Spectral Asymptotics of Neural Network Loss Landscapes: An Exact Decomposition of the Curvature Exponent

In three linesTheoretical study of neural network loss landscape geometry. Authors prove a Spectral Alignment Decomposition explaining why curvature exponent α varies across layer types (α≈2 convolutions, α≈1 transformer attention, α<1 MLP). Empirical validation on 93 layers, 5 architectures, 3 datasets with ~2% median error.

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