1\begin{table}[p]2\centering\scriptsize3\begin{threeparttable}4\caption{Ablation (exponential, $N = 1,572,864$): 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 & $q$ & $m = 96$ \\8\midrule9(1) & exact & 0 & 13.223 \\10(1) & exact & 1 & 0.139 \\11(1) & exact & 2 & 1.55e-5 \\12(1) & exact & 3 & 2.42e-13 \\13(1) & stale & 1 & 0.273 \\14(1) & stale & 2 & 0.003 \\15(1) & stale & 3 & 2.98e-5 \\16(1) & single & 1 & 0.139 \\17(1) & single & 2 & 1.55e-5 \\18(1) & single & 3 & 2.42e-13 \\19(1,2) & exact & 0 & 0.323 \\20(1,2) & exact & 1 & 1.29e-4 \\21(1,2) & exact & 2 & 3.32e-11 \\22(1,2) & exact & 3 & 1.57e-13 \\23(1,2) & stale & 1 & 0.003 \\24(1,2) & stale & 2 & 3.27e-5 \\25(1,2) & stale & 3 & 3.35e-7 \\26(1,2) & single & 1 & 1.29e-4 \\27(1,2) & single & 2 & 3.32e-11 \\28(1,2) & single & 3 & 1.57e-13 \\29(1,3) & exact & 0 & 0.437 \\30(1,3) & exact & 1 & 1.94e-4 \\31(1,3) & exact & 2 & 5.28e-11 \\32(1,3) & exact & 3 & 1.64e-13 \\33(1,2,4) & exact & 0 & 0.316 \\34(1,2,4) & exact & 1 & 1.30e-4 \\35(1,2,4) & exact & 2 & 3.44e-11 \\36(1,2,4) & exact & 3 & 1.51e-13 \\37(1,2,4) & stale & 1 & 0.003 \\38(1,2,4) & stale & 2 & 3.43e-5 \\39(1,2,4) & stale & 3 & 3.55e-7 \\40(1,2,4) & single & 1 & 1.30e-4 \\41(1,2,4) & single & 2 & 3.44e-11 \\42(1,2,4) & single & 3 & 1.51e-13 \\43(1,2,3) & exact & 0 & 0.446 \\44(1,2,3) & exact & 1 & 2.70e-4 \\45(1,2,3) & exact & 2 & 1.75e-10 \\46(1,2,3) & exact & 3 & 1.54e-13 \\47(1,2,4,8) & exact & 0 & 0.387 \\48(1,2,4,8) & exact & 1 & 1.98e-4 \\49(1,2,4,8) & exact & 2 & 8.24e-11 \\50(1,2,4,8) & exact & 3 & 1.53e-13 \\51(1,2,3,4) & exact & 0 & 1.003 \\52(1,2,3,4) & exact & 1 & 0.001 \\53(1,2,3,4) & exact & 2 & 5.56e-9 \\54(1,2,3,4) & exact & 3 & 1.43e-13 \\55\midrule56(1) & $b$-bit Hessian, $b=2$ & 1 & 0.140 \\57(1) & $b$-bit Hessian, $b=3$ & 1 & 0.140 \\58(1) & $b$-bit Hessian, $b=4$ & 1 & 0.140 \\59(1) & $b$-bit Hessian, $b=6$ & 1 & 0.091 \\60(1) & $b$-bit Hessian, $b=8$ & 1 & 0.140 \\61(1) & $b$-bit Hessian, $b=12$ & 1 & 0.139 \\62(1) & $b$-bit Hessian, $b=16$ & 1 & 0.139 \\63(1) & $b$-bit Hessian, $b=24$ & 1 & 0.139 \\64(1) & $b$-bit Hessian, $b=52$ & 1 & 0.139 \\65(1) & $b$-bit score, $b=2$ & 1 & 1.792 \\66(1) & $b$-bit score, $b=3$ & 1 & 0.728 \\67(1) & $b$-bit score, $b=4$ & 1 & 0.522 \\68(1) & $b$-bit score, $b=6$ & 1 & 0.165 \\69(1) & $b$-bit score, $b=8$ & 1 & 0.142 \\70(1) & $b$-bit score, $b=12$ & 1 & 0.139 \\71(1) & $b$-bit score, $b=16$ & 1 & 0.139 \\72(1) & $b$-bit score, $b=24$ & 1 & 0.139 \\73(1) & $b$-bit score, $b=52$ & 1 & 0.139 \\74(1) & $b$-bit both, $b=2$ & 1 & 1.482 \\75(1) & $b$-bit both, $b=3$ & 1 & 0.985 \\76(1) & $b$-bit both, $b=4$ & 1 & 0.310 \\77(1) & $b$-bit both, $b=6$ & 1 & 0.129 \\78(1) & $b$-bit both, $b=8$ & 1 & 0.143 \\79(1) & $b$-bit both, $b=12$ & 1 & 0.139 \\80(1) & $b$-bit both, $b=16$ & 1 & 0.139 \\81(1) & $b$-bit both, $b=24$ & 1 & 0.139 \\82(1) & $b$-bit both, $b=52$ & 1 & 0.139 \\83(1,2) & $b$-bit Hessian, $b=2$ & 1 & 5.20e-4 \\84(1,2) & $b$-bit Hessian, $b=3$ & 1 & 5.20e-4 \\85(1,2) & $b$-bit Hessian, $b=4$ & 1 & 5.20e-4 \\86(1,2) & $b$-bit Hessian, $b=6$ & 1 & 5.20e-4 \\87(1,2) & $b$-bit Hessian, $b=8$ & 1 & 4.80e-4 \\88(1,2) & $b$-bit Hessian, $b=12$ & 1 & 1.29e-4 \\89(1,2) & $b$-bit Hessian, $b=16$ & 1 & 1.29e-4 \\90(1,2) & $b$-bit Hessian, $b=24$ & 1 & 1.29e-4 \\91(1,2) & $b$-bit Hessian, $b=52$ & 1 & 1.29e-4 \\92(1,2) & $b$-bit score, $b=2$ & 1 & 0.034 \\93(1,2) & $b$-bit score, $b=3$ & 1 & 0.017 \\94(1,2) & $b$-bit score, $b=4$ & 1 & 0.008 \\95(1,2) & $b$-bit score, $b=6$ & 1 & 0.002 \\96(1,2) & $b$-bit score, $b=8$ & 1 & 5.35e-4 \\97(1,2) & $b$-bit score, $b=12$ & 1 & 1.37e-4 \\98(1,2) & $b$-bit score, $b=16$ & 1 & 1.29e-4 \\99(1,2) & $b$-bit score, $b=24$ & 1 & 1.29e-4 \\100(1,2) & $b$-bit score, $b=52$ & 1 & 1.29e-4 \\101(1,2) & $b$-bit both, $b=2$ & 1 & 0.034 \\102(1,2) & $b$-bit both, $b=3$ & 1 & 0.017 \\103(1,2) & $b$-bit both, $b=4$ & 1 & 0.008 \\104(1,2) & $b$-bit both, $b=6$ & 1 & 0.002 \\105(1,2) & $b$-bit both, $b=8$ & 1 & 6.71e-4 \\106(1,2) & $b$-bit both, $b=12$ & 1 & 1.38e-4 \\107(1,2) & $b$-bit both, $b=16$ & 1 & 1.29e-4 \\108(1,2) & $b$-bit both, $b=24$ & 1 & 1.29e-4 \\109(1,2) & $b$-bit both, $b=52$ & 1 & 1.29e-4 \\110(1,2,4) & $b$-bit Hessian, $b=2$ & 1 & 4.74e-4 \\111(1,2,4) & $b$-bit Hessian, $b=3$ & 1 & 4.74e-4 \\112(1,2,4) & $b$-bit Hessian, $b=4$ & 1 & 4.74e-4 \\113(1,2,4) & $b$-bit Hessian, $b=6$ & 1 & 4.74e-4 \\114(1,2,4) & $b$-bit Hessian, $b=8$ & 1 & 4.33e-4 \\115(1,2,4) & $b$-bit Hessian, $b=12$ & 1 & 1.41e-4 \\116(1,2,4) & $b$-bit Hessian, $b=16$ & 1 & 1.30e-4 \\117(1,2,4) & $b$-bit Hessian, $b=24$ & 1 & 1.30e-4 \\118(1,2,4) & $b$-bit Hessian, $b=52$ & 1 & 1.30e-4 \\119(1,2,4) & $b$-bit score, $b=2$ & 1 & 0.033 \\120(1,2,4) & $b$-bit score, $b=3$ & 1 & 0.017 \\121(1,2,4) & $b$-bit score, $b=4$ & 1 & 0.008 \\122(1,2,4) & $b$-bit score, $b=6$ & 1 & 0.002 \\123(1,2,4) & $b$-bit score, $b=8$ & 1 & 5.47e-4 \\124(1,2,4) & $b$-bit score, $b=12$ & 1 & 1.33e-4 \\125(1,2,4) & $b$-bit score, $b=16$ & 1 & 1.30e-4 \\126(1,2,4) & $b$-bit score, $b=24$ & 1 & 1.30e-4 \\127(1,2,4) & $b$-bit score, $b=52$ & 1 & 1.30e-4 \\128(1,2,4) & $b$-bit both, $b=2$ & 1 & 0.033 \\129(1,2,4) & $b$-bit both, $b=3$ & 1 & 0.017 \\130(1,2,4) & $b$-bit both, $b=4$ & 1 & 0.008 \\131(1,2,4) & $b$-bit both, $b=6$ & 1 & 0.002 \\132(1,2,4) & $b$-bit both, $b=8$ & 1 & 7.26e-4 \\133(1,2,4) & $b$-bit both, $b=12$ & 1 & 1.44e-4 \\134(1,2,4) & $b$-bit both, $b=16$ & 1 & 1.30e-4 \\135(1,2,4) & $b$-bit both, $b=24$ & 1 & 1.30e-4 \\136(1,2,4) & $b$-bit both, $b=52$ & 1 & 1.30e-4 \\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