\begin{table}[p]
\centering\scriptsize
\begin{threeparttable}
\caption{Ablation (exponential, $N = 3,145,728$): RMS of $\sqrt N\,\lVert\tilde\theta - \widehat\theta_N\rVert$ by split pattern, order $r$, Newton rounds $q$ and curvature used (exact / stale averaged local / single machine); quantized exact curvature with $b$ mantissa bits for $q = 1$.}\label{tab:abl_exponential}
\begin{tabular}{@{}llrr@{}}
\toprule
Pattern & curvature & $q$ & $m = 192$ \\
\midrule
(1) & exact & 0 & 9.283 \\
(1) & exact & 1 & 0.049 \\
(1) & exact & 2 & 1.33e-6 \\
(1) & exact & 3 & 2.18e-13 \\
(1) & stale & 1 & 0.096 \\
(1) & stale & 2 & 5.04e-4 \\
(1) & stale & 3 & 2.61e-6 \\
(1) & single & 1 & 0.049 \\
(1) & single & 2 & 1.33e-6 \\
(1) & single & 3 & 2.18e-13 \\
(1,2) & exact & 0 & 0.179 \\
(1,2) & exact & 1 & 2.96e-5 \\
(1,2) & exact & 2 & 1.48e-12 \\
(1,2) & exact & 3 & 2.24e-13 \\
(1,2) & stale & 1 & 8.95e-4 \\
(1,2) & stale & 2 & 4.61e-6 \\
(1,2) & stale & 3 & 2.37e-8 \\
(1,2) & single & 1 & 2.96e-5 \\
(1,2) & single & 2 & 1.48e-12 \\
(1,2) & single & 3 & 2.24e-13 \\
(1,3) & exact & 0 & 0.197 \\
(1,3) & exact & 1 & 3.26e-5 \\
(1,3) & exact & 2 & 1.42e-12 \\
(1,3) & exact & 3 & 2.18e-13 \\
(1,2,4) & exact & 0 & 0.208 \\
(1,2,4) & exact & 1 & 4.12e-5 \\
(1,2,4) & exact & 2 & 3.07e-12 \\
(1,2,4) & exact & 3 & 2.24e-13 \\
(1,2,4) & stale & 1 & 0.001 \\
(1,2,4) & stale & 2 & 5.58e-6 \\
(1,2,4) & stale & 3 & 2.89e-8 \\
(1,2,4) & single & 1 & 4.12e-5 \\
(1,2,4) & single & 2 & 3.07e-12 \\
(1,2,4) & single & 3 & 2.24e-13 \\
(1,2,3) & exact & 0 & 0.297 \\
(1,2,3) & exact & 1 & 8.73e-5 \\
(1,2,3) & exact & 2 & 1.39e-11 \\
(1,2,3) & exact & 3 & 2.26e-13 \\
(1,2,4,8) & exact & 0 & 0.256 \\
(1,2,4,8) & exact & 1 & 6.22e-5 \\
(1,2,4,8) & exact & 2 & 6.94e-12 \\
(1,2,4,8) & exact & 3 & 2.22e-13 \\
(1,2,3,4) & exact & 0 & 0.679 \\
(1,2,3,4) & exact & 1 & 4.78e-4 \\
(1,2,3,4) & exact & 2 & 4.57e-10 \\
(1,2,3,4) & exact & 3 & 2.20e-13 \\
\midrule
(1) & $b$-bit Hessian, $b=2$ & 1 & 0.050 \\
(1) & $b$-bit Hessian, $b=3$ & 1 & 0.050 \\
(1) & $b$-bit Hessian, $b=4$ & 1 & 0.050 \\
(1) & $b$-bit Hessian, $b=6$ & 1 & 0.098 \\
(1) & $b$-bit Hessian, $b=8$ & 1 & 0.052 \\
(1) & $b$-bit Hessian, $b=12$ & 1 & 0.049 \\
(1) & $b$-bit Hessian, $b=16$ & 1 & 0.049 \\
(1) & $b$-bit Hessian, $b=24$ & 1 & 0.049 \\
(1) & $b$-bit Hessian, $b=52$ & 1 & 0.049 \\
(1) & $b$-bit score, $b=2$ & 1 & 1.224 \\
(1) & $b$-bit score, $b=3$ & 1 & 0.540 \\
(1) & $b$-bit score, $b=4$ & 1 & 0.342 \\
(1) & $b$-bit score, $b=6$ & 1 & 0.082 \\
(1) & $b$-bit score, $b=8$ & 1 & 0.050 \\
(1) & $b$-bit score, $b=12$ & 1 & 0.049 \\
(1) & $b$-bit score, $b=16$ & 1 & 0.049 \\
(1) & $b$-bit score, $b=24$ & 1 & 0.049 \\
(1) & $b$-bit score, $b=52$ & 1 & 0.049 \\
(1) & $b$-bit both, $b=2$ & 1 & 1.115 \\
(1) & $b$-bit both, $b=3$ & 1 & 0.630 \\
(1) & $b$-bit both, $b=4$ & 1 & 0.266 \\
(1) & $b$-bit both, $b=6$ & 1 & 0.119 \\
(1) & $b$-bit both, $b=8$ & 1 & 0.053 \\
(1) & $b$-bit both, $b=12$ & 1 & 0.049 \\
