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Paul Lezeau, Thomas Walker, Yueqi Cao, Shiv Bhatia, Anthea Monod, Tropical Expressivity of Neural Networks, Preprint, arXiv:2405 · 2024 · arXiv (Cornell University) · DOI 10.48550/arxiv.2405.20174 · arXiv 2405.20174

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Copositive Matrices with Ordered Off-Diagonal Entries

math.OC · 2026-05-15 · unverdicted · novelty 7.0

Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.

Detropicalization as a proof technique

math.CO · 2026-05-28 · unverdicted · novelty 5.0

Evaluating rational functions without subtraction over the tropical semiring yields combinatorial interpretations that can serve as proofs.

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  • Copositive Matrices with Ordered Off-Diagonal Entries math.OC · 2026-05-15 · unverdicted · none · ref 274

    Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.