An optimization artificial neural networks model is developed for solving the ill-posed inverse transport problem associated with localizing radioactive sources in a medium with known properties and dimensions. The model is based on the recurrent (or feedback) Hop-field network with fixed weights. The source distribution is determined based on the response of a limited number of external detectors of known spatial deployment in conjunction with a radiation transport model. The algorithm is tested and evaluated for a large number of simulated two-dimensional cases. Computations are carried out at different noise levels to account for statistical errors encountered in engineering applications. The sensitivity to noise is found to depend on the number of detectors and on their spatial deployment. A pretest empirical procedure is, therefore, suggested for determining an effective arrangement of detectors for a given problem.