Collaborative Rational Speech Act (CRSA)

• CRSA is a collaborative extension of RSA that models multi-turn dialogues with sequential pragmatic reasoning and explicit private and shared information.
• It employs an information-theoretic gain function from rate-distortion theory to iteratively optimize speaker and listener updates based on dialogue history.
• CRSA demonstrates enhanced task accuracy and sharper information transfer in settings like referential games and medical dialogues compared to traditional RSA methods.

Searching arXiv for the specified paper and related RSA/pragmatics work. Collaborative Rational Speech Act (CRSA) is an information-theoretic extension of the Rational Speech Act (RSA) framework for multi-turn, collaborative dialogue in which both interlocutors hold private information and must reason about a shared task outcome through sequential utterances. It was introduced to address a limitation of standard RSA and related extensions: while RSA provides a principled account of pragmatic reasoning, existing formulations are not naturally suited to settings where dialogue history, role alternation, and asymmetric private states jointly determine communicative behavior. CRSA models this setting by conditioning speaker and listener inferences on the full dialogue history and by optimizing a gain function adapted from rate-distortion theory, thereby extending the single-turn RSA gain to a setting with two private-meaning spaces and a shared target variable (Estienne et al., 18 Jul 2025).

1. Conceptual basis and relation to RSA

The standard RSA framework is formulated over a meaning space $M$ and an utterance space $U$, with a speaker $S(u \mid m)$ that produces utterances given intended meanings and a listener $L(m \mid u)$ that infers meanings from utterances. A prior $P(m)$ over meanings and a cost function $C(u)$ complete the basic specification. In this formulation, the speaker trades off an entropy term over utterances against a listener-oriented value term, producing the canonical recursive updates between speaker and listener distributions (Estienne et al., 18 Jul 2025).

In the exposition associated with CRSA, the RSA gain is written as

$$G_{\rm RSA}(L,S) \;=\; H_{S}(U\mid M) \;+\; \alpha\,\mathbb{E}_{(m,u)\sim S(m)P(m)}\big[V_L(u,m)\big],$$

where

$$H_S(U\mid M) \;=\; -\sum_{m\in M}\!P(m)\sum_{u\in U} S(u\mid m)\,\log S(u\mid m)$$

and

$V_L(u,m)\;=\;\log L(m\mid u)\;-\;C(u).$

Alternating maximization yields the familiar RSA recursion

$$S_{k+1}(u\mid m)\;\propto\;\exp\!\Big(\alpha\,\big[\log L_k(m\mid u)-C(u)\big]\Big), \quad L_{k+1}(m\mid u)\;\propto\;S_{k+1}(u\mid m)\,P(m).$$

This gain-based perspective is central to CRSA, because the collaborative extension preserves the same optimization logic while replacing single-turn semantics with history-conditioned multi-agent inference (Estienne et al., 18 Jul 2025).

CRSA is also aligned with an information-theoretic reinterpretation of RSA developed in work on scalable pragmatic communication. That line of work describes RSA as either a light-efficiency or rate-distortion objective, emphasizing entropy, mutual information, and listener decodability. It provides the broader theoretical context for viewing pragmatic speaker-listener pairs as solutions to information-optimization problems rather than solely recursive symbolic updates (Hu et al., 2021). This suggests that CRSA should be understood not merely as a dialogue-specific heuristic, but as a structured extension of information-theoretic RSA to interactive settings.

2. Formal definition of the collaborative model

CRSA assumes a multi-turn dialogue with two agents, $U$0 and $U$1, interacting over $U$2 turns. At turn $U$3, one agent acts as speaker $U$4, the other as listener $U$5, and the roles then swap. Each agent $U$6 possesses a private meaning $U$7 drawn from a discrete space $U$8, and these private states remain fixed throughout the dialogue. In addition, there is a shared task outcome $U$9, such as a referent location or a medical diagnosis. The dialogue history up to turn $S(u \mid m)$0 is

$S(u \mid m)$1

and both agents share a fixed prior

$S(u \mid m)$2

which is permuted appropriately when roles swap (Estienne et al., 18 Jul 2025).

At a given turn, the CRSA speaker distribution is

$S(u \mid m)$3

the speaker’s posterior over current utterances given its private meaning and the history. The corresponding listener distribution is

$S(u \mid m)$4

the listener’s posterior over the task outcome given its own private meaning, the current utterance, and the dialogue history (Estienne et al., 18 Jul 2025).

