In a knowledge graph, an unobserved link is not necessarily false. Some links used as training negatives are hidden positives: true relationships that have not yet been recorded. Type filtering can concentrate these links among the plausible candidates used for hard-negative sampling.

What the comparison means

Because the hard pool contains all hidden positives, the probability that a uniformly sampled link is a hidden positive is Pu / Ng for random sampling and Pu / Nh for hard sampling. Multiplying these probabilities by k gives the expected hidden-positive counts per batch.

With Ng = 100, Pu = 10, Nh = 50, and k = 10, expected contamination increases from 10% to 20%, and the expected counts increase from 1 to 2. For Pu > 0, the enrichment ratio is Ng / Nh. If Nh equals Ng, the two methods have the same expected contamination. If Pu is zero, both rates are zero and their ratio is undefined.

Illustrative mode deliberately selects a batch with the expected number of hidden positives, rounded to the nearest integer when needed. It is a teaching example. Random mode independently samples each pool without replacement; a single batch can differ from its expectation or even reverse the ordering. Resampling keeps the constructed pools fixed.

This example demonstrates what happens when type filtering enriches hidden positives. It does not imply that every hard-negative mining method does so. Here, “false-negative contamination” means the fraction of sampled negatives that are actually positive, rather than the classifier metric FN / (TP + FN).