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LIT-769: Language Evolution by Iterated Learning With Bayesian Agents

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Properties5
StatusActive — read 2026-10-09 (NOTE-599); worth reading as the analytic result behind iterated learning: a chain of learners who share a prior and each sample a hypothesis from their posterior is a Gibbs sampler, so the probability that a learner holds a language converges to its prior probability whatever the amount of data passed on, and the data produced converge to the prior predictive. Learners who take the MAP hypothesis run stochastic EM instead: the outcome centres on the prior's mode but depends on data amount and noise, and in the two-language case is the same for every prior strength α between 0.5 and 1 − ε, so weak biases can be amplified. Equal-fitness populations share the equilibrium. Source of THEORY-155.
Tagslinguistics, probabilistic-modeling, cognition, compositionality
SupportsCLAIM-066 — Kirby, Cornish and Smith show structure emerging under transmission with an experimenter's filter, not filtering by measured inductive biases, and Griffiths and Kalish's convergence to the prior holds only for sampling learners, CLAIM-090 — Serial transmission is reconstructive and filtered by the transmitters' inductive biases, so a stable endpoint can be far from the ancestral utterance while remaining interpretable
Cited as “paper” byNOTE-599 — Language Evolution by Iterated Learning With Bayesian Agents
Cited as “source” byTHEORY-155 — Iterated learning by Bayesian agents who sample from the posterior converges, in an ergodic chain, to the shared prior

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Thomas L. Griffiths and Michael L. Kalish (2007), Cognitive Science 31(3):441–480 — DOI-10.1080/15326900701326576

Key takeaways

  • Sampling learners converge to the prior (§4, Eqs. 25–36). If every learner shares a prior P(h) and a likelihood matched to production, and samples h from P(h|d), the prior is the stationary distribution of the chain on hypotheses and the prior predictive that of the chain on data. The amount of data passed on changes only the speed (via the second eigenvalue), not the endpoint, so structure can emerge without a bottleneck, but only if the prior favours it.
  • It is a Gibbs sampler (§4.2): alternately drawing h given d and d given h is the systematic-scan Gibbs sampler for P(d|h)P(h).
  • MAP learners run stochastic EM (§5): the transmitted data are the latent variable and there are no observations, so the outcome concentrates near the prior’s mode. In the two-language case (Table 1) the stationary probability of the favoured language is (s + (1 − s)ε) / (s + 2(1 − s)ε), independent of the prior α whenever ε < 1 − α: a weak bias does as much as a strong one.
  • Compositionality simulation (§6): 4 compositional and 256 holistic languages. Under sampling, long-run frequencies match the prior at every data size; under MAP the prior’s favourite dominates (no compositional language ever, when they get 1% of the prior mass; with half of it, holistic languages appear only once learners see three or more utterances).
  • Populations (§7): with equal fitness, the same distribution is the stable equilibrium of an unbounded population. The authors warn that selection could break the correspondence, and close by extending the conclusion, unanalysed, to “legends, religious concepts, and social norms”.

The laboratory counterpart is LIT-771, which cites this paper only in a block of model references (NOTE-596). The paper does not cite Bartlett (LIT-768), whose serial reproduction of a folk tale is the classical case its closing extrapolation describes.

Standing in the record

Filed on 2026-10-09 at the owner’s request, as one of the works in the reference list of the owner’s working manuscript (October 2026) that the record did not yet hold. See the curation entry of that day.

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