---
title: "Pragmatic Reasoning in Structured Signaling Games (2023)"
description: "The authors define a structured signaling game , in which both agents share a similarity matrix Z over the… 8 references, cited by 1 paper here."
authors: ["Emil Carlsson", "Devdatt Dubhashi"]
year: 2023
venue: "arXiv:2305.10167"
source: "https://arxiv.org/abs/2305.10167"
doi: "10.48550/arxiv.2305.10167"
arxiv: "2305.10167"
licence: "CC BY 4.0 (arXiv)"
licence_url: "http://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/carlsson-2023-pragmatic-reasoning-structured-signaling-games/"
---
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# Pragmatic Reasoning in Structured Signaling Games

**Authors:** Emil Carlsson and [Devdatt Dubhashi](https://md.research.elamur.ai/free/en/authors/devdatt-dubhashi/) · **Year:** 2023 · **Venue:** arXiv:2305.10167 · **Licence:** [CC BY 4.0 (arXiv)](http://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2305.10167) · [PDF](https://arxiv.org/pdf/2305.10167) · [DOI 10.48550/arxiv.2305.10167](https://doi.org/10.48550/arxiv.2305.10167) · [arXiv 2305.10167](https://arxiv.org/abs/2305.10167) · [OpenAlex](https://openalex.org/W4377115287)

**Citations:** 0 citations (OpenAlex, 2026-10-14) · 1 in our library, of the 149,439 papers whose bibliographies we read

## Summary
Classic signaling games and the Rational Speech Act (RSA) model treat every listener mistake as equally bad. Some meaning spaces, colors for example, have a natural notion of closeness, so mixing up two similar shades should cost less than mixing up distant ones. The authors define a *structured signaling game*, in which both agents share a similarity matrix Z over the meanings in the context. They also propose *structured-RSA* (sRSA), where the speaker's utility is the negative of a similarity-sensitive surprisal adapted from Leinster's work on structured entropy. When Z is the identity matrix, sRSA reduces exactly to ordinary RSA. They test it in two ways: by applying pragmatic recursion to World Color Survey naming data, and by training neural agents with REINFORCE in a color reference game. Efficiency is judged against the complexity/accuracy information-theoretic frontier and a well-formedness criterion. sRSA reaches nearly optimal efficiency after one or two recursion steps, while plain RSA does not approach the frontier. The study suggests that domain structure should enter the reasoning loop itself, not only the lexicon.

## Key points
- The data come from the WCS: 110 languages with about 25 speakers each. Colors are Munsell chips placed in CIELAB space, and perceptual similarity decays exponentially with CIELAB distance.
- Complexity is measured as I(M;W) and accuracy as I(W;U).
  - The optimal frontier comes from Blahut-Arimoto with annealing.
  - The well-formedness frontier comes from Correlation Clustering.
- When the recursion starts from the WCS naming data, sRSA moves close to the frontier after a single step. At the limit, RSA drifts away from the frontier while sRSA converges near it.
- The learning setup has these components:
  - **Agents:** small networks with one hidden layer of 25 ReLU units and a sigmoid output.
  - **Training:** 5-color contexts, recursion depths 0–5, α = 5, SGD at learning rate 0.001, 10,000 updates with batch size 100.
  - **Seeds:** 100 per configuration.
- At depth 2, sRSA agents end up closest to the frontier. A plain RL baseline is surprisingly more efficient than RSA agents. As reasoning depth grows, the learned meaning functions become more ambiguous, yet communication stays accurate.

## Interesting ideas
- Weighting the listener's surprise by how alike the confused meanings are gives graded penalties instead of all-or-nothing ones, which is useful wherever near-misses matter.
- The extension collapses to the standard model when the similarity matrix is the identity, which provides a built-in correctness check for any generalized scorer.
- Pragmatic reasoning can begin from an empirical speaker built from observed usage counts, instead of from an idealized literal listener. One or two refinement steps then suffice.
- Deeper recursion is not always better: with standard RSA, accuracy fell after a few steps. This argues for capping reasoning depth and measuring the effect.
- The authors separate "structure inside the lexicon" (graded meaning networks) from "structure inside the inference loop," and show that only the latter explains the gain. This is a clean ablation design.

