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 symbols for target image classification 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 solve the symbolic complexity for classification, which is the minimum number of symbols in the message for successful communication. We use the SMS algorithm to create datasets with different symbolic complexity to empirically show that data with higher symbolic complexity increases the number of effective symbols in the emergent language.

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