Langevin Monte Carlo discretization error is controlled by average coordinate-wise smoothness rather than global smoothness in the strongly log-concave setting.
The generalization error of random features regression: precise asymptotics and the double descent curve
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Extends high-dimensional KRR to product kernels, proving convergence rates that recover minimax optimality for source condition s ≤ 1, saturation for s > 1, and multiple-descent phenomena with respect to sample size n.
Derives adaptive generalization bounds {c_m / N^{1/(2∨m)}} for digital ML models via new concentration of measure results on finite metric spaces, with c_m = O(sqrt(m)).
Repetition of training data produces a systematic eval loss peak at intermediate repeat counts whose location scales with model size, quantifiable as large compute-equivalent loss even at modest repetition fractions.
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Improved Guarantees for Langevin Monte Carlo with Average Smoothness
Langevin Monte Carlo discretization error is controlled by average coordinate-wise smoothness rather than global smoothness in the strongly log-concave setting.