  Multi-user multiple-input multiple-output (MU-MIMO) systems can be used to
meet high throughput requirements of 5G and beyond networks. A base station
serves many users in an uplink MU-MIMO system, leading to a substantial
multi-user interference (MUI). Designing a high-performance detector for
dealing with a strong MUI is challenging. This paper analyses the performance
degradation caused by the posterior distribution approximation used in the
state-of-the-art message passing (MP) detectors in the presence of high MUI. We
develop a graph neural network based framework to fine-tune the MP detectors'
cavity distributions and thus improve the posterior distribution approximation
in the MP detectors. We then propose two novel neural network based detectors
which rely on the expectation propagation (EP) and Bayesian parallel
interference cancellation (BPIC), referred to as the GEPNet and GPICNet
detectors, respectively. The GEPNet detector maximizes detection performance,
while GPICNet detector balances the performance and complexity. We provide
proof of the permutation equivariance property, allowing the detectors to be
trained only once, even in the systems with dynamic changes of the number of
users. The simulation results show that the proposed GEPNet detector
performance approaches maximum likelihood performance in various configurations
and GPICNet detector doubles the multiplexing gain of BPIC detector.
