The paper derives a DAG-indexed block decomposition of the neural network Hessian into Gauss-Newton and tensor components and introduces stochastic O(P) metrics for inter-layer curvature interactions such as resonance and geometric coupling.
]⊤ intersects non-smoothness hyperplanes transversally), the set of non-smooth points has Lebesgue measure zero
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Inter-Layer Hessian Analysis of Neural Networks with DAG Architectures
The paper derives a DAG-indexed block decomposition of the neural network Hessian into Gauss-Newton and tensor components and introduces stochastic O(P) metrics for inter-layer curvature interactions such as resonance and geometric coupling.