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selfretrieval

confirmedshipPythonSystems & data structuresJuly 12, 2026

the question

Is every stored point in an HNSW index retrievable by querying with its own vector at k=1, at some search budget?

what came out

Confirmed. A full self-retrieval census finds an irreducible floor of stored vectors no budget can return: at M=16, 795 of 100,000 (0.8 percent) returned 0 of 795 even at ef=8000. Almost all (789) have zero in-edges from the neighbor-selection heuristic; symmetrizing the graph at equal degree removes them.

method & receipts

  • Result: confirmed
  • Pre-registered the prediction was written down and committed before the run.
  • Reproducible one script re-runs the whole thing from scratch.
  • Tested — a correctness/benchmark suite ships alongside the code.

→ read the code and re-run it

github.com/v-code01/selfretrieval