SourceFaithful Rule Extraction for Differentiable Rule Learning Models
The paper proves that DRUM's output for any fact is determined by summing weighted counts of distinct groundings of rule bodies in the input data (Lemma 1). Standard datalog rules fire on any single match regardless of count, so they cannot express this counting. Theorem 1 shows the standard extraction is sound only when the extraction threshold γ is at least the model's prediction threshold β, and Theorem 2 proves that for some DRUM configurations no datalog program at all is both sound and complete. Empirically, across 13 benchmark datasets and four threshold values, the extracted rules cover at most 6.25% of the model's predictions (Table 2), confirming the theoretical incompleteness in practice.