\begin{table}[p]
\centering\scriptsize
\begin{threeparttable}
\caption{Ablation (exponential, $N = 6,291,456$): 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}{@{}llrrr@{}}
\toprule
Pattern & curvature & $q$ & $m = 24$ & $m = 96$ \\
\midrule
(1) & exact & 0 & 109.037 & 26.408 \\
(1) & exact & 1 & 4.740 & 0.278 \\
(1) & exact & 2 & 0.009 & 3.08e-5 \\
(1) & exact & 3 & 3.20e-8 & 4.80e-13 \\
(1) & stale & 1 & 8.721 & 0.545 \\
(1) & stale & 2 & 0.378 & 0.006 \\
(1) & stale & 3 & 0.015 & 5.91e-5 \\
(1) & single & 1 & 4.740 & 0.278 \\
(1) & single & 2 & 0.009 & 3.08e-5 \\
(1) & single & 3 & 3.20e-8 & 4.79e-13 \\
(1,2) & exact & 0 & 9.972 & 0.601 \\
(1,2) & exact & 1 & 0.040 & 1.77e-4 \\
(1,2) & exact & 2 & 6.42e-7 & 2.22e-11 \\
(1,2) & exact & 3 & 3.08e-13 & 3.14e-13 \\
(1,2) & stale & 1 & 0.360 & 0.006 \\
(1,2) & stale & 2 & 0.014 & 6.18e-5 \\
(1,2) & stale & 3 & 5.74e-4 & 6.35e-7 \\
(1,2) & single & 1 & 0.040 & 1.77e-4 \\
(1,2) & single & 2 & 6.42e-7 & 2.22e-11 \\
(1,2) & single & 3 & 3.08e-13 & 3.14e-13 \\
(1,3) & exact & 0 & 15.613 & 0.870 \\
(1,3) & exact & 1 & 0.097 & 3.28e-4 \\
(1,3) & exact & 2 & 3.79e-6 & 5.65e-11 \\
(1,3) & exact & 3 & 2.95e-13 & 3.11e-13 \\
(1,2,4) & exact & 0 & 2.032 & 0.312 \\
(1,2,4) & exact & 1 & 0.002 & 6.55e-5 \\
(1,2,4) & exact & 2 & 2.82e-9 & 5.44e-12 \\
(1,2,4) & exact & 3 & 3.18e-13 & 3.14e-13 \\
(1,2,4) & stale & 1 & 0.083 & 0.003 \\
(1,2,4) & stale & 2 & 0.003 & 3.32e-5 \\
(1,2,4) & stale & 3 & 1.33e-4 & 3.43e-7 \\
(1,2,4) & single & 1 & 0.002 & 6.55e-5 \\
(1,2,4) & single & 2 & 2.82e-9 & 5.44e-12 \\
(1,2,4) & single & 3 & 3.18e-13 & 3.14e-13 \\
(1,2,3) & exact & 0 & 1.647 & 0.429 \\
(1,2,3) & exact & 1 & 0.002 & 1.30e-4 \\
(1,2,3) & exact & 2 & 3.09e-9 & 2.25e-11 \\
(1,2,3) & exact & 3 & 3.08e-13 & 3.10e-13 \\
(1,2,4,8) & exact & 0 & 1.395 & 0.380 \\
(1,2,4,8) & exact & 1 & 0.001 & 9.80e-5 \\
(1,2,4,8) & exact & 2 & 1.01e-9 & 1.20e-11 \\
(1,2,4,8) & exact & 3 & 3.11e-13 & 3.13e-13 \\
(1,2,3,4) & exact & 0 & 2.247 & 0.957 \\
(1,2,3,4) & exact & 1 & 0.003 & 6.46e-4 \\
(1,2,3,4) & exact & 2 & 1.11e-8 & 6.13e-10 \\
(1,2,3,4) & exact & 3 & 3.04e-13 & 3.10e-13 \\
\midrule
(1) & $b$-bit Hessian, $b=2$ & 1 & 4.546 & 0.277 \\
