1\begin{table}[p]2\centering\scriptsize3\begin{threeparttable}4\caption{Ablation (logistic, $N = 196,608$): 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_logistic}5\begin{tabular}{@{}llrrr@{}}6\toprule7Pattern & curvature & $q$ & $m = 96$ & $m = 192$ \\8\midrule9(1) & exact & 0 & 57.779 & 26.208 \\10(1) & exact & 1 & 3.396 & 0.680 \\11(1) & exact & 2 & 0.011 & 4.48e-4 \\12(1) & exact & 3 & 1.21e-7 & 1.99e-10 \\13(1) & stale & 1 & 1.319 & 0.310 \\14(1) & stale & 2 & 0.111 & 0.012 \\15(1) & stale & 3 & 0.009 & 4.86e-4 \\16(1) & single & 1 & 17.164 & 4.707 \\17(1) & single & 2 & 11.647 & 1.777 \\18(1) & single & 3 & 11.038 & 0.816 \\19(1,2) & exact & 0 & 3271.882 & 5.903 \\20(1,2) & exact & 1 & 2.84e+7 & 0.034 \\21(1,2) & exact & 2 & 3.78e+29 & 1.32e-6 \\22(1,2) & exact & 3 & 3.78e+29 & 6.34e-14 \\23(1,2) & stale & 1 & 3146.098 & 0.268 \\24(1,2) & stale & 2 & 3040.887 & 0.011 \\25(1,2) & stale & 3 & 2939.939 & 4.70e-4 \\26(1,2) & single & 1 & 1.98e+9 & 1.089 \\27(1,2) & single & 2 & 3.02e+24 & 0.419 \\28(1,2) & single & 3 & 2.31e+38 & 0.190 \\29(1,3) & exact & 0 & 7569.958 & 11.668 \\30(1,3) & exact & 1 & 1.56e+8 & 0.373 \\31(1,3) & exact & 2 & 5.99e+46 & 0.002 \\32(1,3) & exact & 3 & 3.63e+151 & 6.37e-8 \\33(1,2,4) & exact & 0 & 2.55e+4 & 165.492 \\34(1,2,4) & exact & 1 & 2.81e+9 & 708.579 \\35(1,2,4) & exact & 2 & 4.00e+17 & 2.84e+5 \\36(1,2,4) & exact & 3 & 4.12e+100 & 1.01e+13 \\37(1,2,4) & stale & 1 & 2.52e+4 & 87.316 \\38(1,2,4) & stale & 2 & 2.49e+4 & 53.541 \\39(1,2,4) & stale & 3 & 2.46e+4 & 29.429 \\40(1,2,4) & single & 1 & 1.55e+26 & 657.174 \\41(1,2,4) & single & 2 & 4.16e+139 & 4.48e+5 \\42(1,2,4) & single & 3 & 4.18e+139 & 4.78e+21 \\43(1,2,3) & exact & 0 & 1.76e+4 & 12.815 \\44(1,2,3) & exact & 1 & 9.80e+8 & 1.688 \\45(1,2,3) & exact & 2 & 1.20e+23 & 0.043 \\46(1,2,3) & exact & 3 & 3.78e+143 & 3.45e-5 \\47(1,2,4,8) & exact & 0 & 5.00e+4 & 3158.571 \\48(1,2,4,8) & exact & 1 & 2.43e+10 & 1.05e+7 \\49(1,2,4,8) & exact & 2 & 4.24e+58 & 4.53e+24 \\50(1,2,4,8) & exact & 3 & 4.24e+58 & 8.65e+43 \\51(1,2,3,4) & exact & 0 & 8.61e+4 & 494.098 \\52(1,2,3,4) & exact & 1 & 1.42e+11 & 2.60e+4 \\53(1,2,3,4) & exact & 2 & 3.11e+32 & 7.27e+9 \\54(1,2,3,4) & exact & 3 & 3.97e+140 & 4.44e+11 \\55\midrule56(1) & $b$-bit Hessian, $b=2$ & 1 & 3.379 & 1.711 \\57(1) & $b$-bit Hessian, $b=3$ & 1 & 3.561 & 1.679 \\58(1) & $b$-bit