Active user detection is a standard problem that concerns many applications using random access channels in cellular or ad hoc networks. Despite being known for a long time, such a detection problem is complex, and standard algorithms for blind detection have to trade between high computational complexity and detection error probability. Traditional algorithms rely on various theoretical frameworks, including compressive sensing and bayesian detection, and lead to iterative algorithms, e.g. orthogonal matching pursuit (OMP). However, none of these algorithms have been proven to achieve optimal performance. This paper proposes a deep learning based algorithm (NN-MAP) able to improve on the performance of state-of-the-art algorithm while reducing detection time, with a codebook known at training time.