(1) & $b$-bit Hessian, $b=3$ & 1 & 10.382 & 0.277 \\
(1) & $b$-bit Hessian, $b=4$ & 1 & 2.422 & 0.277 \\
(1) & $b$-bit Hessian, $b=6$ & 1 & 4.311 & 0.140 \\
(1) & $b$-bit Hessian, $b=8$ & 1 & 4.779 & 0.266 \\
(1) & $b$-bit Hessian, $b=12$ & 1 & 4.740 & 0.278 \\
(1) & $b$-bit Hessian, $b=16$ & 1 & 4.740 & 0.278 \\
(1) & $b$-bit Hessian, $b=24$ & 1 & 4.740 & 0.278 \\
(1) & $b$-bit Hessian, $b=52$ & 1 & 4.740 & 0.278 \\
(1) & $b$-bit score, $b=2$ & 1 & 18.990 & 3.612 \\
(1) & $b$-bit score, $b=3$ & 1 & 2.371 & 1.401 \\
(1) & $b$-bit score, $b=4$ & 1 & 8.324 & 1.115 \\
(1) & $b$-bit score, $b=6$ & 1 & 5.381 & 0.380 \\
(1) & $b$-bit score, $b=8$ & 1 & 4.742 & 0.283 \\
(1) & $b$-bit score, $b=12$ & 1 & 4.738 & 0.278 \\
(1) & $b$-bit score, $b=16$ & 1 & 4.740 & 0.278 \\
(1) & $b$-bit score, $b=24$ & 1 & 4.740 & 0.278 \\
(1) & $b$-bit score, $b=52$ & 1 & 4.740 & 0.278 \\
(1) & $b$-bit both, $b=2$ & 1 & 8.546 & 2.990 \\
(1) & $b$-bit both, $b=3$ & 1 & 2.959 & 1.919 \\
(1) & $b$-bit both, $b=4$ & 1 & 5.936 & 0.561 \\
(1) & $b$-bit both, $b=6$ & 1 & 4.952 & 0.268 \\
(1) & $b$-bit both, $b=8$ & 1 & 4.780 & 0.271 \\
(1) & $b$-bit both, $b=12$ & 1 & 4.738 & 0.278 \\
(1) & $b$-bit both, $b=16$ & 1 & 4.740 & 0.278 \\
(1) & $b$-bit both, $b=24$ & 1 & 4.740 & 0.278 \\
(1) & $b$-bit both, $b=52$ & 1 & 4.740 & 0.278 \\
(1,2) & $b$-bit Hessian, $b=2$ & 1 & 0.040 & 5.01e-4 \\
(1,2) & $b$-bit Hessian, $b=3$ & 1 & 0.040 & 5.01e-4 \\
(1,2) & $b$-bit Hessian, $b=4$ & 1 & 0.040 & 5.01e-4 \\
(1,2) & $b$-bit Hessian, $b=6$ & 1 & 0.040 & 5.01e-4 \\
(1,2) & $b$-bit Hessian, $b=8$ & 1 & 0.039 & 5.01e-4 \\
(1,2) & $b$-bit Hessian, $b=12$ & 1 & 0.040 & 1.89e-4 \\
(1,2) & $b$-bit Hessian, $b=16$ & 1 & 0.040 & 1.77e-4 \\
(1,2) & $b$-bit Hessian, $b=24$ & 1 & 0.040 & 1.77e-4 \\
(1,2) & $b$-bit Hessian, $b=52$ & 1 & 0.040 & 1.77e-4 \\
(1,2) & $b$-bit score, $b=2$ & 1 & 0.521 & 0.064 \\
(1,2) & $b$-bit score, $b=3$ & 1 & 0.498 & 0.032 \\
(1,2) & $b$-bit score, $b=4$ & 1 & 0.314 & 0.016 \\
(1,2) & $b$-bit score, $b=6$ & 1 & 0.084 & 0.004 \\
(1,2) & $b$-bit score, $b=8$ & 1 & 0.045 & 0.001 \\
(1,2) & $b$-bit score, $b=12$ & 1 & 0.040 & 1.91e-4 \\
