Searching the tower (Algorithm 5) & the recall payoff·5 min
Recall@10 under a budget
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Recall@10 = (your top-10 ∩ the true top-10) / 10, averaged over queries. But recall alone is gameable — brute force scores 1.0. So we also count L2 comparisons per query and cap them. HNSW must hit the recall floor while touching a tiny fraction of the database.
The contract
On the course corpus, brute force makes N comparisons/query at recall 1.0 — and fails, because it blows the comparison budget. HNSW at efSearch = 64 makes a few hundred comparisons/query at recall ~0.97 — and passes. That gap is the entire value of the index.