fix(linalg): correct multivector distance aggregation

[ddupg]

Background

While implementing distributed batch vector search in lance-ray#5263, I compared the indexed and flat search paths in Lance Core and found that they used different multivector distance baselines.

For a query with M sub-vectors, the indexed path used:

M - sum(max similarity)

while the flat path used:

1 - sum(max similarity)

The results therefore differed by M - 1; for example, a perfect match with M = 2 returned 0 from the indexed path but -1 from the flat path.

Changes

• For float metrics, directly compute distance(Q, V) = sum_i min_j d(q_i, v_j).
• For Hamming, use the same aggregation, distance(Q, V) = sum_i min_j hamming(q_i, v_j), without an outer 1 - ... conversion.
• Add unit and end-to-end coverage for flat, indexed, and partially indexed search paths.

Testing

• cargo test -p lance-linalg
• test_multivec_ann and test_multivec_search_paths

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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[lance-gatekeeper]

✅ Gate recommendation: approve.

This preserves the additive late-interaction contract by summing each query sub-vector’s nearest stored-vector distance. That directly matches indexed scoring, corrects Hamming ordering, and is cleaner than retaining metric-specific similarity baselines. The regression covers flat, partially indexed, and fully indexed search paths.

[yanghua]

LGTM