source: arxiv statistics ml: retraining seeks stable signals
level: research
predictive models that influence future data create a feedback loop known as performativity. retraining, or repeated risk minimization, is the standard way to handle this: train on new data, deploy, and repeat. prior work showed that if the model's effect on data is small, retraining reaches a fixed point. but it was unclear why fixed points should exist at all, or what happens when the model's influence is strong.
the paper introduces the stable signal principle. it assumes the prediction target has at least a small component that does not depend on the model, like an item's intrinsic quality. the authors prove that if this stable signal is nonzero, retraining always converges to a unique fixed point, regardless of how much the model shifts the data distribution. they also show the fixed point is stable and can be found efficiently.
the results apply to common loss functions and model classes. the stable signal acts as an anchor that prevents the feedback loop from diverging. this gives a theoretical guarantee for retraining in real-world systems like recommendation engines or pricing algorithms, where models constantly reshape the data they learn from. the work also connects to concept drift and provides conditions under which retraining tracks a moving target.
why it matters: it provides a theoretical foundation for retraining in ai systems that influence their own training data, ensuring convergence even under strong feedback loops.
source: arxiv statistics ml: retraining seeks stable signals