracted material does not establish a direct neural-network theorem, so the expected ML payoff is moderate and should be tested first on small polynomial or tensorized MLPs.