The model defines a joint distribution over the current utterance and latent variables: $S(u \mid m)$5 where $S(u \mid m)$6 is derived from past speakers’ turn-by-turn models. The listener value is

$S(u \mid m)$7

The CRSA gain at turn $S(u \mid m)$8 is then given as

$S(u \mid m)$9

The corresponding entropy term is written as

$L(m \mid u)$0

Two extensions relative to single-turn RSA are explicit in this formulation: all distributions are conditioned on the full dialogue history $L(m \mid u)$1, and the model jointly tracks two private-meaning spaces $L(m \mid u)$2 and $L(m \mid u)$3 together with a shared target $L(m \mid u)$4 (Estienne et al., 18 Jul 2025).

3. Optimization procedure and belief tracking

CRSA is optimized by block alternating maximization in the same spirit as RSA. At each turn $L(m \mid u)$5, optimization alternates between a speaker update and a listener update. For iteration $L(m \mid u)$6, the speaker update is

$L(m \mid u)$7

The listener update is

$L(m \mid u)$8

The quantities $L(m \mid u)$9 and $P(m)$0 represent each agent’s evolving belief about the unknown private state of the interlocutor (Estienne et al., 18 Jul 2025).

In practice, the alternating updates are run until the CRSA gain converges, with an example convergence criterion given as $P(m)$1 (Estienne et al., 18 Jul 2025). This makes explicit that CRSA is not only a representational extension of RSA but also a computational procedure that preserves iterative best-response structure.

The role of belief tracking is especially important. Because each agent has a private state and dialogue unfolds over multiple turns, the optimization does not simply decode a fixed meaning from an isolated utterance. Instead, each update integrates uncertainty about the interlocutor’s private meaning, the history-dependent generative process, and the shared task variable. This suggests that CRSA occupies an intermediate position between classical pragmatic models and more general interactive inference frameworks: it remains interpretable through explicit probabilistic updates, yet it incorporates the core structural ingredients of collaboration, namely role alternation, private information, and history-sensitive reasoning.

4. Information-theoretic interpretation and scalability context

CRSA is described as an information-theoretic extension of RSA that optimizes a gain function adapted from rate-distortion theory (Estienne et al., 18 Jul 2025). This framing places it in a line of work that interprets pragmatic communication as a constrained optimization over informativeness, entropy, and listener recovery, rather than only as nested Bayesian recursion.

In "Scalable pragmatic communication via self-supervision" (Hu et al., 2021), two related objectives are distinguished: the LE-RSA objective

$P(m)$2

and the RD-RSA objective

$P(m)$3

The first rewards speaker entropy and listener decodability; the second rewards mutual information and listener decodability. That work also states that in the limit $P(m)$4 one recovers classical RSA recursion, and for $P(m)$5 one recovers pure channel-design objectives (Hu et al., 2021). CRSA’s turnwise gain is directly analogous in structure: it retains an entropy term and a listener-value term, but extends both to dialogue-conditioned, two-agent settings (Estienne et al., 18 Jul 2025).

The information-theoretic perspective matters for two reasons. First, it clarifies why CRSA can be viewed as a principled generalization rather than an ad hoc conversational heuristic. Second, it connects CRSA to scalable neural pragmatics. The self-supervised architecture described in (Hu et al., 2021) uses jointly optimized speaker and listener modules, trained with minibatch estimates of LE-RSA or RD-RSA losses, and characterizes their joint learning dynamics as an emergent cooperative behavior without explicit turn-taking recursions. A plausible implication is that CRSA’s formalism can be situated within a broader family of pragmatic systems where recursive reasoning is approximated or realized through optimization over shared objectives.

The CRSA exposition itself also identifies potential extensions: moving from discrete $P(m)$6 to continuous latent-space embeddings; token-level RSA/CRSA for open-ended LLM generation; scaling to more than two agents or non-stationary private states $P(m)$7; and integration with POMDP-style RL policies to jointly optimize information gathering and task reward (Estienne et al., 18 Jul 2025). These are presented as potential extensions rather than established components of the model.

