📄 A Rate–Distortion view of human pragmatic reasoning?

Summary

The Rational Speech Act (RSA) framework models pragmatics as a speaker and a listener who recursively reason about each other. Earlier work, based only on numeric simulations, conjectured that each round of this recursion raises expected communicative utility. This short paper tests that conjecture analytically and ties RSA to Shannon's Rate–Distortion (RD) theory.

The authors prove that RSA updates form an alternating maximization (AM) procedure. What RSA optimizes is not expected utility alone. It is a combined objective: expected utility plus the conditional entropy of the speaker's productions, where higher entropy stands for lower effort. As a result, expected utility can actually fall at deeper recursion levels.

They then propose RD-RSA. In this variant, the speaker trades utility against the mutual information between meanings and utterances, which makes the speaker's soft-max depend on the marginal utterance probability. On the human reference-game data of Vogel et al. (2014), RD-RSA fits as well as RSA. Unlike RSA, it has no built-in bias toward uninformative, random utterances. The result gives pragmatic reasoning a principled information-theoretic basis.

Key points

• Standard RSA setup: the listener is Bayesian, L(m|u) ∝ S(u|m)P(m), with a shared prior P(m). The speaker is a soft-max, S(u|m) ∝ exp(αV), where the utility is V = log L(m|u) − C(u).
• Theorem: for every α ≥ 0, each speaker or listener step increases G_α = H_S(U|M) + α·E_S[V_L]. This makes RSA an AM algorithm in the sense of Csiszár and Shields (2004).
• The authors give counter-examples in which expected utility falls with recursion depth while conditional entropy rises. These cases disprove the assertion, put forward by Peloquin et al. (2019) and Yuan et al. (2018), that RSA's recursion always yields higher utility.
• RD-RSA minimizes F_α = I_S(M;U) − α·E_S[V_L]. Its speaker is S(u|m) ∝ S(u)·exp(αV), and the marginal S(u) is re-estimated at every iteration. The listener stays Bayesian.
• Evaluation used simulated reasoning trajectories against human reference-game behavior from Vogel et al. (2014). RD-RSA matched RSA's fit, and the analysis showed that only RSA leans toward non-informative production.

Interesting ideas

• I1. The paper recasts an iterative heuristic procedure as coordinate ascent on one explicit objective. This shows what each step actually improves and why "more iterations" need not mean "better" on the metric you care about.
• I2. Weighting a speaker's choice by the running marginal frequency of utterances removes a drift toward uniform, uninformative choices. The fix is cheap and applies to any soft-max chooser among alternatives.
• I3. The authors treat speaker and listener as encoder and decoder, so communication cost is measured in bits as mutual information between meanings and utterances.
• I4. The authors refute a popular conjecture by finding explicit counter-examples, instead of relying on simulations that seemed to support it.
• I5. Two models with different theoretical motivations are compared on the same human behavioral data and also on their built-in biases, not just on fit.

For Mova

How these ideas could serve Mova, our small open language model — its files, stages and tests:

• I1 (frames): The implicature reasoner in prag could log an explicit objective value after each speaker/listener step, so every inference round is explainable and convergence can be checked.
• I2 (back): When generation picks among paraphrases of a meaning graph, the soft-max could be multiplied by an iteratively updated utterance marginal, which favors consistent, informative wordings over random variety.
• I3 (back): The text → graph → text compressor could report I(M;U)-style rate alongside reconstruction quality, giving a principled rate–distortion curve for comparing settings.
• I4 (learn): Evaluation could include targeted searches for inputs where a supposedly monotone repair or self-play loop gets worse, serving as negative controls.
• I5 (answer): When choosing between alternative pragmatic readers, check for systematic biases (e.g., toward vague answers) as well as test accuracy.