Model collapse is iterated learning — transmission chains converge to the receiver's prior, not the message's deep structure

The seed asked whether a story's serial-reproduction "half-life" lines up with the per-generation rate of model collapse. The literature answers something sharper: they are the same process, and what survives transmission is not the message's deep structure but the receivers' shared prior.

Core claim 1 — model collapse IS iterated learning. Self-training instantiates a transmission chain whose fixed point is the model's own inductive bias. Tier 1 (arXiv primary). Quote: "iterative self-training monotonically amplifies prior biases" and "We show that iterated learning theory from cultural evolution fills this gap" (Guo, Wu & Yiu 2026, arXiv:2605.23054).

Core claim 2 — the human "how many retellings" number is tiny. Tier 1. Quote: "iterated learning converged to a linear function with positive slope in only a few generations for 28 of the 32 families of learners" (Kalish, Griffiths & Lewandowsky 2007). The chain forgets the seed data and reverts to the prior within ~1–4 generations regardless of what it started from.

Core claim 3 — the rates DON'T straightforwardly align, and the reason is the bottleneck. Tier 1. The LLM chain uses a "50,000-passage bottleneck [that] is wider than typical human experiments … slowing but not eliminating bias amplification," and compositionality is non-monotonic (rises then falls) because "compression without communicative grounding drives … non-monotonic compositionality" (arXiv:2605.23054). Substrate-independent mechanism, but bottleneck width sets the pace — so there is no single shared half-life.

Why this was hop-worthy

It bridges the vault's cognitive-science "deep structure / schema-restructuring" cluster to its ML "recursive degradation" cluster: Bartlett's leveling, Gersick's deep structure, and model collapse are three faces of "what a durable core survives repeated transformation" — answer: the transmitter's prior.

Further leads

• Morgan & Levy (2016) — the human regularization curve LLM gradients match at R²=0.94.
• Ferdinand et al. (2019) — dynamics hold for non-Bayesian gradient learners (substrate-independence).
• Schaeffer et al. (2025) — eight distinct formal definitions of "model collapse."

Hop chain

Chain: Bartlett serial-reproduction half-life → model collapse as iterated learning → what survives is the prior

Hop 1: "Model Collapse as Cultural Evolution" — https://arxiv.org/abs/2605.23054

• Hook type: Cross-domain bridge (cognitive-science iterated-learning theory ↔ 2026 LLM model collapse; lands on AI).
• Hook: A 2026 paper claims model collapse is not just statistical degradation but a cultural-transmission phenomenon.
• Why followed: Highest-priority hook type, and it directly answers the seed's bridge.
• Key findings: Self-training = one step of Bayesian iterated learning; compositionality is non-monotonic; LLM regularization gradients match human curves (R²=0.94).

Hop 2: Kalish, Griffiths & Lewandowsky 2007 — https://langev.com/pdf/kalish07iteratedLearning.pdf

• Hook type: Surprising claim (quantitative).
• Hook: Human chains "converged … in only a few generations."
• Why followed: It is the literal "how many retellings" number the seed asked for.
• Key findings: 28/32 families reverted to the positive-linear prior within a few generations regardless of seed data — transmission reveals inductive bias rather than preserving content.

Hop 3: vault note — claim-gersick-1991-punctuated-equilibrium-deep-structure

• Hook type: Cross-domain bridge (confirmed bridge candidate; would link the model-collapse hook to the org-change "deep structure" node).
• Hook: Gersick's "deep structure" — the durable order that survives equilibrium — uses the seed's exact phrase.
• Why followed: A bridge candidate outranks a raw mid-band score; it reframes "deep structure that survives retelling" as the shared prior.
• Key findings: "Deep structure" has already migrated paleontology → biology → org theory → knowledge base in the vault; iterated learning supplies the transmission-side face of the same idea.

Hop 4: Guo/Wu/Yiu 2026 §2.2 (mechanism zoom-in) — https://arxiv.org/abs/2605.23054

• Hook type: Mechanism question.
• Hook: WHY does self-training degenerate rather than merely lose noise?
• Why followed: The concept (collapse) was now in hand; the mechanism wasn't.
• Key findings: Compression pressure without communicative grounding causes compositionality to rise then fall; only task-grounded filtering (not random filtering) sustains structure.

Saved hooks not followed:

• Morgan & Levy (2016) human regularization curve (R²=0.94 LLM match) — from arXiv:2605.23054 — the tightest human/LLM quantitative alignment claim; deserves its own verification hop.
• Schaeffer et al. (2025) "eight distinct definitions of model collapse" — from arXiv:2605.23054 — a definitional-fragmentation story worth its own note.
• Ferdinand et al. (2019) substrate-independence — from arXiv:2605.23054 — bridges Bayesian and gradient learners.

Surprise: expected the human decay half-life and the model-collapse per-generation rate to line up on a shared timescale — found there is no shared timescale; the mechanism is substrate-independent but the bottleneck width sets the pace (LLM 50k-passage bottleneck is wider than human experiments, so slower). Surprise: expected serial reproduction to erode toward the story's own gist — found chains converge to the learners' prior regardless of the source, so what "survives" is the receiver's inductive bias, not any residue of the original. Surprise: expected model collapse to be monotonic decay — found compositionality is non-monotonic (rises, then falls) unless there is communicative grounding.

post-worthy: maybe — a clean cross-domain bridge (Bartlett/Gersick "deep structure" ↔ LLM model collapse) with a memorable one-liner ("what survives transmission is the prior, not the message"), but needs the Morgan & Levy R²=0.94 human-curve match verified before it carries real weight.