Can dialogue systems track both speakers' beliefs across turns?

The Rational Speech Act (RSA) framework models pragmatic reasoning as recursive social inference between speakers and listeners. But RSA has a fundamental limitation for dialogue: it handles single utterances, not evolving multi-turn conversations. CRSA fixes this by integrating a multi-turn gain function grounded in interactive rate-distortion theory.

The key extension: Both agents have private information. Each produces utterances conditioned on the full dialogue history. The gain function tracks evolving beliefs of both interlocutors — not just one listener inferring one speaker's intent, but bidirectional, progressive convergence of shared understanding.

Demonstrated on: referential games and template-based doctor-patient dialogues (disease diagnosis from symptoms). CRSA captures the progression from partial to shared understanding across turns.

A critical limitation acknowledged: there is no systematic way to model the meaning spaces, which are always application-dependent. And shifting from utterance-level to token-level reasoning (for scaling to real LLMs) may influence pragmatic capabilities — the reasoning granularity problem is unresolved.

This provides the mathematical framework that current LLM dialogue systems lack. Since the fluency gap — llm text is linguistically well-formed but communicatively empty because fluency substitutes for the grounding work that makes communication meaningful, CRSA offers a principled alternative: pragmatic reasoning grounded in information theory rather than next-token prediction. The question is whether token-level LLM generation can implement utterance-level pragmatic optimization.

Since Why do standard alignment methods ignore partner interventions?, CRSA's bidirectional belief tracking is the theoretical complement to the counterfactual invariance approach — one addresses it through reward engineering, the other through information-theoretic architecture.