## For Mova

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

- **I1** (frames): When choosing between candidate referents for coreference or a referring expression, Mova could penalize confusing near-identical entities less than unrelated ones. Similarity could come from WordNet distance or shared frame roles.
- **I2** (learn): Any similarity-aware metric or loss Mova adopts could be tested with an identity matrix as a negative control. With that input it must reproduce the old numbers exactly.
- **I3** (back): Generation of referring expressions could start from corpus frequencies of how entities are named. It would then apply a shallow pragmatic pass to resolve ambiguity in the current world of the text.
- **I4** (frames): Implicature and speech-act reasoning in prag could be limited to depth 1–2, keeping each step explainable and avoiding degenerate deep-recursion outputs.
- **I5** (learn): When a component improves, Mova could run a matched ablation that keeps the same knowledge but removes it from the reasoning step. This would show which layer actually earns the improvement.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Chalmers University of Technology](https://md.research.elamur.ai/free/en/universities/chalmers-university-of-technology/) — University, Gothenburg, Sweden · 12 works · 515 citations

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🧭 Topics (1): [🧮 Reasoning](https://md.research.elamur.ai/free/en/topics/reasoning/) · 1,426 works

## Cite

Cite as: Emil Carlsson and Devdatt Dubhashi. 2023. Pragmatic Reasoning in Structured Signaling Games. arXiv:2305.10167.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{carlsson2023pragmatic,
  title = {{Pragmatic Reasoning in Structured Signaling Games}},
  author = {Emil Carlsson and Devdatt Dubhashi},
  year = {2023},
  doi = {10.48550/arxiv.2305.10167},
  eprint = {2305.10167},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2305.10167}
}
```

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## References

8 references, 3 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. Emil Carlsson, Devdatt Dubhashi, and Fredrik D. Johansson. Learning approximate and exact numeral systems via reinforcement learning. Proceedings of the Annual Meeting of the Cognitive Science Society, 43, 2021. [↗](https://doi.org/10.48550/arxiv.2105.13857)
2. Rahma Chaabouni, Eugene Kharitonov, Emmanuel Dupoux, and Marco Baroni. Communicating artificial neural networks develop efficient color-naming systems. Proceedings of the National Academy of Sciences, 118, 03 2021. [↗](https://doi.org/10.1073/pnas.2016569118)
3. Richard S. Cook, Paul Kay, and Terry Regier. Chapter 9 - the world color survey database. In Henri Cohen and Claire Lefebvre, editors, Handbook of Categorization in Cognitive Science, pages 223–241. Elsevier Science Ltd, Oxford, 2005. [find](https://scholar.google.com/scholar?q=Richard+S%2E+Cook%2C+Paul+Kay%2C+and+Terry+Regier%2E+Chapter+9+%2D+the+world+color+survey+database%2E+In+Henri+Cohen+and+Claire+Lefebvre%2C+editors%2C+Handbook+of+Categorization+in+Cognitive+Science%2C+pages+223%E2%80%93241%2E+E)
4. Judith Degen, Robert Hawkins, Caroline Graf, Elisa Kreiss, and Noah Goodman. When redundancy is useful: A bayesian approach to ”overinformative” referring expressions. Psychological Review, 127, 04 2020. [↗](https://doi.org/10.1037/rev0000186)
