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.
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A counterexample disproves the conjecture that minimal filling architectures of polynomial neural networks always have unimodal hidden layer widths.
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Copositive Matrices with Ordered Off-Diagonal Entries
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.
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Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects
A counterexample disproves the conjecture that minimal filling architectures of polynomial neural networks always have unimodal hidden layer widths.