1\begin{table}[p]2\centering\scriptsize3\begin{threeparttable}4\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}5\begin{tabular}{@{}llrr@{}}6\toprule7Pattern & curvature & $q$ & $m = 192$ \\8\midrule9(1) & exact & 0 & 9.283 \\10(1) & exact & 1 & 0.049 \\11(1) & exact & 2 & 1.33e-6 \\12(1) & exact & 3 & 2.18e-13 \\13(1) & stale & 1 & 0.096 \\14(1) & stale & 2 & 5.04e-4 \\15(1) & stale & 3 & 2.61e-6 \\16(1) & single & 1 & 0.049 \\17(1) & single & 2 & 1.33e-6 \\18(1) & single & 3 & 2.18e-13 \\19(1,2) & exact & 0 & 0.179 \\20(1,2) & exact & 1 & 2.96e-5 \\21(1,2) & exact & 2 & 1.48e-12 \\22(1,2) & exact & 3 & 2.24e-13 \\23(1,2) & stale & 1 & 8.95e-4 \\24(1,2) & stale & 2 & 4.61e-6 \\25(1,2) & stale & 3 & 2.37e-8 \\26(1,2) & single & 1 & 2.96e-5 \\27(1,2) & single & 2 & 1.48e-12 \\28(1,2) & single & 3 & 2.24e-13 \\29(1,3) & exact & 0 & 0.197 \\30(1,3) & exact & 1 & 3.26e-5 \\31(1,3) & exact & 2 & 1.42e-12 \\32(1,3) & exact & 3 & 2.18e-13 \\33(1,2,4) & exact & 0 & 0.208 \\34(1,2,4) & exact & 1 & 4.12e-5 \\35(1,2,4) & exact & 2 & 3.07e-12 \\36(1,2,4) & exact & 3 & 2.24e-13 \\37(1,2,4) & stale & 1 & 0.001 \\38(1,2,4) & stale & 2 & 5.58e-6 \\39(1,2,4) & stale & 3 & 2.89e-8 \\40(1,2,4) & single & 1 & 4.12e-5 \\41(1,2,4) & single & 2 & 3.07e-12 \\42(1,2,4) & single & 3 & 2.24e-13 \\43(1,2,3) & exact & 0 & 0.297 \\44(1,2,3) & exact & 1 & 8.73e-5 \\45(1,2,3) & exact & 2 & 1.39e-11 \\46(1,2,3) & exact & 3 & 2.26e-13 \\47(1,2,4,8) & exact & 0 & 0.256 \\48(1,2,4,8) & exact & 1 & 6.22e-5 \\49(1,2,4,8) & exact & 2 & 6.94e-12 \\50(1,2,4,8) & exact & 3 & 2.22e-13 \\51(1,2,3,4) & exact & 0 & 0.679 \\52(1,2,3,4) & exact & 1 & 4.78e-4 \\53(1,2,3,4) & exact & 2 & 4.57e-10 \\54(1,2,3,4) & exact & 3 & 2.20e-13 \\55\midrule56(1) & $b$-bit Hessian, $b=2$ & 1 & 0.050 \\57(1) & $b$-bit Hessian, $b=3$ & 1 & 0.050 \\58(1) & $b$-bit Hessian, $b=4$ & 1 & 0.050 \\59(1) & $b$-bit Hessian, $b=6$ & 1 & 0.098 \\60(1) & $b$-bit Hessian, $b=8$ & 1 & 0.052 \\61(1) & $b$-bit Hessian, $b=12$ & 1 & 0.049 \\62(1) & $b$-bit Hessian, $b=16$ & 1 & 0.049 \\63(1) & $b$-bit Hessian, $b=24$ & 1 & 0.049 \\64(1) & $b$-bit Hessian, $b=52$ & 1 & 0.049 \\65(1) & $b$-bit score, $b=2$ & 1 & 1.224 \\66(1) & $b$-bit score, $b=3$ & 1 & 0.540 \\67(1) & $b$-bit score, $b=4$ & 1 & 0.342 \\68(1) & $b$-bit score, $b=6$ & 1 & 0.082 \\69(1) & $b$-bit score, $b=8$ & 1 & 0.050 \\70(1) & $b$-bit score, $b=12$ & 1 & 0.049 \\71(1) & $b$-bit score, $b=16$ & 1 & 0.049 \\72(1) & $b$-bit score, $b=24$ & 1 & 0.049 \\73(1) & $b$-bit score, $b=52$ & 1 & 0.049 \\74(1) & $b$-bit both, $b=2$ & 1 & 1.115 \\75(1) & $b$-bit both, $b=3$ & 1 & 0.630 \\76(1) & $b$-bit both, $b=4$ & 1 & 0.266 \\77(1) & $b$-bit both, $b=6$ & 1 & 0.119 \\78(1) & $b$-bit both, $b=8$ & 1 & 0.053 \\79(1) & $b$-bit both, $b=12$ & 1 & 0.049 \\80(1) & $b$-bit both, $b=16$ & 1 & 0.049 \\81(1) & $b$-bit both, $b=24$ & 1 & 0.049 \\82(1) & $b$-bit both, $b=52$ & 1 & 0.049 \\83(1,2) & $b$-bit Hessian, $b=2$ & 1 & 1.97e-4 \\84(1,2) & $b$-bit Hessian, $b=3$ & 1 & 1.97e-4 \\85(1,2) & $b$-bit Hessian, $b=4$ & 1 & 1.97e-4 \\86(1,2) & $b$-bit Hessian, $b=6$ & 1 & 1.97e-4 \\87(1,2) & $b$-bit Hessian, $b=8$ & 1 & 1.89e-4 \\88(1,2) & $b$-bit Hessian, $b=12$ & 1 & 3.53e-5 \\89(1,2) & $b$-bit Hessian, $b=16$ & 1 & 2.97e-5 \\90(1,2) & $b$-bit Hessian, $b=24$ & 1 & 2.96e-5 \\91(1,2) & $b$-bit Hessian, $b=52$ & 1 & 2.96e-5 \\92(1,2) & $b$-bit score, $b=2$ & 1 & 0.018 \\93(1,2) & $b$-bit score, $b=3$ & 1 & 0.009 \\94(1,2) & $b$-bit score, $b=4$ & 1 & 0.005 \\95(1,2) & $b$-bit score, $b=6$ & 1 & 0.001 \\96(1,2) & $b$-bit score, $b=8$ & 1 & 2.98e-4 \\97(1,2) & $b$-bit score, $b=12$ & 1 & 3.39e-5 \\98(1,2) & $b$-bit score, $b=16$ & 1 & 2.96e-5 \\99(1,2) & $b$-bit score, $b=24$ & 1 & 2.96e-5 \\100(1,2) & $b$-bit score, $b=52$ & 1 & 2.96e-5 \\101(1,2) & $b$-bit both, $b=2$ & 1 & 0.018 \\102(1,2) & $b$-bit both, $b=3$ & 1 & 0.009 \\103(1,2) & $b$-bit both, $b=4$ & 1 & 0.005 \\104(1,2) & $b$-bit both, $b=6$ & 1 & 0.001 \\105(1,2) & $b$-bit both, $b=8$ & 1 & 3.40e-4 \\106(1,2) & $b$-bit both, $b=12$ & 1 & 3.84e-5 \\107(1,2) & $b$-bit both, $b=16$ & 1 & 2.97e-5 \\108(1,2) & $b$-bit both, $b=24$ & 1 & 2.96e-5 \\109(1,2) & $b$-bit both, $b=52$ & 1 & 2.96e-5 \\110(1,2,4) & $b$-bit Hessian, $b=2$ & 1 & 2.27e-4 \\111(1,2,4) & $b$-bit Hessian, $b=3$ & 1 & 2.27e-4 \\112(1,2,4) & $b$-bit Hessian, $b=4$ & 1 & 2.27e-4 \\113(1,2,4) & $b$-bit Hessian, $b=6$ & 1 & 2.27e-4 \\114(1,2,4) & $b$-bit Hessian, $b=8$ & 1 & 2.17e-4 \\115(1,2,4) & $b$-bit Hessian, $b=12$ & 1 & 4.90e-5 \\116(1,2,4) & $b$-bit Hessian, $b=16$ & 1 & 4.12e-5 \\117(1,2,4) & $b$-bit Hessian, $b=24$ & 1 & 4.12e-5 \\118(1,2,4) & $b$-bit Hessian, $b=52$ & 1 & 4.12e-5 \\119(1,2,4) & $b$-bit score, $b=2$ & 1 & 0.022 \\120(1,2,4) & $b$-bit score, $b=3$ & 1 & 0.011 \\121(1,2,4) & $b$-bit score, $b=4$ & 1 & 0.006 \\122(1,2,4) & $b$-bit score, $b=6$ & 1 & 0.001 \\123(1,2,4) & $b$-bit score, $b=8$ & 1 & 3.57e-4 \\124(1,2,4) & $b$-bit score, $b=12$ & 1 & 4.56e-5 \\125(1,2,4) & $b$-bit score, $b=16$ & 1 & 4.14e-5 \\126(1,2,4) & $b$-bit score, $b=24$ & 1 & 4.12e-5 \\127(1,2,4) & $b$-bit score, $b=52$ & 1 & 4.12e-5 \\128(1,2,4) & $b$-bit both, $b=2$ & 1 & 0.022 \\129(1,2,4) & $b$-bit both, $b=3$ & 1 & 0.011 \\130(1,2,4) & $b$-bit both, $b=4$ & 1 & 0.006 \\131(1,2,4) & $b$-bit both, $b=6$ & 1 & 0.001 \\132(1,2,4) & $b$-bit both, $b=8$ & 1 & 4.33e-4 \\133(1,2,4) & $b$-bit both, $b=12$ & 1 & 5.31e-5 \\134(1,2,4) & $b$-bit both, $b=16$ & 1 & 4.14e-5 \\135(1,2,4) & $b$-bit both, $b=24$ & 1 & 4.12e-5 \\136(1,2,4) & $b$-bit both, $b=52$ & 1 & 4.12e-5 \\137\bottomrule138\end{tabular}139\begin{tablenotes}\footnotesize140\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}.141\end{tablenotes}142\end{threeparttable}143\end{table}144