  We investigate the potential of tensor network based machine learning methods
to scale to large image and text data sets. For that, we study how the mutual
information between a subregion and its complement scales with the subsystem
size $L$, similarly to how it is done in quantum many-body physics. We find
that for text, the mutual information scales as a power law $L^\nu$ with a
close to volume law exponent, indicating that text cannot be efficiently
described by 1D tensor networks. For images, the scaling is close to an area
law, hinting at 2D tensor networks such as PEPS could have an adequate
expressibility. For the numerical analysis, we introduce a mutual information
estimator based on autoregressive networks, and we also use convolutional
neural networks in a neural estimator method.
