  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.
