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To understand how agents can communicate abstract procedures without a pre-shared vocabulary, the authors train a sender-receiver neural system where a speaker infers input-output transformation rules and emits an invented eight-symbol protocol for an unexposed listener to execute. While training purely on communicative task reward causes symbol collapse and produces coarse label clusters, incorporating listener error gradients and expressive pressure forces the emergence of a structured semantic geometry. Consequently, the resulting protocol generalizes out-of-distribution, successfully transferring three-step composite transformation rules never encountered during training to entirely new listener networks.
Scalar reinforcement collapses emergent multi-agent communication into degenerate, coarse labels, whereas passing listener error gradients directly back to the speaker forces continuous semantic representations that unlock compositional generalization.
How can a rule inferred from examples reach someone who never saw them, without a shared code? Patients with severe aphasia do it by gesture or sketch. One network sees worked examples and emits eight invented symbols; a second, blind to them, applies them to a new input. Rewarded for the second's success, the first learns a code carrying rules to three-step transformations training never presents, which new learners acquire. Like invented human languages, the code has two regimes: under reward alone the speaker drifts to one message, as human languages lose words under plain transmission; expressive pressure keeps messages differentiated. Success on new rules tracks how much the message says about the rule, not how varied messages are. The learning signal shapes the code: reward sorts many rules under few fixed labels; the listener's error gradient gives each rule a region of similar messages, telling rules apart far better.