A Combinatorial Approach to Neural Emergent Communication

Substantial research on deep learning-based emergent communication uses the referential game framework, specifically the Lewis signaling game, however we argue that successful communication in this game typically only need one or two effective symbols (i.e. message length) because of a sampling pitfall in the training data. To address this issue, we provide a theoretical analysis and introduce a combinatorial algorithm SolveMinSym (SMS) to determine the minimum number of symbols for successful communication min(|M|) in the Lewis signaling game. We use SMS algorithm to create datasets with different min(|M|) to empirically show that higher min(|M|) for the training data increases the number of effective symbols in the emergent language.