用双层疫情模型分析合成数据污染如何在AI系统中传播
Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics
- 将数据和模型视为两个交互的群体，建模污染传播与免疫衰减机制
- 计算出传播阈值R0>1，表明污染在三种情景下都会持续扩散
- 发现检测能力是关键干预点，多源数据混合效果有限
训练使用合成数据会导致模型退化，现有分析将其视为单一链条的恶化。实际上，人工智能生态涉及交叉污染：模型从其他模型获取合成数据，生成新合成文本，并污染共享语料库。我们提出双层耦合SIR/SIRS框架——一种现象学均场模型，将数据语料库和人工智能模型视为两个相互作用的群体，各自具有易感、感染、恢复组分，并通过跨层传播连接。SIRS变体（我们的主要推荐）包含免疫衰减，反映过滤后的语料库和重新训练的模型仍可能再次被污染。我们通过下一代矩阵推导基本再生数 $R_0 = \sqrt{β_D β_M / [(γ_D+μ_D)(γ_M+μ_M)]}$，并应用标准流行病阈值结果于双层系统。基于公开AI文本流行度数据的场景校准显示，在三种情景下均呈现超临界动态（$R_0 > 1$）；Sobol敏感性分析识别出合成文本检测为最高杠杆参数。双部网络代理模型在密集网络中确认了均场一致性（$R^2 > 0.96$），但在异质性下退化。GPT-2污染链实验（192次运行，涵盖WikiText和Shakespeare）显示剂量-响应退化与多样性损失，与阈值图景定性一致。匹配预算的源多样性实验（1,088次运行）提供初步证据表明多源混合可轻微缓解退化，但在低污染比例时效应消失。干预分析表明，基于检测的过滤和群体免疫为最高杠杆策略。
原文摘要 · Abstract (English)
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 $R_0 = \sqrt{β_D β_M / [(γ_D+μ_D)(γ_M+μ_M)]}$ 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.
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