Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics
Researchers propose a bilayer SIR/SIRS framework to model cross-contamination between AI models and data corpora, finding synthetic text detection and herd immunity as key intervention strategies.
[2606.05168] Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics
[Submitted on 14 Apr 2026]
Title:Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics
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Abstract:Training on synthetic data causes model collapse, but existing analyses treat this as single-chain degradation. In reality, the AI ecosystem involves cross-contamination: models ingest synthetic data from other models, produce new synthetic text, and contaminate shared corpora. We propose a bilayer coupled SIR/SIRS framework -- a phenomenological mean-field model treating data corpora and AI models as two interacting populations, each with susceptible, infected, and recovered compartments linked by cross-layer transmission. The SIRS variant (our primary recommendation) incorporates immunity waning, reflecting that filtered corpora and retrained models remain susceptible to re-contamination. We derive the basic reproduction number $R_0 = \sqrt{\beta_D \beta_M / [(\gamma_D+\mu_D)(\gamma_M+\mu_M)]}$ via the Next Generation Matrix and apply standard epidemic threshold results to the bilayer system. Illustrative scenario-based calibration from public AI text prevalence data yields supercritical dynamics ($R_0 > 1$) across three scenarios; Sobol sensitivity analysis identifies synthetic-text detection as the highest-leverage parameter. A bipartite-network agent-based model confirms mean-field consistency ($R^2 > 0.96$) for dense networks but degrades under heterogeneity. GPT-2 contamination chain experiments (192 runs across WikiText and Shakespeare) show dose-response degradation and diversity loss qualitatively consistent with the threshold picture. Matched-budget source-diversity experiments (1,088 runs) provide suggestive evidence that multi-source mixing modestly attenuates collapse, but the effect vanishes at lower contamination fractions. Intervention analysis identifies detection-based filtering and herd immunity as the highest-leverage strategies.
Comments: 24 pages, 15 figures
Subjects:
Computation and Language (cs.CL); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
MSC classes: 92D30, 68T07
ACM classes: I.2.6; I.6.5
Cite as: arXiv:2606.05168 [cs.CL]
(or arXiv:2606.05168v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2606.05168
arXiv-issued DOI via DataCite
Submission history
From: Xiangyu Wang [view email] [v1] Tue, 14 Apr 2026 06:49:30 UTC (212 KB)
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