1\begin{table}[p]2\centering\scriptsize3\begin{threeparttable}4\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}5\begin{tabular}{@{}llrrr@{}}6\toprule7Pattern & curvature & $q$ & $m = 24$ & $m = 96$ \\8\midrule9(1) & exact & 0 & 109.045 & 26.408 \\10(1) & exact & 1 & 4.741 & 0.278 \\11(1) & exact & 2 & 0.009 & 3.08e-5 \\12(1) & exact & 3 & 3.20e-8 & 4.80e-13 \\13(1) & stale & 1 & 8.723 & 0.545 \\14(1) & stale & 2 & 0.378 & 0.006 \\15(1) & stale & 3 & 0.015 & 5.91e-5 \\16(1) & single & 1 & 4.741 & 0.278 \\17(1) & single & 2 & 0.009 & 3.08e-5 \\18(1) & single & 3 & 3.20e-8 & 4.79e-13 \\19(1,2) & exact & 0 & 9.932 & 0.601 \\20(1,2) & exact & 1 & 0.039 & 1.77e-4 \\21(1,2) & exact & 2 & 6.32e-7 & 2.22e-11 \\22(1,2) & exact & 3 & 2.86e-13 & 3.14e-13 \\23(1,2) & stale & 1 & 0.359 & 0.006 \\24(1,2) & stale & 2 & 0.014 & 6.18e-5 \\25(1,2) & stale & 3 & 5.72e-4 & 6.35e-7 \\26(1,2) & single & 1 & 0.039 & 1.77e-4 \\27(1,2) & single & 2 & 6.32e-7 & 2.22e-11 \\28(1,2) & single & 3 & 2.86e-13 & 3.14e-13 \\29(1,3) & exact & 0 & 15.578 & 0.870 \\30(1,3) & exact & 1 & 0.097 & 3.28e-4 \\31(1,3) & exact & 2 & 3.76e-6 & 5.65e-11 \\32(1,3) & exact & 3 & 2.89e-13 & 3.11e-13 \\33(1,2,4) & exact & 0 & 2.100 & 0.312 \\34(1,2,4) & exact & 1 & 0.002 & 6.55e-5 \\35(1,2,4) & exact & 2 & 3.07e-9 & 5.44e-12 \\36(1,2,4) & exact & 3 & 2.93e-13 & 3.14e-13 \\37(1,2,4) & stale & 1 & 0.086 & 0.003 \\38(1,2,4) & stale & 2 & 0.003 & 3.32e-5 \\39(1,2,4) & stale & 3 & 1.38e-4 & 3.43e-7 \\40(1,2,4) & single & 1 & 0.002 & 6.55e-5 \\41(1,2,4) & single & 2 & 3.07e-9 & 5.44e-12 \\42(1,2,4) & single & 3 & 2.93e-13 & 3.14e-13 \\43(1,2,3) & exact & 0 & 1.697 & 0.429 \\44(1,2,3) & exact & 1 & 0.002 & 1.30e-4 \\45(1,2,3) & exact & 2 & 3.23e-9 & 2.25e-11 \\46(1,2,3) & exact & 3 & 3.03e-13 & 3.10e-13 \\47(1,2,4,8) & exact & 0 & 1.302 & 0.380 \\48(1,2,4,8) & exact & 1 & 9.81e-4 & 9.80e-5 \\49(1,2,4,8) & exact & 2 & 8.24e-10 & 1.20e-11 \\50(1,2,4,8) & exact & 3 & 2.93e-13 & 3.13e-13 \\51(1,2,3,4) & exact & 0 & 2.411 & 0.957 \\52(1,2,3,4) & exact & 1 & 0.004 & 6.46e-4 \\53(1,2,3,4) & exact & 2 & 1.96e-8 & 6.13e-10 \\54(1,2,3,4) & exact & 3 & 3.01e-13 & 3.10e-13 \\55\midrule56(1) & $b$-bit Hessian, $b=2$ & 1 & 4.546 & 0.277 \\57(1) & $b$-bit Hessian, $b=3$ & 1 & 10.384 & 0.277 \\58(1) & $b$-bit