  It is known that a trained Restricted Boltzmann Machine (RBM) on the binary
Monte Carlo Ising spin configurations, generates a series of iterative
reconstructed spin configurations which spontaneously flow and stabilize to the
critical point of physical system. Here we construct a variety of Neural
Network (NN) flows using the RBM and (variational) autoencoders, to study the
q-state Potts and clock models on the square lattice for q = 2, 3, 4. The NN
are trained on Monte Carlo spin configurations at various temperatures. We find
that the trained NN flow does develop a stable point that coincides with
critical point of the q-state spin models. The behavior of the NN flow is
nontrivial and generative, since the training is unsupervised and without any
prior knowledge about the critical point and the Hamiltonian of the underlying
spin model. Moreover, we find that the convergence of the flow is independent
of the types of NNs and spin models, hinting a universal behavior. Our results
strengthen the potential applicability of the notion of the NN flow in studying
various states of matter and offer additional evidence on the connection with
the Renormalization Group flow.
