Conductivity imaging represents one of the most important tasks in medical imaging. In this talk we discuss a neural network-based technique for imaging the conductivity from the magnitude of the internal current density. It is achieved by formulating the problem as the relaxed weighted least-gradient problem, and then approximating the minimizer by standard feedforward neural networks. We derive bounds on two components of the generalization error, i.e., approximation error and statistical error, explicitly in terms of properties of the neural networks (i.e., depth, total number of parameters, and the bound of the network parameters). We illustrate the performance and distinct features of the proposed approach on several numerical experiments.