When convoking privacy, group membership verification checks if a biometric trait corresponds to one member of a group without revealing the identity of that member. Similarly , group membership identification states which group the individual belongs to, without knowing his/her identity. A recent contribution provides privacy and security for group membership protocols through the joint use of two mechanisms: quantizing biometric templates into discrete embeddings, and aggregating several templates into one group representation. This paper significantly improves that contribution because it jointly learns how to embed and aggregate instead of imposing fixed and hard coded rules. This is demonstrated by exposing the mathematical underpinnings of the learning stage before showing the improvements through an extensive series of experiments targeting face recognition. Overall, experiments show that learning yields an excellent trade-off between security / privacy and the verification / identification performances.