---
title: "Human iterated-learning chains converge to the learners' shared prior within a few generations, regardless of the seed input"
type: "claim"
status: "seedling"
audit_status: "capture-verified"
source_url: "https://langev.com/pdf/kalish07iteratedLearning.pdf"
source_author: "Michael L. Kalish, Thomas L. Griffiths, Stephan Lewandowsky"
source_date: "2007-01-01T00:00:00.000Z"
source_venue: "Psychonomic Bulletin & Review 14:288–294 (2007)"
source_quote: "iterated learning converged to a linear function with positive slope in only a few generations for 28 of the 32 families of learners"
source_tier: 1
provenance: "Promotion from 10-inbox/raw/2026-07-11-hop-model-collapse-is-iterated-learning.md, 2026-07-12"
origin: "batch"
derived_from: "10-inbox/raw/2026-07-11-hop-model-collapse-is-iterated-learning.md"
writer_model: "claude-sonnet-5"
date_created: "2026-07-12T00:00:00.000Z"
tags: ["iterated-learning","cultural-evolution","serial-reproduction","function-learning","inductive-bias","cognitive-science"]
audits: ["2026-07-12 claude-opus-4-8"]
---


In Kalish, Griffiths & Lewandowsky's (2007) iterated function-learning
experiments, participants were shown a scatter of (x, y) points generated by
the previous participant's guesses and asked to predict y for new x values;
their predictions became the training data for the next participant in the
chain. Across 32 independently-seeded chains ("families of learners"),
regardless of the function the chain started from, "iterated learning
converged to a linear function with positive slope in only a few generations
for 28 of the 32 families of learners." The chains did not preserve or
gradually erode the seed function — they snapped to a shared prior (a
positive-linear relationship) within roughly one to four transmission steps.

This is the empirical anchor for the claim that
[[claim-iterated-learning-theory-reframes-model-collapse-as-cultural-evolution|iterated-learning
theory]] applies to [[claim-model-collapse-recursive-training-erases-distribution-tails|AI
model collapse]]: both are transmission chains whose fixed point is the
learner population's own inductive bias, not the transmitted content. It is
also a modern, quantified counterpart to Bartlett's serial-reproduction
findings that a durable "deep structure" — see
[[claim-gersick-1991-punctuated-equilibrium-deep-structure]] for the
organizational-theory cognate of that phrase — survives repeated
retransmission while surface content does not; see
[[question-bartlett-distortion-typology-maps-to-model-collapse-failure-modes]]
for the open question of whether Bartlett's own distortion typology maps onto
collapse failure modes specifically.

> [!note] Seek's commentary: The number that matters here is "a few
> generations" for 28 of 32 chains — this is a tight, falsifiable result, not
> a vague trend, and it's the actual "how many retellings" figure a Bartlett
> comparison needs. Worth chasing whether the four non-converging families
> share a property (e.g. specific seed functions resistant to the prior). —
> Seek