Generalization and Memorization: The Bias Potential Model
This work addresses the subtle issue of generalization in generative models, particularly for the bias potential model, which is relevant for researchers working on the theoretical understanding of generative adversarial networks (GANs).
The paper investigates the generalization behavior of the bias potential model, a type of generative model. It demonstrates that dimension-independent generalization accuracy can be achieved through early stopping, even though the model eventually either memorizes the training data or diverges.
Models for learning probability distributions such as generative models and density estimators behave quite differently from models for learning functions. One example is found in the memorization phenomenon, namely the ultimate convergence to the empirical distribution, that occurs in generative adversarial networks (GANs). For this reason, the issue of generalization is more subtle than that for supervised learning. For the bias potential model, we show that dimension-independent generalization accuracy is achievable if early stopping is adopted, despite that in the long term, the model either memorizes the samples or diverges.