Gradient descent paths align with tangent spaces to gradient extremals and concentrate in valleys around talwegs, with alignment rates set by spectral gaps or the smallest Hessian eigenvalue under non-resonance conditions.
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Gradient extremals, talwegs, valleys, and directional alignment for generic gradient descent
Gradient descent paths align with tangent spaces to gradient extremals and concentrate in valleys around talwegs, with alignment rates set by spectral gaps or the smallest Hessian eigenvalue under non-resonance conditions.