(1,2) & $b$-bit score, $b=16$ & 1 & 0.040 & 1.77e-4 \\
(1,2) & $b$-bit score, $b=24$ & 1 & 0.040 & 1.77e-4 \\
(1,2) & $b$-bit score, $b=52$ & 1 & 0.040 & 1.77e-4 \\
(1,2) & $b$-bit both, $b=2$ & 1 & 0.489 & 0.064 \\
(1,2) & $b$-bit both, $b=3$ & 1 & 0.456 & 0.032 \\
(1,2) & $b$-bit both, $b=4$ & 1 & 0.323 & 0.016 \\
(1,2) & $b$-bit both, $b=6$ & 1 & 0.084 & 0.004 \\
(1,2) & $b$-bit both, $b=8$ & 1 & 0.044 & 0.001 \\
(1,2) & $b$-bit both, $b=12$ & 1 & 0.040 & 2.01e-4 \\
(1,2) & $b$-bit both, $b=16$ & 1 & 0.040 & 1.77e-4 \\
(1,2) & $b$-bit both, $b=24$ & 1 & 0.040 & 1.77e-4 \\
(1,2) & $b$-bit both, $b=52$ & 1 & 0.040 & 1.77e-4 \\
(1,2,4) & $b$-bit Hessian, $b=2$ & 1 & 0.002 & 2.57e-4 \\
(1,2,4) & $b$-bit Hessian, $b=3$ & 1 & 0.002 & 2.57e-4 \\
(1,2,4) & $b$-bit Hessian, $b=4$ & 1 & 0.002 & 2.57e-4 \\
(1,2,4) & $b$-bit Hessian, $b=6$ & 1 & 0.002 & 2.57e-4 \\
(1,2,4) & $b$-bit Hessian, $b=8$ & 1 & 0.004 & 2.54e-4 \\
(1,2,4) & $b$-bit Hessian, $b=12$ & 1 & 0.002 & 7.28e-5 \\
(1,2,4) & $b$-bit Hessian, $b=16$ & 1 & 0.002 & 6.58e-5 \\
(1,2,4) & $b$-bit Hessian, $b=24$ & 1 & 0.002 & 6.55e-5 \\
(1,2,4) & $b$-bit Hessian, $b=52$ & 1 & 0.002 & 6.55e-5 \\
(1,2,4) & $b$-bit score, $b=2$ & 1 & 0.194 & 0.033 \\
(1,2,4) & $b$-bit score, $b=3$ & 1 & 0.107 & 0.016 \\
(1,2,4) & $b$-bit score, $b=4$ & 1 & 0.048 & 0.009 \\
(1,2,4) & $b$-bit score, $b=6$ & 1 & 0.014 & 0.002 \\
(1,2,4) & $b$-bit score, $b=8$ & 1 & 0.004 & 5.51e-4 \\
(1,2,4) & $b$-bit score, $b=12$ & 1 & 0.002 & 6.97e-5 \\
(1,2,4) & $b$-bit score, $b=16$ & 1 & 0.002 & 6.55e-5 \\
(1,2,4) & $b$-bit score, $b=24$ & 1 & 0.002 & 6.55e-5 \\
(1,2,4) & $b$-bit score, $b=52$ & 1 & 0.002 & 6.55e-5 \\
(1,2,4) & $b$-bit both, $b=2$ & 1 & 0.194 & 0.033 \\
(1,2,4) & $b$-bit both, $b=3$ & 1 & 0.107 & 0.016 \\
(1,2,4) & $b$-bit both, $b=4$ & 1 & 0.048 & 0.009 \\
(1,2,4) & $b$-bit both, $b=6$ & 1 & 0.014 & 0.002 \\
(1,2,4) & $b$-bit both, $b=8$ & 1 & 0.005 & 6.03e-4 \\
(1,2,4) & $b$-bit both, $b=12$ & 1 & 0.002 & 7.66e-5 \\
(1,2,4) & $b$-bit both, $b=16$ & 1 & 0.002 & 6.58e-5 \\
(1,2,4) & $b$-bit both, $b=24$ & 1 & 0.002 & 6.55e-5 \\
(1,2,4) & $b$-bit both, $b=52$ & 1 & 0.002 & 6.55e-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}