Geometric Foundations of Systematic Generalization in Emergent Social Syntax

This paper studies systematic generalization in emergent communication within multi-agent reinforcement learning. We show that generalization failure persists despite the emergence of compositional syntax, increased exploration, or reward factorization. Instead, we identify representation geometry as the primary bottleneck. By modeling emergent social syntax as a graph and analyzing its Laplacian spectrum, we reveal that generalization failure corresponds to high-frequency, geometrically entangled representation modes. We introduce Laplacian-aware geometric regularization, which causally enables zero-shot generalization. Once representation geometry is aligned, exploration becomes strongly beneficial, achieving up to 87.5% success on unseen symbolic combinations. These results establish representation geometry as a key determinant of systematic generalization in emergent communication.