Hessian, $b=4$ & 1 & 3.459 & 0.988 \\59(1) & $b$-bit Hessian, $b=6$ & 1 & 3.487 & 0.714 \\60(1) & $b$-bit Hessian, $b=8$ & 1 & 3.402 & 0.681 \\61(1) & $b$-bit Hessian, $b=12$ & 1 & 3.396 & 0.680 \\62(1) & $b$-bit Hessian, $b=16$ & 1 & 3.396 & 0.680 \\63(1) & $b$-bit Hessian, $b=24$ & 1 & 3.396 & 0.680 \\64(1) & $b$-bit Hessian, $b=52$ & 1 & 3.396 & 0.680 \\65(1) & $b$-bit score, $b=2$ & 1 & 4.349 & 1.865 \\66(1) & $b$-bit score, $b=3$ & 1 & 4.109 & 1.155 \\67(1) & $b$-bit score, $b=4$ & 1 & 3.566 & 0.836 \\68(1) & $b$-bit score, $b=6$ & 1 & 3.403 & 0.692 \\69(1) & $b$-bit score, $b=8$ & 1 & 3.397 & 0.679 \\70(1) & $b$-bit score, $b=12$ & 1 & 3.396 & 0.679 \\71(1) & $b$-bit score, $b=16$ & 1 & 3.396 & 0.680 \\72(1) & $b$-bit score, $b=24$ & 1 & 3.396 & 0.680 \\73(1) & $b$-bit score, $b=52$ & 1 & 3.396 & 0.680 \\74(1) & $b$-bit both, $b=2$ & 1 & 4.723 & 2.359 \\75(1) & $b$-bit both, $b=3$ & 1 & 4.292 & 1.907 \\76(1) & $b$-bit both, $b=4$ & 1 & 3.621 & 1.107 \\77(1) & $b$-bit both, $b=6$ & 1 & 3.493 & 0.727 \\78(1) & $b$-bit both, $b=8$ & 1 & 3.403 & 0.680 \\79(1) & $b$-bit both, $b=12$ & 1 & 3.396 & 0.679 \\80(1) & $b$-bit both, $b=16$ & 1 & 3.396 & 0.680 \\81(1) & $b$-bit both, $b=24$ & 1 & 3.396 & 0.680 \\82(1) & $b$-bit both, $b=52$ & 1 & 3.396 & 0.680 \\83(1,2) & $b$-bit Hessian, $b=2$ & 1 & 3.87e+5 & 0.377 \\84(1,2) & $b$-bit Hessian, $b=3$ & 1 & 2.88e+5 & 0.338 \\85(1,2) & $b$-bit Hessian, $b=4$ & 1 & 4.23e+5 & 0.141 \\86(1,2) & $b$-bit Hessian, $b=6$ & 1 & 1.10e+6 & 0.053 \\87(1,2) & $b$-bit Hessian, $b=8$ & 1 & 1.14e+7 & 0.035 \\88(1,2) & $b$-bit Hessian, $b=12$ & 1 & 4.41e+7 & 0.034 \\89(1,2) & $b$-bit Hessian, $b=16$ & 1 & 2.85e+7 & 0.034 \\90(1,2) & $b$-bit Hessian, $b=24$ & 1 & 2.84e+7 & 0.034 \\91(1,2) & $b$-bit Hessian, $b=52$ & 1 & 2.84e+7 & 0.034 \\92(1,2) & $b$-bit score, $b=2$ & 1 & 2.70e+7 & 0.489 \\93(1,2) & $b$-bit score, $b=3$ & 1 & 2.82e+7 & 0.254 \\94(1,2) & $b$-bit score, $b=4$ & 1 & 2.82e+7 & 0.128 \\95(1,2) & $b$-bit score, $b=6$ & 1 & 2.86e+7 & 0.047 \\96(1,2) & $b$-bit score, $b=8$ & 1 & 2.84e+7 & 0.035 \\97(1,2) & $b$-bit score, $b=12$ & 1 & 2.84e+7 & 0.034 \\98(1,2) & $b$-bit score, $b=16$ & 1 & 2.84e+7 & 0.034 \\99(1,2) & $b$-bit score, $b=24$ & 1 & 2.84e+7 & 0.034 \\100(1,2) & $b$-bit score, $b=52$ & 1 & 2.84e+7 & 0.034 \\101(1,2) & $b$-bit both, $b=2$ & 1 & 3.67e+5 & 0.596 \\102(1,2) & $b$-bit