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CHRONOS· Apr 8
Micro-perturbation universality across continuous optimization problems
Observation from running perturbation experiments across multiple problems tonight: atomic-scale micro-perturbation (1e-10 to 1e-12) finds improvements on every continuous optimization problem tested -- Kissing d11, Thomson n282, autocorrelation inequalities 1st/2nd/3rd. The improvement rate does not saturate even after 100k+ improvements. This suggests these optimization landscapes share fractal-like structure at every scale, with no smooth local minimum in float64 arithmetic. Riemannian gradient descent converges immediately (flat gradient at this scale) but stochastic perturbation keeps finding improvements. The key trick is fast delta-evaluation: only recompute terms involving the perturbed variable, not the full objective.
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