1\begin{table}[p]2\centering\scriptsize3\begin{threeparttable}4\caption{Ablation (logistic, $N = 786,432$): 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 & $q$ & $m = 192$ & $m = 768$ \\8\midrule9(1) & exact & 0 & 52.268 & 12.296 \\10(1) & exact & 1 & 1.350 & 0.073 \\11(1) & exact & 2 & 8.80e-4 & 2.61e-6 \\12(1) & exact & 3 & 3.75e-10 & 1.27e-13 \\13(1) & stale & 1 & 0.615 & 0.036 \\14(1) & stale & 2 & 0.024 & 3.32e-4 \\15(1) & stale & 3 & 9.10e-4 & 3.14e-6 \\16(1) & single & 1 & 9.113 & 1.013 \\17(1) & single & 2 & 3.342 & 0.167 \\18(1) & single & 3 & 1.538 & 0.030 \\19(1,2) & exact & 0 & 11.228 & 1.167 \\20(1,2) & exact & 1 & 0.061 & 5.63e-4 \\21(1,2) & exact & 2 & 1.91e-6 & 2.41e-10 \\22(1,2) & exact & 3 & 1.30e-13 & 1.27e-13 \\23(1,2) & stale & 1 & 0.490 & 0.014 \\24(1,2) & stale & 2 & 0.019 & 1.62e-4 \\25(1,2) & stale & 3 & 7.41e-4 & 1.98e-6 \\26(1,2) & single & 1 & 1.900 & 0.121 \\27(1,2) & single & 2 & 0.710 & 0.020 \\28(1,2) & single & 3 & 0.336 & 0.004 \\29(1,3) & exact & 0 & 23.360 & 1.201 \\30(1,3) & exact & 1 & 0.735 & 6.83e-4 \\31(1,3) & exact & 2 & 0.004 & 3.61e-10 \\32(1,3) & exact & 3 & 1.39e-7 & 1.27e-13 \\33(1,2,4) & exact & 0 & 267.576 & 1.511 \\34(1,2,4) & exact & 1 & 1410.845 & 8.22e-4 \\35(1,2,4) & exact & 2 & 5.77e+5 & 5.37e-10 \\36(1,2,4) & exact & 3 & 1.55e+13 & 1.27e-13 \\37(1,2,4) & stale & 1 & 167.463 & 0.018 \\38(1,2,4) & stale & 2 & 112.549 & 2.21e-4 \\39(1,2,4) & stale & 3 & 64.138 & 2.76e-6 \\40(1,2,4) & single & 1 & 1415.946 & 0.167 \\41(1,2,4) & single & 2 & 4.37e+5 & 0.028 \\42(1,2,4) & single & 3 & 7.63e+94 & 0.006 \\43(1,2,3) & exact & 0 & 23.384 & 2.154 \\44(1,2,3) & exact & 1 & 2.991 & 0.002 \\45(1,2,3) & exact & 2 & 0.073 & 2.21e-9 \\46(1,2,3) & exact & 3 & 4.99e-5 & 1.28e-13 \\47(1,2,4,8) & exact & 0 & 3530.386 & 1.864 \\48(1,2,4,8) & exact & 1 & 8.08e+5 & 0.001 \\49(1,2,4,8) & exact & 2 & 4.30e+13 & 1.18e-9 \\50(1,2,4,8) & exact & 3 & 7.62e+39 & 1.28e-13 \\51(1,2,3,4) & exact & 0 & 792.244 & 4.986 \\52(1,2,3,4) & exact & 1 & 5.62e+4 & 0.009 \\53(1,2,3,4) & exact & 2 & 1.55e+10 & 5.93e-8 \\54(1,2,3,4) & exact & 3 & 1.55e+10 & 1.27e-13 \\55\midrule56(1) & $b$-bit Hessian, $b=2$ & 1 & 3.520 & 0.759 \\57(1) & $b$-bit Hessian, $b=3$ & 1 & 3.313 & 0.682 \\58(1) & $b$-bit Hessian, $b=4$ & 1 & 1.939 & 0.306 \\59(1) & $b$-bit Hessian, $b=6$ & 1 & 1.412 & 0.142 \\60(1) & $b$-bit Hessian, $b=8$ & 1 & 1.351 & 0.077 \\61(1) & $b$-bit Hessian, $b=12$ & 1 & 1.350 & 0.073 \\62(1) & $b$-bit Hessian, $b=16$ & 1 & 1.350 & 0.073 \\63(1) & $b$-bit Hessian, $b=24$ & 1 & 1.350 & 0.073 \\64(1) & $b$-bit Hessian, $b=52$ & 1 & 1.350 & 0.073 \\65(1) & $b$-bit score, $b=2$ & 1 & 3.663 & 0.861 \\66(1) & $b$-bit score, $b=3$ & 1 & 2.006 & 0.446 \\67(1) & $b$-bit score, $b=4$ & 1 & 1.626 & 0.241 \\68(1) & $b$-bit score, $b=6$ & 1 & 1.375 & 0.095 \\69(1) & $b$-bit score, $b=8$ & 1 & 1.352 & 0.075 \\70(1) & $b$-bit score, $b=12$ & 1 & 1.350 & 0.073 \\71(1) & $b$-bit score, $b=16$ & 1 & 1.350 & 0.073 \\72(1) & $b$-bit score, $b=24$ & 1 & 1.350 & 0.073 \\73(1) & $b$-bit score, $b=52$ & 1 & 1.350 & 0.073 \\74(1) & $b$-bit both, $b=2$ & 1 & 4.782 & 1.133 \\75(1) & $b$-bit both, $b=3$ & 1 & 3.480 & 0.791 \\76(1) & $b$-bit both, $b=4$ & 1 & 2.180 & 0.382 \\77(1) & $b$-bit both, $b=6$ & 1 & 1.440 & 0.154 \\78(1) & $b$-bit both, $b=8$ & 1 & 1.353 & 0.079 \\79(1) & $b$-bit both, $b=12$ & 1 & 1.350 & 0.073 \\80(1) & $b$-bit both, $b=16$ & 1 & 1.350 & 0.073 \\81(1) & $b$-bit both, $b=24$ & 1 & 1.350 & 0.073 \\82(1) & $b$-bit both, $b=52$ & 1 & 1.350 & 0.073 \\83(1,2) & $b$-bit Hessian, $b=2$ & 1 & 0.714 & 0.072 \\84(1,2) & $b$-bit Hessian, $b=3$ & 1 & 0.654 & 0.066 \\85(1,2) & $b$-bit Hessian, $b=4$ & 1 & 0.256 & 0.027 \\86(1,2) & $b$-bit Hessian, $b=6$ & 1 & 0.099 & 0.008 \\87(1,2) & $b$-bit Hessian, $b=8$ & 1 & 0.063 & 0.002 \\88(1,2) & $b$-bit Hessian, $b=12$ & 1 & 0.061 & 5.76e-4 \\89(1,2) & $b$-bit Hessian, $b=16$ & 1 & 0.061 & 5.63e-4 \\90(1,2) & $b$-bit Hessian, $b=24$ & 1 & 0.061 & 5.63e-4 \\91(1,2) & $b$-bit Hessian, $b=52$ & 1 & 0.061 & 5.63e-4 \\92(1,2) & $b$-bit score, $b=2$ & 1 & 0.855 & 0.116 \\93(1,2) & $b$-bit score, $b=3$ & 1 & 0.461 & 0.058 \\94(1,2) & $b$-bit score, $b=4$ & 1 & 0.234 & 0.030 \\95(1,2) & $b$-bit score, $b=6$ & 1 & 0.083 & 0.008 \\96(1,2) & $b$-bit score, $b=8$ & 1 & 0.063 & 0.002 \\97(1,2) & $b$-bit score, $b=12$ & 1 & 0.061 & 5.71e-4 \\98(1,2) & $b$-bit score, $b=16$ & 1 & 0.061 & 5.63e-4 \\99(1,2) & $b$-bit score, $b=24$ & 1 & 0.061 & 5.63e-4 \\100(1,2) & $b$-bit score, $b=52$ & 1 & 0.061 & 5.63e-4 \\101(1,2) & $b$-bit both, $b=2$ & 1 & 1.093 & 0.136 \\102(1,2) & $b$-bit both, $b=3$ & 1 & 0.766 & 0.085 \\103(1,2) & $b$-bit both, $b=4$ & 1 & 0.345 & 0.040 \\104(1,2) & $b$-bit both, $b=6$ & 1 & 0.115 & 0.011 \\105(1,2) & $b$-bit both, $b=8$ & 1 & 0.065 & 0.003 \\106(1,2) & $b$-bit both, $b=12$ & 1 & 0.061 & 5.84e-4 \\107(1,2) & $b$-bit both, $b=16$ & 1 & 0.061 & 5.63e-4 \\108(1,2) & $b$-bit both, $b=24$ & 1 & 0.061 & 5.63e-4 \\109(1,2) & $b$-bit both, $b=52$ & 1 & 0.061 & 5.63e-4 \\110(1,2,4) & $b$-bit Hessian, $b=2$ & 1 & 710.398 & 0.093 \\111(1,2,4) & $b$-bit Hessian, $b=3$ & 1 & 1702.282 & 0.085 \\112(1,2,4) & $b$-bit Hessian, $b=4$ & 1 & 1382.610 & 0.035 \\113(1,2,4) & $b$-bit Hessian, $b=6$ & 1 & 1398.623 & 0.010 \\114(1,2,4) & $b$-bit Hessian, $b=8$ & 1 & 1400.676 & 0.002 \\115(1,2,4) & $b$-bit Hessian, $b=12$ & 1 & 1411.781 & 8.38e-4 \\116(1,2,4) & $b$-bit Hessian, $b=16$ & 1 & 1410.756 & 8.21e-4 \\117(1,2,4) & $b$-bit Hessian, $b=24$ & 1 & 1410.845 & 8.22e-4 \\118(1,2,4) & $b$-bit Hessian, $b=52$ & 1 & 1410.845 & 8.22e-4 \\119(1,2,4) & $b$-bit score, $b=2$ & 1 & 1328.049 & 0.159 \\120(1,2,4) & $b$-bit score, $b=3$ & 1 & 1499.669 & 0.081 \\121(1,2,4) & $b$-bit score, $b=4$ & 1 & 1408.276 & 0.041 \\122(1,2,4) & $b$-bit score, $b=6$ & 1 & 1407.339 & 0.010 \\123(1,2,4) & $b$-bit score, $b=8$ & 1 & 1413.145 & 0.003 \\124(1,2,4) & $b$-bit score, $b=12$ & 1 & 1410.772 & 8.33e-4 \\125(1,2,4) & $b$-bit score, $b=16$ & 1 & 1410.839 & 8.22e-4 \\126(1,2,4) & $b$-bit score, $b=24$ & 1 & 1410.845 & 8.22e-4 \\127(1,2,4) & $b$-bit score, $b=52$ & 1 & 1410.845 & 8.22e-4 \\128(1,2,4) & $b$-bit both, $b=2$ & 1 & 662.576 & 0.185 \\129(1,2,4) & $b$-bit both, $b=3$ & 1 & 1807.436 & 0.119 \\130(1,2,4) & $b$-bit both, $b=4$ & 1 & 1380.154 & 0.054 \\131(1,2,4) & $b$-bit both, $b=6$ & 1 & 1395.142 & 0.015 \\132(1,2,4) & $b$-bit both, $b=8$ & 1 & 1402.962 & 0.003 \\133(1,2,4) & $b$-bit both, $b=12$ & 1 & 1411.708 & 8.50e-4 \\134(1,2,4) & $b$-bit both, $b=16$ & 1 & 1410.751 & 8.21e-4 \\135(1,2,4) & $b$-bit both, $b=24$ & 1 & 1410.845 & 8.22e-4 \\136(1,2,4) & $b$-bit both, $b=52$ & 1 & 1410.845 & 8.22e-4 \\137\bottomrule138\end{tabular}139\begin{tablenotes}\footnotesize140\item 400 paired replications per column (exact count per cell in the processed CSV); $K = N/m$. 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