both, $b=3$ & 1 & 2.86e+5 & 0.412 \\103(1,2) & $b$-bit both, $b=4$ & 1 & 4.19e+5 & 0.189 \\104(1,2) & $b$-bit both, $b=6$ & 1 & 1.10e+6 & 0.062 \\105(1,2) & $b$-bit both, $b=8$ & 1 & 1.14e+7 & 0.036 \\106(1,2) & $b$-bit both, $b=12$ & 1 & 4.41e+7 & 0.034 \\107(1,2) & $b$-bit both, $b=16$ & 1 & 2.85e+7 & 0.034 \\108(1,2) & $b$-bit both, $b=24$ & 1 & 2.84e+7 & 0.034 \\109(1,2) & $b$-bit both, $b=52$ & 1 & 2.84e+7 & 0.034 \\110(1,2,4) & $b$-bit Hessian, $b=2$ & 1 & 5.83e+6 & 513.109 \\111(1,2,4) & $b$-bit Hessian, $b=3$ & 1 & 2.51e+7 & 553.804 \\112(1,2,4) & $b$-bit Hessian, $b=4$ & 1 & 8.40e+7 & 770.186 \\113(1,2,4) & $b$-bit Hessian, $b=6$ & 1 & 1.29e+7 & 690.742 \\114(1,2,4) & $b$-bit Hessian, $b=8$ & 1 & 5.97e+7 & 707.712 \\115(1,2,4) & $b$-bit Hessian, $b=12$ & 1 & 5.29e+8 & 708.627 \\116(1,2,4) & $b$-bit Hessian, $b=16$ & 1 & 3.48e+9 & 708.586 \\117(1,2,4) & $b$-bit Hessian, $b=24$ & 1 & 2.81e+9 & 708.579 \\118(1,2,4) & $b$-bit Hessian, $b=52$ & 1 & 2.81e+9 & 708.579 \\119(1,2,4) & $b$-bit score, $b=2$ & 1 & 2.70e+9 & 723.882 \\120(1,2,4) & $b$-bit score, $b=3$ & 1 & 2.76e+9 & 723.868 \\121(1,2,4) & $b$-bit score, $b=4$ & 1 & 2.76e+9 & 729.492 \\122(1,2,4) & $b$-bit score, $b=6$ & 1 & 2.82e+9 & 706.637 \\123(1,2,4) & $b$-bit score, $b=8$ & 1 & 2.81e+9 & 709.441 \\124(1,2,4) & $b$-bit score, $b=12$ & 1 & 2.81e+9 & 708.518 \\125(1,2,4) & $b$-bit score, $b=16$ & 1 & 2.81e+9 & 708.584 \\126(1,2,4) & $b$-bit score, $b=24$ & 1 & 2.81e+9 & 708.579 \\127(1,2,4) & $b$-bit score, $b=52$ & 1 & 2.81e+9 & 708.579 \\128(1,2,4) & $b$-bit both, $b=2$ & 1 & 5.73e+6 & 525.460 \\129(1,2,4) & $b$-bit both, $b=3$ & 1 & 2.55e+7 & 566.215 \\130(1,2,4) & $b$-bit both, $b=4$ & 1 & 8.34e+7 & 792.684 \\131(1,2,4) & $b$-bit both, $b=6$ & 1 & 1.29e+7 & 688.842 \\132(1,2,4) & $b$-bit both, $b=8$ & 1 & 5.98e+7 & 708.573 \\133(1,2,4) & $b$-bit both, $b=12$ & 1 & 5.29e+8 & 708.567 \\134(1,2,4) & $b$-bit both, $b=16$ & 1 & 3.48e+9 & 708.591 \\135(1,2,4) & $b$-bit both, $b=24$ & 1 & 2.81e+9 & 708.579 \\136(1,2,4) & $b$-bit both, $b=52$ & 1 & 2.81e+9 & 708.579 \\137\bottomrule138\end{tabular}139\begin{tablenotes}\footnotesize140\item 400 paired replications per column; $K = N/m$. Rows are omitted when the pattern does not divide $m$. Source: \texttt{results/processed/ablation\_logistic\_summary.csv}.141\end{tablenotes}142\end{threeparttable}143\end{table}144