Boltzmann Energy Minimization for Attack Path Re-Ranking in Knowledge Retrieval

Standard retrieval systems return facts ranked by individual relevance to a query, ignoring how facts connect to form coherent procedural sequences. We propose Boltzmann Energy Re-Ranking: modeling fact-to-fact connections as an energy landscape where low-energy paths represent well-connected attack chains. Given candidate facts from any retrieval system, we construct a pairwise energy matrix (using learned classifiers, explicit relationship edges, and co-occurrence statistics), run beam search to find minimum-energy paths, then compute Boltzmann probabilities over the path ensemble to re-rank candidates. Evaluated on 75,867 cybersecurity knowledge facts, Boltzmann re-ranking improves path completeness by +17% over FAISS baseline. Combined with geometric manifold retrieval (companion paper), the two approaches achieve complementary strengths: manifold retrieval excels at multi-hop discovery (+28% path completeness), while Boltzmann re-ranking excels at attack path planning (+35% path completeness). A lightweight query router combining both achieves 80% overall path completeness — +20% over FAISS at 3.2s average latency.