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; BF10>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.
As scaling laws push the training of frontier large language models (LLMs) toward ever-growing data requirements, training pipelines are approaching a regime where much of the publicly available online text may be consumed. At the same time, widespread LLM usage increases the volume of machine-generated content on the web; together, these trends raise the likelihood of generated text re-entering future training corpora, increasing the associated risk of performance degradation often called model collapse. In practice, model developers address this concern through data cleaning, watermarking, synthetic-data policies, or, in some cases, blissful ignorance. However, the problem of model collapse in generative models has not been examined from a learning-theoretic perspective: we study it through the theoretical lens of the language generation in the limit framework, introducing a replay adversary that augments the example stream with the generator's own past outputs. Our main contribution is a fine-grained learning-theoretic characterization of when replay fundamentally limits generation: while replay is benign for the strongest notion of uniform generation, it provably creates separations for the weaker notions of non-uniform generation and generation in the limit. Interestingly, our positive results mirror heuristics widely used in practice, such as data cleaning, watermarking, and output filtering, while our separations show when these ideas can fail.
Successive self-training on a language model's own outputs is widely characterized as a process of flattening: diversity drops, distributions narrow, and the text becomes "more like itself." We provide evidence that this characterization is incomplete. Across eleven generations of self-training on five models (GPT-2 124M, Pythia-410M, Pythia-1.4B, OPT-1.3B, Pythia-2.8B), language is not flattened uniformly -- it is restructured. Surface markers (discourse connectives, hedges, em-dashes) rise, while mid- and deep-syntactic structures (questions, parentheticals, passives, subjunctives) collapse. We formalize this asymmetric collapse as the Structural Depth Hypothesis (SDH): the per-generation decay rate of a linguistic feature is predicted primarily by its structural depth -- the number of nested syntactic dependencies it requires -- and only secondarily by its generation-zero output frequency. Pooling 17-feature panels from five models spanning three architecture families (N=85), the pooled Spearman correlation is rho=0.540 (p < 10^{-6}; cluster-bootstrap 95% CI [0.434, 0.634]), while frequency is a substantially weaker predictor (rho=0.225). A matched human-text fine-tuning control yields rho=0.039 (p=0.88), confirming the gradient is self-training-specific. We further document a Superficial Complexity Paradox: aggregate complexity proxies (dep-tree depth, TTR, word length) all rise as the underlying clause structure dies, with direct implications for training-data curation and LLM-text detection.
Model-generated text is finding its way back into training corpora, and there is plenty of evidence that training on such data over and over collapses output diversity. Prior work has studied the phenomenon itself: which protocols and which data mixtures cause collapse. But different models behave very differently under the same process. We fix one recursive contamination protocol and let 13 publicly released checkpoints form an ecosystem that shares a common corpus for five generations. The unique 4-gram outcome after five generations ranges from 0.187 to 0.940 across checkpoints, a roughly five-fold spread: some models are barely touched, others degenerate into repetitive fragments. Changing the composition of the shared pool or mixing in human text keeps the Spearman correlation of the ordering at 0.91--0.97, and changing the random seed keeps it at 0.93--0.98. Whether a model collapses easily under recursive training is, then, a property of the checkpoint itself, and one that has gone largely unexamined. Parameter scale alone does not explain it, since a three-size ladder within one family is not monotonic in size, and none of the static indicators we tested predicts it either. What does work is cheap: let a model iterate on its own output for two or three generations, and its fragility in the larger ecosystem can be inferred from that alone. Collapse speed also responds to intervention. Tightening top-p, which cuts the low-probability tail at generation time, nearly stops collapse within three generations and stabilizes six checkpoints spanning the whole spectrum together, while data-side filtering slows collapse without stopping it.