Model Collapse as Cultural Evolution

Abstract: Model collapse, the progressive degradation of LLMs trained on their own outputs, has been characterized statistically but lacks a linguistic explanation for which structures degrade, in what order, and why. We show that iterated learning theory from cultural evolution fills this gap. We derive five falsifiable predictions, distinguish those uniquely discriminative for the theory from confirmatory ones, and test them by self-training LLaMA-2-7B and Mistral-7B over 10 generations in English, German, and Turkish. The critical discriminative finding: compositionality follows a non-monotonic trajectory (initially rising, then falling) under unfiltered self-training. This signature persists with maximally regular seed data (ruling out noise removal) and is sustained only by task-grounded filtering, not random filtering, providing the first LLM-scale evidence for the compression-communication tradeoff. All predictions are confirmed with large effect sizes (Hedges' $g > 1.6$; $\mathrm{BF}_{10} > 100$), and LLM regularization gradients closely match human behavioral data ($R² = 0.94$). These results reframe model collapse as a cultural transmission phenomenon and yield concrete principles for self-training pipeline design.

• The paper shows that self-training causes compositional systematicity to rise from 0.41 to 0.47 by generation 3 before falling to 0.31 by generation 10, supporting iterated learning theory over purely monotonic collapse accounts.
• The experiments find that rare linguistic variants, pragmatic constructions, irregular morphology, and distributional diversity degrade fastest, while syntactic structures and frequent forms persist longer across English, German, and Turkish.
• The paper demonstrates that quality-based, task-grounded filtering preserves compositionality at 0.48 versus 0.31 without filtering, whereas random data reduction has no meaningful protective effect, offering a practical safeguard for synthetic-data pipelines.

Overview and motivation

Model collapse—the progressive degradation of LLMs trained recursively on their own outputs—has been characterized primarily through statistical estimation theory, which describes distributional tail loss and variance reduction but offers little explanation of which linguistic structures degrade, in what order, and why. The paper under review proposes that iterated learning theory from cultural evolution supplies this missing explanatory layer. Building on the formal correspondence between LLM self-evolution and Bayesian iterated learning established by Ren et al., the authors extend the framework to natural language with weight-based fine-tuning, derive five falsifiable predictions whose discriminative status is explicitly categorized, and test them through controlled self-training experiments spanning 10 generations, two model families (LLaMA-2-7B and Mistral-7B), and three typologically distinct languages (English, German, Turkish).

The central claim is bold but carefully hedged: model collapse is not merely statistical noise accumulation but a cultural transmission phenomenon in which a model's inductive biases play the role of a Bayesian prior, progressively amplified across generations. Crucially, the paper distinguishes predictions that any generic collapse account would make (confirmatory) from those uniquely predicted by iterated learning theory (discriminative), and designs controls to adjudicate between them.

Theoretical framework and discriminative predictions

The theoretical core rests on Griffiths and Kalish's result that chains of Bayesian learners converge to the learner's prior, extended by Ferdinand et al.'s demonstration that these dynamics persist even for non-Bayesian gradient-based learners. The authors map four specific LLM biases onto iterated learning dynamics: frequency bias from next-token training drives frequency-dependent loss; simplicity bias drives morphological regularization; local coherence bias from autoregressive factorization drives dimension-specific degradation ordering; and compression without communicative grounding drives compositionality dynamics.

Five predictions are derived, each assigned a discriminative status:

• P1 (partially discriminative): low-frequency variants are lost first along a log-linear gradient matching human regularization data.
• P2 (confirmatory): morphological regularity increases monotonically.
• P3 (partially discriminative): pragmatic constructions degrade before syntactic ones.
• P4 (uniquely discriminative, critical test): compositional systematicity follows a non-monotonic trajectory—rising then falling—under unfiltered self-training, and is sustained only by task-grounded filtering.
• P5 (confirmatory): Zipf exponents decrease, reflecting distributional narrowing.

P4 is the linchpin. Generic model collapse predicts only monotonic degradation; only the compression–communication tradeoff of Kirby et al.—whereby compositionality requires both transmission bottleneck and communicative pressure—predicts an initial rise followed by decline.

Experimental design

The pipeline implements iterated learning with a consequential design choice: at every generation, fine-tuning starts from the same frozen base model rather than the previous fine-tuned checkpoint, so the transmission chain runs through the data ($D_0 \to D_1 \to \dots \to D_{10}$), not through parameters. This isolates data-induced degradation from parameter drift and mirrors the iterated learning paradigm where each learner begins from the same prior. Each generation samples 50,000 continuations at temperature $\tau = 0.8$ with nucleus sampling, applies one of three filters, and fine-tunes for 3 epochs. Five independent seeds per condition support inference via Hedges' $g$, bootstrap-$t$ CIs, Bayesian HDIs, and Bayes factors.