Hessian, $b=4$ & 1 & 2.423 & 0.277 \\59(1) & $b$-bit Hessian, $b=6$ & 1 & 4.312 & 0.140 \\60(1) & $b$-bit Hessian, $b=8$ & 1 & 4.778 & 0.266 \\61(1) & $b$-bit Hessian, $b=12$ & 1 & 4.741 & 0.278 \\62(1) & $b$-bit Hessian, $b=16$ & 1 & 4.741 & 0.278 \\63(1) & $b$-bit Hessian, $b=24$ & 1 & 4.741 & 0.278 \\64(1) & $b$-bit Hessian, $b=52$ & 1 & 4.741 & 0.278 \\65(1) & $b$-bit score, $b=2$ & 1 & 18.981 & 3.612 \\66(1) & $b$-bit score, $b=3$ & 1 & 2.378 & 1.401 \\67(1) & $b$-bit score, $b=4$ & 1 & 8.316 & 1.115 \\68(1) & $b$-bit score, $b=6$ & 1 & 5.450 & 0.380 \\69(1) & $b$-bit score, $b=8$ & 1 & 4.729 & 0.283 \\70(1) & $b$-bit score, $b=12$ & 1 & 4.740 & 0.278 \\71(1) & $b$-bit score, $b=16$ & 1 & 4.741 & 0.278 \\72(1) & $b$-bit score, $b=24$ & 1 & 4.741 & 0.278 \\73(1) & $b$-bit score, $b=52$ & 1 & 4.741 & 0.278 \\74(1) & $b$-bit both, $b=2$ & 1 & 8.538 & 2.990 \\75(1) & $b$-bit both, $b=3$ & 1 & 2.952 & 1.919 \\76(1) & $b$-bit both, $b=4$ & 1 & 5.928 & 0.561 \\77(1) & $b$-bit both, $b=6$ & 1 & 5.020 & 0.268 \\78(1) & $b$-bit both, $b=8$ & 1 & 4.767 & 0.271 \\79(1) & $b$-bit both, $b=12$ & 1 & 4.740 & 0.278 \\80(1) & $b$-bit both, $b=16$ & 1 & 4.741 & 0.278 \\81(1) & $b$-bit both, $b=24$ & 1 & 4.741 & 0.278 \\82(1) & $b$-bit both, $b=52$ & 1 & 4.741 & 0.278 \\83(1,2) & $b$-bit Hessian, $b=2$ & 1 & 0.040 & 5.01e-4 \\84(1,2) & $b$-bit Hessian, $b=3$ & 1 & 0.040 & 5.01e-4 \\85(1,2) & $b$-bit Hessian, $b=4$ & 1 & 0.040 & 5.01e-4 \\86(1,2) & $b$-bit Hessian, $b=6$ & 1 & 0.040 & 5.01e-4 \\87(1,2) & $b$-bit Hessian, $b=8$ & 1 & 0.039 & 5.01e-4 \\88(1,2) & $b$-bit Hessian, $b=12$ & 1 & 0.040 & 1.89e-4 \\89(1,2) & $b$-bit Hessian, $b=16$ & 1 & 0.039 & 1.77e-4 \\90(1,2) & $b$-bit Hessian, $b=24$ & 1 & 0.039 & 1.77e-4 \\91(1,2) & $b$-bit Hessian, $b=52$ & 1 & 0.039 & 1.77e-4 \\92(1,2) & $b$-bit score, $b=2$ & 1 & 0.503 & 0.064 \\93(1,2) & $b$-bit score, $b=3$ & 1 & 0.471 & 0.032 \\94(1,2) & $b$-bit score, $b=4$ & 1 & 0.311 & 0.016 \\95(1,2) & $b$-bit score, $b=6$ & 1 & 0.088 & 0.004 \\96(1,2) & $b$-bit score, $b=8$ & 1 & 0.042 & 0.001 \\97(1,2) & $b$-bit score, $b=12$ & 1 & 0.040 & 1.91e-4 \\98(1,2) & $b$-bit score, $b=16$ & 1 & 0.039 & 1.77e-4 \\99(1,2) & $b$-bit score, $b=24$ & 1 & 0.039 & 1.77e-4 \\100(1,2) & $b$-bit score, $b=52$ & 1 & 0.039 & 1.77e-4 \\101(1,2) & $b$-bit both, $b=2$ & 1 & 0.473 & 0.064 \\102(1,2) & $b$-bit both, $b=3$ & 1 & 0.430 & 0.032 \\103(1,2) & $b$-bit both, $b=4$ & 1 & 0.312 & 0.016 \\104(1,2) & $b$-bit both, $b=6$ & 1 & 0.081 & 0.004 \\105(1,2) & $b$-bit both, $b=8$ & 1 & 0.041 & 0.001 \\106(1,2) & $b$-bit both, $b=12$ & 1 & 0.040 & 2.01e-4 \\107(1,2) & $b$-bit both, $b=16$ & 1 & 0.039 & 1.77e-4 \\108(1,2) & $b$-bit both, $b=24$ & 1 & 0.039 & 1.77e-4 \\109(1,2) & $b$-bit both, $b=52$ & 1 & 0.039 & 1.77e-4 \\110(1,2,4) & $b$-bit Hessian, $b=2$ & 1 & 0.003 & 2.57e-4 \\111(1,2,4) & $b$-bit Hessian, $b=3$ & 1 & 0.003 & 2.57e-4 \\112(1,2,4) & $b$-bit Hessian, $b=4$ & 1 & 0.003 & 2.57e-4 \\113(1,2,4) & $b$-bit Hessian, $b=6$ & 1 & 0.003 & 2.57e-4 \\114(1,2,4) & $b$-bit Hessian, $b=8$ & 1 & 0.004 & 2.54e-4 \\115(1,2,4) & $b$-bit Hessian, $b=12$ & 1 & 0.002 & 7.28e-5 \\116(1,2,4) & $b$-bit Hessian, $b=16$ & 1 & 0.002 & 6.58e-5 \\117(1,2,4) & $b$-bit Hessian, $b=24$ & 1 & 0.002 & 6.55e-5 \\118(1,2,4) & $b$-bit Hessian, $b=52$ & 1 & 0.002 & 6.55e-5 \\119(1,2,4) & $b$-bit score, $b=2$ & 1 & 0.213 & 0.033 \\120(1,2,4) & $b$-bit score, $b=3$ & 1 & 0.106 & 0.016 \\121(1,2,4) & $b$-bit score, $b=4$ & 1 & 0.055 & 0.009 \\122(1,2,4) & $b$-bit score, $b=6$ & 1 & 0.014 & 0.002 \\123(1,2,4) & $b$-bit score, $b=8$ & 1 & 0.004 & 5.51e-4 \\124(1,2,4) & $b$-bit score, $b=12$ & 1 & 0.002 & 6.97e-5 \\125(1,2,4) & $b$-bit score, $b=16$ & 1 & 0.002 & 6.55e-5 \\126(1,2,4) & $b$-bit score, $b=24$ & 1 & 0.002 & 6.55e-5 \\127(1,2,4) & $b$-bit score, $b=52$ & 1 & 0.002 & 6.55e-5 \\128(1,2,4) & $b$-bit both, $b=2$ & 1 & 0.214 & 0.033 \\129(1,2,4) & $b$-bit both, $b=3$ & 1 & 0.106 & 0.016 \\130(1,2,4) & $b$-bit both, $b=4$ & 1 & 0.055 & 0.009 \\131(1,2,4) & $b$-bit both, $b=6$ & 1 & 0.014 & 0.002 \\132(1,2,4) & $b$-bit both, $b=8$ & 1 & 0.005 & 6.03e-4 \\133(1,2,4) & $b$-bit both, $b=12$ & 1 & 0.002 & 7.66e-5 \\134(1,2,4) & $b$-bit both, $b=16$ & 1 & 0.002 & 6.58e-5 \\135(1,2,4) & $b$-bit both, $b=24$ & 1 & 0.002 & 6.55e-5 \\136(1,2,4) & $b$-bit both, $b=52$ & 1 & 0.002 & 6.55e-5 \\137\bottomrule138\end{tabular}139\begin{tablenotes}\footnotesize140\item 300--1000 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\_exponential\_summary.csv}.141\end{tablenotes}142\end{threeparttable}143\end{table}144