For ReLU networks with width at least two in input and hidden layers, an open set of parameters is identifiable, implying functional dimension equals parameter count minus hidden neurons.
Activation degree thresholds and expressiveness of polynomial neural networks , url =
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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.
For large monomial activation degree, critical points in deep fully-connected networks coincide exactly with subnetwork configurations where neurons are inactive or redundant.
citing papers explorer
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Most ReLU Networks Admit Identifiable Parameters
For ReLU networks with width at least two in input and hidden layers, an open set of parameters is identifiable, implying functional dimension equals parameter count minus hidden neurons.
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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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Singular Learning and Occam's Razor in Deep Monomial Networks
For large monomial activation degree, critical points in deep fully-connected networks coincide exactly with subnetwork configurations where neurons are inactive or redundant.