Generalization and Overfitting in Matrix Product State Machine Learning Architectures
This work addresses generalization issues in tensor network-based models, providing insights for researchers in quantum-inspired machine learning, though it is incremental in scope.
The study investigated overfitting in matrix product state (MPS) machine learning architectures by testing on artificial and MNIST data, finding that overfitting occurs with one-dimensional data but is minimal or absent with more complex data like MNIST.
While overfitting and, more generally, double descent are ubiquitous in machine learning, increasing the number of parameters of the most widely used tensor network, the matrix product state (MPS), has generally lead to monotonic improvement of test performance in previous studies. To better understand the generalization properties of architectures parameterized by MPS, we construct artificial data which can be exactly modeled by an MPS and train the models with different number of parameters. We observe model overfitting for one-dimensional data, but also find that for more complex data overfitting is less significant, while with MNIST image data we do not find any signatures of overfitting. We speculate that generalization properties of MPS depend on the properties of data: with one-dimensional data (for which the MPS ansatz is the most suitable) MPS is prone to overfitting, while with more complex data which cannot be fit by MPS exactly, overfitting may be much less significant.