Siloed Local Verifiers Prune Tail Modes and Trigger Power-Law Diversity Decay in Recursive Training

The arXiv paper demonstrates that data selection, previously assumed protective, becomes a collapse accelerator when each verifier sees only a fragmented slice of the target distribution. In healthcare consortia and proprietary finance silos, local manifolds lack coverage of rare modes. Selection therefore prunes samples outside the observed reference, converting a safeguard into an active homogenizer. Theoretical analysis proves power-law decay in output diversity as recursion depth increases. Empirical tests compare single-silo selection against Wasserstein proxy references constructed across silos without raw data exchange. Local selection on skewed distributions produces rapid tail erosion; collaborative proxies preserve mode coverage and slow degradation. These results align with prior findings on recursion-induced forgetting and extend them to institutional data fragmentation patterns documented in federated learning deployments. Operationally, pipelines that rely on proprietary or regulated data now face an unavoidable tradeoff between privacy constraints and distributional fidelity. Mitigation requires either explicit proxy construction or external reference signals. Without such measures, repeated training loops in siloed domains will exhibit measurable homogenization within fewer than five recursion cycles. Future pipelines must embed cross-silo reference mechanisms at the selection layer rather than post-hoc filtering. Regulatory pressure on data localization will intensify this requirement.