Lost in Retraining: Roaming the Parameter Space of Exponential Families Under Closed-Loop Learning

• URL: http://arxiv.org/abs/2506.20623v2
• Date: Wed, 09 Jul 2025 08:24:09 GMT
• Title: Lost in Retraining: Roaming the Parameter Space of Exponential Families Under Closed-Loop Learning
• Authors: Fariba Jangjoo, Matteo Marsili, Yasser Roudi,
• Abstract summary: We study closed-loop learning for models that belong to exponential families.<n>We show that maximum likelihood of the parameters endows sufficient statistics with the martingale property.<n>We show that this outcome may be prevented if the data contains at least one data point generated from a ground truth model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Closed-loop learning is the process of repeatedly estimating a model from data generated from the model itself. It is receiving great attention due to the possibility that large neural network models may, in the future, be primarily trained with data generated by artificial neural networks themselves. We study this process for models that belong to exponential families, deriving equations of motions that govern the dynamics of the parameters. We show that maximum likelihood estimation of the parameters endows sufficient statistics with the martingale property and that as a result the process converges to absorbing states that amplify initial biases present in the data. However, we show that this outcome may be prevented if the data contains at least one data point generated from a ground truth model, by relying on maximum a posteriori estimation or by introducing regularisation.

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