Two controls target alternative explanations directly. First, a regularized-seed control uses 50,000 passages generated from a PCFG engineered for maximally regular argument structure and morphology; if the non-monotonic P4 trajectory persists from already-regular seed data, noise removal cannot explain the initial rise. Second, a three-condition filtering experiment contrasts no filtering, random 70% retention (a generic volume-reduction bottleneck), and quality top-70% retention scored by an independent evaluator (LLaMA-2-13B) on extractive QA, NLI coherence, and summarization fidelity—tasks chosen because each tests whether content successfully communicates to a downstream reader, operationalizing communicative pressure.

Four linguistically grounded metrics are tracked: Zipf exponent via maximum-likelihood power-law fitting; morphological regularity over controlled verb sets using UniMorph paradigms; construction diversity over 50 dependency-parse-defined construction types (parser precision ≥ 0.82 even in the rarest quartile); and compositional systematicity adapted from topographic similarity, cross-validated against COGS generalization accuracy. Because topographic similarity can inflate when both meaning and form spaces collapse simultaneously, the authors validate with effective rank, positional disentanglement, and Mantel permutation tests—a collapse-robustness precaution often absent in related work.

Results

The critical test: non-monotonic compositionality

Under unfiltered self-training with natural seed data, compositional systematicity rises from 0.41 to a peak of 0.47 at generation 3 before declining to 0.31 by generation 10 (Hedges' $g = 1.87$, BF$_{10} = 247$). COGS generalization accuracy tracks the same pattern ($0.34 \to 0.39 \to 0.21$). Two findings make this result decisive rather than merely confirmatory:

1. Regularized-seed persistence: with maximally regular PCFG seed data, systematicity still shows a non-monotonic trajectory (plateau, rise to 0.54 at generation 3, decline to 0.33), ruling out noise removal as the driver of the initial rise. Both conditions converge toward similar generation-10 values, consistent with seed-independent convergence to the prior.
2. Filter specificity: random filtering produces a generation-10 trajectory indistinguishable from no filtering ($\sigma = 0.33$ vs. $0.31$; $p = 0.72$), while quality filtering sustains compositionality at $\tau = 0.8$0 ($\tau = 0.8$1 vs. both). Since random filtering removes the same proportion of data, the effect cannot be attributed to volume reduction.

Collapse-robustness diagnostics confirm the rise reflects genuine systematicity: meaning-space effective rank remains stable during generations 0–3 (12.4 → 12.1) while $\tau = 0.8$2 increases, Mantel z-scores exceed the permutation null throughout, and posdis shows the same non-monotonic shape. This constitutes the first LLM-scale demonstration of the compression–communication tradeoff, and it carries a direct practical implication: task-grounded verification, not mere data curation, is what sustains linguistic structure in self-training loops.

Frequency-dependent loss and human regularization gradients

Construction diversity entropy declines steeply by frequency quartile: the rarest quartile retains only 32% of its original entropy by generation 10 versus 88% for the most frequent (Hedges' $\tau = 0.8$3, BF$\tau = 0.8$4). Beyond confirming that rare items are lost—which any sampling process would produce—the discriminative content of P1 lies in the functional form: the LLM regularization gradient closely matches the log-linear human curve of Morgan and Levy ($\tau = 0.8$5, slopes $\tau = 0.8$6 vs. $\tau = 0.8$7). This match supports the hypothesis that frequency-dependent regularization arises from a frequency-independent simplicity bias interacting with a transmission bottleneck, not from human-specific cognitive architecture—an implication the authors state plainly, while noting that whether LLMs share functional (as opposed to formal) biases with humans remains open.

Dimension-specific degradation ordering

Constructions requiring pragmatic or discourse-level competence (left-dislocation, clefts, rhetorical questions) are lost first; core syntactic constructions (simple transitive, copular) survive longest; morphological constructions fall in between. Mean survival generations are 4.2 (pragmatic), 6.1 (morphological), and 8.7 (syntactic), with discourse-level constructions most vulnerable at 3.1. The correlation between CxG entrenchment ranking (log-type-frequency) and survival generation is $\tau = 0.8$8 ($\tau = 0.8$9; Hedges' $g$0). This ordering admits two convergent interpretations—Construction Grammar entrenchment and the formal–functional dissociation in LLMs—and their convergence on the same observed ordering is itself evidence that entrenchment operates partly as a formal-competence phenomenon. Generic collapse accounts predicting uniform degradation cannot explain this structure.