5. Empirical evaluation

CRSA is evaluated on two settings: referential games and template-based doctor-patient dialogues in the medical domain (Estienne et al., 18 Jul 2025). The evaluations are designed to test whether history-conditioned collaborative reasoning improves task performance, information transfer, and distributional sharpness relative to RSA variants and literal baselines.

Referential games

The referential-game setup follows Khani et al. (2018). There are $P(m)$8 cards in a row, each card labeled by $P(m)$9. Agent $C(u)$0 sees letters only; agent $C(u)$1 sees numbers only. The shared goal $C(u)$2 is the position of the unique “A1” card, where $C(u)$3 means “none.” There are 500 simulated rounds with alternating turns, and at each turn an agent utters a position $C(u)$4 (Estienne et al., 18 Jul 2025).

The baselines are YRSA, RSA-per-turn, literal listeners/speakers, and “prior” (no utterances). The reported metrics by turn $C(u)$5 are Accuracy,

$C(u)$6

and Information Gain,

$C(u)$7

With $C(u)$8, CRSA reaches approximately $C(u)$9–$$G_{\rm RSA}(L,S) \;=\; H_{S}(U\mid M) \;+\; \alpha\,\mathbb{E}_{(m,u)\sim S(m)P(m)}\big[V_L(u,m)\big],$$0 accuracy by turn $$G_{\rm RSA}(L,S) \;=\; H_{S}(U\mid M) \;+\; \alpha\,\mathbb{E}_{(m,u)\sim S(m)P(m)}\big[V_L(u,m)\big],$$1–$$G_{\rm RSA}(L,S) \;=\; H_{S}(U\mid M) \;+\; \alpha\,\mathbb{E}_{(m,u)\sim S(m)P(m)}\big[V_L(u,m)\big],$$2, outperforming YRSA at approximately $$G_{\rm RSA}(L,S) \;=\; H_{S}(U\mid M) \;+\; \alpha\,\mathbb{E}_{(m,u)\sim S(m)P(m)}\big[V_L(u,m)\big],$$3 and literal at approximately $$G_{\rm RSA}(L,S) \;=\; H_{S}(U\mid M) \;+\; \alpha\,\mathbb{E}_{(m,u)\sim S(m)P(m)}\big[V_L(u,m)\big],$$4. CRSA also achieves the largest cumulative information gain, approximately $$G_{\rm RSA}(L,S) \;=\; H_{S}(U\mid M) \;+\; \alpha\,\mathbb{E}_{(m,u)\sim S(m)P(m)}\big[V_L(u,m)\big],$$5 bits, versus YRSA-Wt at approximately $$G_{\rm RSA}(L,S) \;=\; H_{S}(U\mid M) \;+\; \alpha\,\mathbb{E}_{(m,u)\sim S(m)P(m)}\big[V_L(u,m)\big],$$6 bits and literal at approximately $$G_{\rm RSA}(L,S) \;=\; H_{S}(U\mid M) \;+\; \alpha\,\mathbb{E}_{(m,u)\sim S(m)P(m)}\big[V_L(u,m)\big],$$7 bits (Estienne et al., 18 Jul 2025).

Doctor-patient dialogues

The second evaluation uses MDDial, attributed to Macherla et al. (2023), and consists of template-based, multi-turn medical interviews in which the patient describes subsets of symptoms and the doctor must infer the correct diagnosis from a candidate set (Estienne et al., 18 Jul 2025). The literal speaker is instantiated through a pretrained LLaMA-3.2B-Instruct model using symptom-conditioned prompts, with the model specification tied to Eq. (8) in the paper (Estienne et al., 18 Jul 2025).

Final listener prediction is evaluated at the last turn of each dialogue. For $$G_{\rm RSA}(L,S) \;=\; H_{S}(U\mid M) \;+\; \alpha\,\mathbb{E}_{(m,u)\sim S(m)P(m)}\big[V_L(u,m)\big],$$8 dialogues and $$G_{\rm RSA}(L,S) \;=\; H_{S}(U\mid M) \;+\; \alpha\,\mathbb{E}_{(m,u)\sim S(m)P(m)}\big[V_L(u,m)\big],$$9, the reported entropies are as follows:

Model	Speaker entropy $$H_S(U\mid M) \;=\; -\sum_{m\in M}\!P(m)\sum_{u\in U} S(u\mid m)\,\log S(u\mid m)$$0	Listener entropy $$H_S(U\mid M) \;=\; -\sum_{m\in M}\!P(m)\sum_{u\in U} S(u\mid m)\,\log S(u\mid m)$$1
CRSA	8.18 nats	2.19 nats
RSA	14.27 nats	2.86 nats
Literal	18.00 nats	3.29 nats

Lower entropy is interpreted as indicating more confident, focused utterance distributions and diagnosis posteriors. On this basis, CRSA is reported to outperform both RSA and a non-pragmatic baseline (Estienne et al., 18 Jul 2025).

