Table 2: Detection performance, mean
± sd over 5 seeds, on the same 40 runs as Table 1 . Clustering is reported as TPR rather than AUROC, since it is a binary flag rather than a continuous score. The
0% rows are false-positive controls, and each reported statistic’s definedness there depends on its own denominator, not on a single shared condition: TPR (
TP/(TP+FN) ) is undefined at
0% poisoning because
TP+FN=0 always — no actual positives exist to recall. AUROC is undefined for the same underlying reason (ground truth contains only the negative class). Precision (
TP/(TP+FP) ) is different:
TP=0 is guaranteed at
0% , but precision is undefined only when
FP=0 too; whenever anything at all is flagged on clean data, precision is a defined
0 , not undefined. CIFAR-10’s agreement precision at
0% demonstrates this directly: it is
0.000 (defined) on 2 of 5 seeds, where something was flagged and flagged incorrectly, and undefined on the other 3, where nothing was flagged at all. FPR (
FP/(FP+TN) ) is undefined only when
FP+TN=0 , which cannot happen on a nonempty clean dataset, since every sample is a true negative or a false positive there — it is always defined at
0% poisoning. PneumoniaMNIST’s clustering FPR at
0% is confirmed at exactly
0.000 across all 5 seeds (
0/4,708 in every case). CIFAR-10’s is not uniformly zero:
0.000 on 3 of 5 seeds, but
3.46% and
3.00% on the other two (
1,731 and
1,499 of
50,000 clean images respectively) — exactly the 2 seeds where agreement precision above is a defined
0.000 rather than undefined, confirming the logical link between the two columns. This seed-dependent clean-data false-positive pattern on CIFAR-10, absent on PneumoniaMNIST, is discussed in Section 6 and is not yet explained.