Confirmatory results: regularization and narrowing

Morphological regularity increases monotonically across all three languages (English $g$1: 0.62 → 0.87; German: 0.48 → 0.70; Turkish: 0.71 → 0.91; Hedges' $g$2), with irregular verb forms declining 42.7% in English by generation 10. Regularization respects usage-based predictions: low-frequency irregulars (wrung → *wringed) regularize by generation 3, while high-frequency forms (went) resist until generation 10, appearing in syntactically appropriate contexts 94% of the time—productive regularization rather than hallucination. The Zipf exponent decreases monotonically ($g$3: 1.07 → 0.82 for LLaMA-2; 1.07 → 0.86 for Mistral), with power-law fits preferred over lognormal and exponential alternatives at all generations ($g$4AIC > 4).

Sensitivity analyses

Temperature manipulations confirm the predicted parametric role of bottleneck severity: lowering $g$5 from 1.0 to 0.5 shifts the P4 peak from generation 4 to generation 2, and a 10× narrower corpus bottleneck shifts it to generations 1–2. Notably, at $g$6 with quality filtering, compositionality is partially overwhelmed ($g$7 vs. 0.48 at $g$8), consistent with Kirby et al.'s prediction that extreme compression pressure can override communicative pressure. Mistral-7B replicates all five predictions with similar effect sizes and identical peak timing, indicating architecture-independence. Convergence analysis characterizes the generation-10 attractor narrowly across seeds ($g$9, $t$0), fitting an exponential decay with rate $t$1 unfiltered and $t$2 under quality filtering—communicative pressure slows convergence to the prior, exactly as theory predicts.

Positioning within the literature

The paper occupies a specific niche between two literatures. Statistical accounts of collapse (tail-loss irreversibility, self-consuming loop formalism, scaling-law analyses, strong collapse from small synthetic fractions) describe the mechanics but not the linguistic phenomenology; the closest precedent measured diversity decline without an evolutionary framework or discriminative test. On the other side, Ren et al. proved monotonic bias amplification for in-context iterated learning but cannot predict the non-monotonic trajectory observed here; reconciling the two requires weight-based fine-tuning, where compression-induced reorganization can transiently increase systematicity before convergence to the prior. The framework also unifies otherwise disparate findings: degenerate vocabularies in LLM referential games instantiate compression without communicative pressure; the success of Constitutional AI and self-play relative to pure self-training reflects quality-grounded selection; and data accumulation's protective effect parallels diverse speaker populations in human cultural evolution.

Limitations and open questions

The authors concede six limitations, several of which bear directly on the strength of the claims. The framework is an empirically motivated structural correspondence, not a formal equivalence; the conditions under which SGD fine-tuning approximates Bayesian posterior sampling remain unresolved. Construction diversity and compositionality are tested only in English, pending validated cross-linguistic inventories such as UCxn. The quality filter is a unilateral evaluator rather than an interactive dialogue partner, so it models communicative pressure only approximately; evaluator-independence checks with Flan-T5-XL mitigate family confounds but do not substitute for human evaluators or interactive settings. Experiments use 7B-parameter models with a 50,000-passage bottleneck roughly 1,000× wider than typical human experiments, so quantitative extrapolation to larger models and narrower bottlenecks requires validation. Human comparisons rely on published curves rather than parallel human–LLM experiments. Finally, the quality filter aggregates QA, NLI, and summarization into a single signal; whether different task mixes preserve different linguistic structures is left untested. A further open question raised by the human-gradient match is whether the generation-10 attractor more closely resembles child or adult learner biases.

Conclusion

This paper reframes model collapse as a cultural transmission process and substantiates the reframing with the elements a strong empirical claim requires: predictions sorted by discriminative status, controls targeting the leading alternatives, collapse-robust metric validation, cross-model and cross-linguistic replication, and large effect sizes throughout (all Hedges' $t$3; BF$t$4). The uniquely discriminative finding—that compositionality rises before falling, persists from maximally regular seed data, and is sustained only by task-grounded filtering—provides LLM-scale evidence for the compression–communication tradeoff and yields concrete pipeline-design principles: use task-grounded rather than random filtering, prefer different-family evaluators, and treat bottleneck width as a tunable parameter governing convergence rate. The residual gaps—formal grounding of the SGD–Bayes correspondence, interactive communicative pressure, and scaling behavior—are clearly stated and define the immediate agenda for subsequent work on synthetic-data training dynamics.