发表机构
Max Planck Institute for Intelligent Systems; Tübingen AI Center（马克斯·普朗克智能系统研究所; 图宾根人工智能中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究大规模预测模型性能表现现象下重新训练问题，提出稳定信号原理，证明存在稳定信号时经正则化的重复风险最小化会收敛到该信号方向，扩展分析范围并应用于语言建模数据反馈回路。
AI 中文摘要
大规模部署的预测模型会影响未来数据，即性能表现现象。应对方法是在新数据上训练模型并重复此过程，即重新训练或重复风险最小化，这会在模型和数据间形成反馈回路。关于性能预测的结果揭示了这种动态：若模型对数据影响小，重新训练会达到固定点。本文提出稳定信号原理来解决固定点为何自然存在以及模型影响强时如何控制重新训练的问题。从预测目标有与模型无关的稳定信号这一假设出发，证明了存在非零稳定信号时，经适当正则化的重复风险最小化会几何收敛到稳定信号方向，即便模型对目标影响相对于稳定信号任意大。正则化自然成为控制性能表现的力量，而非促进泛化。还将分析扩展到多种情况，稳定信号视角也适用于语言建模中的数据反馈回路。
英文摘要
Predictive models deployed at scale influence future data, a phenomenon called performativity. And there is always one way to cope: Train the model on new data, deploy it again, and repeat. This process, called retraining or repeated risk minimization, creates a feedback loop between model and data that real-world learning systems can't avoid. Results on performative prediction shed light on this dynamic: If the model's influence on the data is small, retraining reaches a fixed point. What remains open is why fixed points should naturally exist, and what governs retraining when the model's influence is strong. In this work we develop a new perspective on retraining -- the stable signal principle -- that addresses these questions. We start from the assumption that the prediction target has at least some small model-independent component, a stable signal, such as the intrinsic quality of an item. We prove that when a nonzero stable signal exists, repeated risk minimization, suitably regularized, converges geometrically to the direction of this stable signal. This is true even if the model's influence on the target is arbitrarily large relative to the stable signal. Regularization emerges naturally as a force to control performativity, rather than to promote generalization, revealing a new facet of an old concept. We extend the analysis to a broad family of affine retraining operators under arbitrary model-induced feature changes, heterogeneous time-varying effects, and nonlinear responses. The stable signal perspective also applies to data feedback loops in language modeling, providing new explanations for the stability of language model training from model-generated data.
CommentsCompanion article to an invited contribution to the Proceedings of the International Congress of Mathematicians (ICM), 2026
