Reduced latent leakage does not reliably predict lower likelihood bias in collider inference

Abstract

Reusable collider representations can be evaluated through downstream discrimination and probes of retained information, but neither quantity directly tests the behaviour of score templates in a profiled likelihood. We test a specific prediction in a controlled two-channel routing protocol: if reduced physics-label readability in a nuisance branch indicates a more inference-robust representation, it should accompany a smaller profiled signal-strength bias under fixed unmodelled shifts. In a public Compact Muon Solenoid $H\rightarrow ZZ\rightarrow4\ell$ workflow, a downstream split of fixed EveNet embeddings preserves signal/background area under the receiver operating characteristic curve ($0.9894\pm0.0004$) while reducing nuisance-branch physics readability from $0.961\pm0.013$ to $0.593\pm0.030$. Probe-sensitivity and effective-rank controls exclude a failed readout and branch collapse. In a separate top quark jet-tagging workflow, the leakage reduction recurs with preserved task performance. Across two development event shards, however, its Spearman association with maximum absolute profiled bias is $0.036$, and three of six material leakage-improving transitions do not reduce that bias. A one-shot preregistered confirmation on an independently accessed shard produces material leakage reductions in all three paired seeds, while the maximum absolute bias increases in two. Thus, within the tested protocol, latent readability is a useful routing diagnostic but not a likelihood-robustness certificate. The result supports a practical validation rule: claims about inference robustness require a prespecified likelihood-facing stress test and held-out confirmation.