Hinging on ideas from physical-layer network coding, some promising proposals of coded random access systems seek to improve system performance (while preserving low complexity) by means of packet repetitions and decoding of linear combinations of colliding packets, whenever the decoding of individual packets fails. The resulting linear combinations are then temporarily stored in the hope of gathering enough linearly independent combinations so as to eventually recover all individual packets through the resolution of a linear system at the end of the contention frame. However, it is unclear which among the numerous linear combinations---whose number grows exponentially with the degree of collision---will have low probability of decoding error. Since no analytical framework exists to determine which combinations are easiest to decode, this makes the case for a machine learning algorithm to assist the receiver in deciding which linear combinations to target. For this purpose, we train neural networks that approximate the error probability for every possible linear combination based on the estimated channel gains and demonstrate the effectiveness of our approach by numerical simulations.