gate_reports/NEGATIVE_RESULT.md

Negative result (a contribution): rank-based coverage objectives fail for rare-lesion retention

Claim

Effective-rank / coding-rate "coverage" objectives — RankMe, coding rate (MCR2-style) — are structurally mismatched to retaining rare, small-region pathology under token pruning. Using them as the pruning objective is worse than simply ranking tokens by lesion-subspace membership.

Mechanism (the transferable part)

A rank-based coverage functional C(S) = effrank(P_L Z_S) is maximized by a retained set that diversely spans the lesion subspace's directions. The decisive property of a small lesion is that it is rare — a few high-membership tokens out of ~196. A set-level rank/coverage objective is insensitive to such a cluster: a handful of tokens cannot materially raise the retained set's effective rank, so the objective spends budget on abundant background directions and drops the lesion. This is a rarity mechanism, not low internal geometry — measured at the operating layer, lesion tokens are not low-rank relative to background (pooled effective rank 339 vs 307; participation ratio 18.9 vs 13.9; research_v4/lesion_spectrum.json). Concentration, not spanning, is what rare-pathology retention needs.

Formally: rank coverage rewards the entropy of the retained set's singular spectrum; lesion retention rewards mass on the top membership tokens. These objectives diverge whenever the critical signal is a rare cluster — of any internal rank. (The synthetic closed-form law of the companion paper isolates a second, distinct route — a genuinely low-rank signal, gap (m-r)/m; real lesions fail via rarity, not low rank.)

Three independent lines of evidence (same verdict)

1. Ablation (decisive). At matched budget, the coverage-floor pruner retains 0.22 vs 0.82 (budget 0.25) and 0.46 vs 0.98 (budget 0.5) of small lesions vs membership top-k; the difference CI excludes 0. The floor does not under-help — it actively hurts. (ablation_floor.json)
2. Faithfulness (principled Gate 2). Under the random-pruning protocol, coverage-drop predicts lesion-detection-drop no better than attention-drop: ρ 0.480 vs 0.479, difference CI includes 0. Coverage is not a superior proxy. (gate_2_baseline.json)
3. Adaptive budget (Gate 4). The "difficulty-adaptive budget" never materializes: aggregate coverage C* is the same on lesion-positive and -negative slices (250.4 vs 247.2), because a 1–3 patch lesion cannot move an aggregate over ~196 tokens. (gate_4_block3.json)

All three reduce to one fact: aggregate rank-coverage is blind to the few tokens that carry a small lesion, even though those tokens are individually highly localizable (Gate 1, AUROC 0.87).

Closed-form law (S1, confirmed by controlled synthetic)

A controlled synthetic isolates the mechanism and yields a closed form (research_v2/s1_crossover.json). Inject a signal of effective rank r across m tokens; select to a budget by a spanning objective (farthest-point / effective-rank) vs a concentration objective (top-energy):

• spanning retention(r) = min(r, m) / m, concentration retention = 1,
• gap(r) = max(0, (m − r) / m), crossover r* = m.

A spanning objective retains a signal only in proportion to its rank; it matches concentration only when the signal is fully diverse (rank = token count). Rare pathology is maximally concentrated (r ≈ 1–3 patches, m small), so rank-based coverage is maximally mismatched there — quantitatively reproducing the covtoken ablation (floor 0.22 vs membership 0.82 ≈ gap (m−1)/m for the dominant 1-patch lesions). The verdict is no longer anecdotal: it is a closed-form prediction.

Why this matters beyond this paper

RankMe-flavored objectives are an increasingly common, tempting choice for medical SSL representation quality and for "coverage"-style regularizers. This result is a warning with a mechanism: for rare-pathology tasks, prefer concentration objectives (energy / membership mass) over rank/spanning objectives. A negative result with a transferable mechanism is citable; "our dual didn't converge" is not. This is the former.

What survives

The label-free lesion subspace (the geometry that produces membership) is intact and is the contribution. The failure is specifically the rank-coverage functional built on top of it and the constrained-optimization machinery that optimized it. Replacing the objective with the membership/energy quantity recovers the result — but then the "constraint + dual" adds nothing over a top-k rule, so it is dropped honestly rather than dressed up.