  How many different ways are there to handwrite digit 3? To quantify this
question imagine extending a dataset of handwritten digits MNIST by sampling
additional images until they start repeating. We call the collection of all
resulting images of digit 3 the "full set." To study the properties of the full
set we introduce a tensor network architecture which simultaneously
accomplishes both classification (discrimination) and sampling tasks.
Qualitatively, our trained network represents the indicator function of the
full set. It therefore can be used to characterize the data itself. We
illustrate that by studying the full sets associated with the digits of MNIST.
  Using quantum mechanical interpretation of our network we characterize the
full set by calculating its entanglement entropy. We also study its geometric
properties such as mean Hamming distance, effective dimension, and size. The
latter answers the question above -- the total number of black and white threes
written MNIST style is $2^{72}$.