(1) & $b$-bit both, $b=16$ & 1 & 0.049 \\
(1) & $b$-bit both, $b=24$ & 1 & 0.049 \\
(1) & $b$-bit both, $b=52$ & 1 & 0.049 \\
(1,2) & $b$-bit Hessian, $b=2$ & 1 & 1.97e-4 \\
(1,2) & $b$-bit Hessian, $b=3$ & 1 & 1.97e-4 \\
(1,2) & $b$-bit Hessian, $b=4$ & 1 & 1.97e-4 \\
(1,2) & $b$-bit Hessian, $b=6$ & 1 & 1.97e-4 \\
(1,2) & $b$-bit Hessian, $b=8$ & 1 & 1.89e-4 \\
(1,2) & $b$-bit Hessian, $b=12$ & 1 & 3.53e-5 \\
(1,2) & $b$-bit Hessian, $b=16$ & 1 & 2.97e-5 \\
(1,2) & $b$-bit Hessian, $b=24$ & 1 & 2.96e-5 \\
(1,2) & $b$-bit Hessian, $b=52$ & 1 & 2.96e-5 \\
(1,2) & $b$-bit score, $b=2$ & 1 & 0.018 \\
(1,2) & $b$-bit score, $b=3$ & 1 & 0.009 \\
(1,2) & $b$-bit score, $b=4$ & 1 & 0.005 \\
(1,2) & $b$-bit score, $b=6$ & 1 & 0.001 \\
(1,2) & $b$-bit score, $b=8$ & 1 & 2.98e-4 \\
(1,2) & $b$-bit score, $b=12$ & 1 & 3.39e-5 \\
(1,2) & $b$-bit score, $b=16$ & 1 & 2.96e-5 \\
(1,2) & $b$-bit score, $b=24$ & 1 & 2.96e-5 \\
(1,2) & $b$-bit score, $b=52$ & 1 & 2.96e-5 \\
(1,2) & $b$-bit both, $b=2$ & 1 & 0.018 \\
(1,2) & $b$-bit both, $b=3$ & 1 & 0.009 \\
(1,2) & $b$-bit both, $b=4$ & 1 & 0.005 \\
(1,2) & $b$-bit both, $b=6$ & 1 & 0.001 \\
(1,2) & $b$-bit both, $b=8$ & 1 & 3.40e-4 \\
(1,2) & $b$-bit both, $b=12$ & 1 & 3.84e-5 \\
(1,2) & $b$-bit both, $b=16$ & 1 & 2.97e-5 \\
(1,2) & $b$-bit both, $b=24$ & 1 & 2.96e-5 \\
(1,2) & $b$-bit both, $b=52$ & 1 & 2.96e-5 \\
(1,2,4) & $b$-bit Hessian, $b=2$ & 1 & 2.27e-4 \\
(1,2,4) & $b$-bit Hessian, $b=3$ & 1 & 2.27e-4 \\
(1,2,4) & $b$-bit Hessian, $b=4$ & 1 & 2.27e-4 \\
(1,2,4) & $b$-bit Hessian, $b=6$ & 1 & 2.27e-4 \\
(1,2,4) & $b$-bit Hessian, $b=8$ & 1 & 2.17e-4 \\
(1,2,4) & $b$-bit Hessian, $b=12$ & 1 & 4.90e-5 \\
(1,2,4) & $b$-bit Hessian, $b=16$ & 1 & 4.12e-5 \\
(1,2,4) & $b$-bit Hessian, $b=24$ & 1 & 4.12e-5 \\
(1,2,4) & $b$-bit Hessian, $b=52$ & 1 & 4.12e-5 \\
(1,2,4) & $b$-bit score, $b=2$ & 1 & 0.022 \\
(1,2,4) & $b$-bit score, $b=3$ & 1 & 0.011 \\
(1,2,4) & $b$-bit score, $b=4$ & 1 & 0.006 \\
(1,2,4) & $b$-bit score, $b=6$ & 1 & 0.001 \\
(1,2,4) & $b$-bit score, $b=8$ & 1 & 3.57e-4 \\
(1,2,4) & $b$-bit score, $b=12$ & 1 & 4.56e-5 \\
(1,2,4) & $b$-bit score, $b=16$ & 1 & 4.14e-5 \\
(1,2,4) & $b$-bit score, $b=24$ & 1 & 4.12e-5 \\
(1,2,4) & $b$-bit score, $b=52$ & 1 & 4.12e-5 \\
(1,2,4) & $b$-bit both, $b=2$ & 1 & 0.022 \\
(1,2,4) & $b$-bit both, $b=3$ & 1 & 0.011 \\
(1,2,4) & $b$-bit both, $b=4$ & 1 & 0.006 \\
(1,2,4) & $b$-bit both, $b=6$ & 1 & 0.001 \\
(1,2,4) & $b$-bit both, $b=8$ & 1 & 4.33e-4 \\
(1,2,4) & $b$-bit both, $b=12$ & 1 & 5.31e-5 \\
(1,2,4) & $b$-bit both, $b=16$ & 1 & 4.14e-5 \\
(1,2,4) & $b$-bit both, $b=24$ & 1 & 4.12e-5 \\
(1,2,4) & $b$-bit both, $b=52$ & 1 & 4.12e-5 \\
\bottomrule
\end{tabular}
\begin{tablenotes}\footnotesize
\item 1000 paired replications per column; $K = N/m$. Rows are omitted when the pattern does not divide $m$. Source: \texttt{results/processed/ablation\_exponential\_summary.csv}.
\end{tablenotes}
\end{threeparttable}
\end{table}