Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metric
This work addresses a fundamental problem in quantum machine learning for researchers and practitioners by providing a framework to analyze generalization, though it appears incremental as it builds on existing concepts like Fisher information and Lie algebras.
The authors tackled the challenge of understanding generalization in quantum machine learning models by introducing the data quantum Fisher information metric (DQFIM) to quantify the capacity of variational quantum algorithms, finding that breaking symmetries in training data can improve generalization and that out-of-distribution generalization can outperform in-distribution cases.
Generalization is the ability of machine learning models to make accurate predictions on new data by learning from training data. However, understanding generalization of quantum machine learning models has been a major challenge. Here, we introduce the data quantum Fisher information metric (DQFIM). It describes the capacity of variational quantum algorithms depending on variational ansatz, training data and their symmetries. We apply the DQFIM to quantify circuit parameters and training data needed to successfully train and generalize. Using the dynamical Lie algebra, we explain how to generalize using a low number of training states. Counter-intuitively, breaking symmetries of the training data can help to improve generalization. Finally, we find that out-of-distribution generalization, where training and testing data are drawn from different data distributions, can be better than using the same distribution. Our work provides a useful framework to explore the power of quantum machine learning models.