Proves Spectral Alignment Decomposition α = 2 + dlogΦ_k / dlogσ_k and validates algebraic transfer identity s = αγ recovers Hessian decay to 2% error across 93 layers with no free parameters.
Products of Many Large Random Matrices and Gradients in Deep Neural Networks,
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Spectral Asymptotics of Neural Network Loss Landscapes: An Exact Decomposition of the Curvature Exponent
Proves Spectral Alignment Decomposition α = 2 + dlogΦ_k / dlogσ_k and validates algebraic transfer identity s = αγ recovers Hessian decay to 2% error across 93 layers with no free parameters.