5. M. Frank, A.G. Emilsson, B. Peloquin, N. Goodman, and C. Potts. Rational speech act models of pragmatic reasoning in reference games. psyarxiv, 2021. Michael C. Frank and Noah D. Goodman. [Predicting pragmatic reasoning in language games](https://md.research.elamur.ai/free/en/papers/frank-2012-predicting-pragmatic-reasoning-language-games/). Science, 336(6084): 998–998, 2012. Drew Fudenberg and David Levine. The Theory of Learning in Games, volume 1. The MIT Press, 1 edition, 1998. Edward Gibson, Richard Futrell, Julian Jara-Ettinger, Kyle Mahowald, Leon Bergen, Sivalogeswaran Ratnasingam, Mitchell Gibson, Steven T. Piantadosi, and Bevil R. Conway. Color naming across languages reflects color use. Proceedings of the National Academy of Sciences, 2017. ISSN 0027-8424. Noah D. Goodman and Michael C. Frank. Pragmatic Language Interpretation as Probabilistic Inference. Trends in Cognitive Sciences, 20(11):818–829, 2016. H. Paul Grice. Logic and conversation. In Maite Ezcurdia and Robert J. Stainton, editors, The Semantics-Pragmatics Boundary in Philosophy, page 47. [↗](https://doi.org/10.17605/osf.io/f9y6b)
6. Broadview Press, 1975. Jennifer Hu, Roger Levy, and Noga Zaslavsky. Scalable pragmatic communication via self-supervision. In ICML Workshop on Self-Supervised Learning for Reasoning and Perception, 2021. Mikael Kågebäck, Emil Carlsson, Devdatt Dubhashi, and Asad Sayeed. A reinforcement-learning approach to efficient communication. PLoS ONE, 15(7):1–26, 2020. Tom Leinster. Entropy and Diversity The Axiomatic Approach. [find](https://scholar.google.com/scholar?q=Broadview+Press%2C+1975%2E+Jennifer+Hu%2C+Roger+Levy%2C+and+Noga+Zaslavsky%2E+Scalable+pragmatic+communication+via+self%2Dsupervision%2E+In+ICML+Workshop+on+Self%2DSupervised+Learning+for+Reasoning+and+Perception%2C+20)
7. Cambridge University Press, 2021. Will Monroe, Robert X.D. Hawkins, Noah D. Goodman, and Christopher Potts. [Colors in context: A pragmatic neural model for grounded language understanding](https://md.research.elamur.ai/free/en/papers/monroe-2017-colors-context-pragmatic-neural-model/). Transactions of the Association for Computational Linguistics, 5:325– 338, 2017. Xenia Ohmer, Michael Franke, and Peter König. Mutual exclusivity in pragmatic agents. Cognitive Science, 46, 2022. Benjamin Peloquin, Noah Goodman, and Michael Frank. The interactions of rational, pragmatic agents lead to efficient language structure and use. Topics in Cognitive Science, 12:433–445, 01 2020. Steven T. Piantadosi, Harry Tily, and Edward Gibson. The communicative function of ambiguity in language. Cognition, 122(3):280–291, 2012. Terry Regier, Paul Kay, and Naveen Khetarpal. Color naming reflects optimal partitions of color space. Proceedings of the National Academy of Sciences of the United States of America, 104(4):1436–1441, 2007. Terry Regier, Charles Kemp, and Paul Kay. Word Meanings across Languages Support Efficient Communication. The Handbook of Language Emergence, (January 2015):237– 263, 2015. Ronald J. Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine Learning, 8(3):229–256, 1992.
8. Noga Zaslavsky, Charles Kemp, Terry Regier, and Naftali Tishby. Efficient compression in color naming and its evolution. Proceedings of the National Academy of Sciences, 115(31):7937[–7942, 2018](https://md.research.elamur.ai/free/en/papers/zaslavsky-2021-rate-distortion-view-human-pragmatic/). Noga Zaslavsky, Jennifer Hu, and Roger Levy. A Rate–Distortion view of human pragmatic reasoning. Proceedings of the Society for Computation in Linguistics, 4, 2021. doi.org/10.7275/gc1z-ck09. [↗](https://doi.org/10.7275/gc1z-ck09)

*Updated 1 November 2026*