The emergence of numerical representations in communicating artificial agents
This addresses the problem of understanding how numerical concepts emerge in AI systems, with incremental insights into the limitations of communication-driven learning.
The study investigated whether communication pressure alone could lead artificial agents to develop numerical representations, finding that while agents achieved high accuracy for trained numerosities, they failed to generalize systematically to unseen ones, resulting in non-compositional codes.
Human languages provide efficient systems for expressing numerosities, but whether the sheer pressure to communicate is enough for numerical representations to arise in artificial agents, and whether the emergent codes resemble human numerals at all, remains an open question. We study two neural network-based agents that must communicate numerosities in a referential game using either discrete tokens or continuous sketches, thus exploring both symbolic and iconic representations. Without any pre-defined numeric concepts, the agents achieve high in-distribution communication accuracy in both communication channels and converge on high-precision symbol-meaning mappings. However, the emergent code is non-compositional: the agents fail to derive systematic messages for unseen numerosities, typically reusing the symbol of the highest trained numerosity (discrete), or collapsing extrapolated values onto a single sketch (continuous). We conclude that the communication pressure alone suffices for precise transmission of learned numerosities, but additional pressures are needed to yield compositional codes and generalisation abilities.