  The stochastic block model (SBM) is widely studied as a benchmark for graph
clustering aka community detection. In practice, graph data often come with
node attributes that bear additional information about the communities.
Previous works modeled such data by considering that the node attributes are
generated from the node community memberships. In this work, motivated by a
recent surge of works in signal processing using deep neural networks as
priors, we propose to model the communities as being determined by the node
attributes rather than the opposite. We define the corresponding model; we call
it the neural-prior SBM. We propose an algorithm, stemming from statistical
physics, based on a combination of belief propagation and approximate message
passing. We analyze the performance of the algorithm as well as the
Bayes-optimal performance. We identify detectability and exact recovery phase
transitions, as well as an algorithmically hard region. The proposed model and
algorithm can be used as a benchmark for both theory and algorithms. To
illustrate this, we compare the optimal performances to the performance of
simple graph neural networks.

Disordered Systems and Neural Networks;Social and Information Networks;Machine Learning