  The exact renormalization group (ERG) for $O(N)$ vector models (at large $N$)
on flat Euclidean space can be interpreted as the bulk dynamics corresponding
to a holographically dual higher spin gauge theory on $AdS_{d+1}$. This was
established in the sense that at large $N$ the generating functional of
correlation functions of single trace operators is reproduced by the on-shell
action of the bulk higher spin theory, which is most simply presented in a
first-order (phase space) formalism. In this paper, we extend the ERG formalism
to the wave functionals of arbitrary states of the $O(N)$ vector model at the
free fixed point. We find that the ERG flow of the ground state and a specific
class of excited states is implemented by the action of unitary operators which
can be chosen to be local. Consequently, the ERG equations provide a continuum
notion of a tensor network. We compare this tensor network with the
entanglement renormalization networks, MERA, and its continuum version, cMERA,
which have appeared recently in holographic contexts. In particular the ERG
tensor network appears to share the general structure of cMERA but differs in
important ways. We comment on possible holographic implications.
