Human referential communication is often thought as coding-decoding a set of symbols, neglecting that establishing shared meanings requires a computational mechanism powerful enough to mutually negotiate them. Sharing the meaning of a novel symbol might rely on similar conceptual inferences across communicators or on statistical similarities in their sensorimotor behaviors. Using magnetoencephalography, we assess spectral, temporal, and spatial characteristics of neural activity evoked when people generate and understand novel shared symbols during live communicative interactions. Solving those communicative problems induced comparable changes in the spectral profile of neural activity of both communicators and addressees. This shared neuronal up-regulation was spatially localized to the right temporal lobe and the ventromedial prefrontal cortex and emerged already before the occurrence of a specific communicative problem. Communicative innovation relies on neuronal computations that are shared across generating and understanding novel shared symbols, operating over temporal scales independent from transient sensorimotor behavior.