Across both tasks, the empirical pattern is consistent: CRSA produces sharper distributions, higher task performance, and stronger information transfer than baselines that either neglect dialogue history, omit pragmatic reasoning, or do not explicitly model the interlocutors’ private states.

6. Interpretation, related approaches, and open issues

The primary interpretive claim associated with CRSA is that by jointly tracking both agents’ private beliefs and conditioning every step on the full history, the model yields more efficient, targeted questions and inferences, thereby capturing the back-and-forth of real collaboration (Estienne et al., 18 Jul 2025). The paper further characterizes CRSA as fully interpretable because each update step maximizes a clear information-theoretic objective adapted from interactive rate-distortion (Estienne et al., 18 Jul 2025). In the context of high-stakes domains such as medicine, this interpretability is presented as relevant to audited and controllable dialogue behavior.

CRSA is closely related to other efforts to extend RSA beyond its classical assumptions. "Scalable pragmatic communication via self-supervision" (Hu et al., 2021) addresses the scalability problem by turning information-theoretic RSA objectives into differentiable neural losses and learning pragmatic policies via self-supervision. That work emphasizes large-scale applicability and self-supervised acquisition of pragmatic behavior. CRSA, by contrast, centers multi-turn collaboration, explicit private states for both agents, and turnwise gain optimization conditioned on dialogue history. The relation is therefore complementary: one contributes a scalable training perspective, the other a formal model of sequential collaborative pragmatics.

Another related direction is "Learning to Mediate Disparities Towards Pragmatic Communication" (Bao et al., 2022), which proposes Pragmatic Rational Speaker (PRS), an RSA extension designed to model speaker-listener disparities. PRS introduces a disparity-adjustment layer in working memory while keeping the base RSA machinery fixed, allowing a speaker to adapt utterances to listener-specific knowledge or perceptual limitations. In referential games with simulated hypernym and limited-vision disparities, PRS improves collaborative accuracy over vanilla RSA (Bao et al., 2022). Relative to PRS, CRSA does not focus on a learned disparity layer; instead, it encodes asymmetry through explicit private meaning spaces, shared priors, and history-conditioned turnwise updates. This suggests a broader taxonomy of post-RSA models: some address multi-turn collaboration, some address scalability, and some address asymmetric interlocutor capabilities.

A common misconception is to treat CRSA as merely “RSA applied repeatedly over turns.” The formalism given for CRSA is more specific than that. It does not only rerun a single-turn speaker-listener recursion at each step; it introduces a dialogue history variable $$H_S(U\mid M) \;=\; -\sum_{m\in M}\!P(m)\sum_{u\in U} S(u\mid m)\,\log S(u\mid m)$$2, a joint prior over two private meanings and a shared target, and belief terms $$H_S(U\mid M) \;=\; -\sum_{m\in M}\!P(m)\sum_{u\in U} S(u\mid m)\,\log S(u\mid m)$$3 and $$H_S(U\mid M) \;=\; -\sum_{m\in M}\!P(m)\sum_{u\in U} S(u\mid m)\,\log S(u\mid m)$$4 for the interlocutors’ hidden states (Estienne et al., 18 Jul 2025). Another misconception would be to conflate its information-theoretic framing with generic neural dialogue optimization. The model’s gain function, listener value, and alternating updates are explicit and interpretable, rather than latent in end-to-end policy learning.

The open issues identified in the CRSA exposition remain prospective. These include continuous latent-state variants, token-level generation for open-ended LLMs, extension to more than two agents or non-stationary private states, and integration with POMDP-style RL policies (Estienne et al., 18 Jul 2025). A plausible implication is that future work will test whether CRSA’s interpretability and collaborative structure can be preserved under the representational and optimization demands of large-scale neural dialogue systems.