Silent Collapse in Recursive Learning Systems

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.

Recursive systems can enter collapse-like regimes -- self-reinforcing amplification, persistent recursion, and narrowing diversity that mask accelerating internal degradation -- before overt failure becomes visible. We introduce Loopzero, a claim-bounded benchmark framework for testing whether recursive failures follow a directional telemetry pattern: rising gain (G), recursive persistence (p), and declining diversity ($δ$). The claim boundary is specified in Lean; the Lean artifact does not verify real telemetry, benchmark validity, or detector performance. We evaluate the bridge on two frozen public-artifact benchmarks: a segmented public-markets benchmark (Volmageddon 2018, COVID MWCB 2020) and a MovieLens-25M offline deterministic recommender replay. Detectors are evaluated under a locked equal-false-positive contract (FP $\in$ [0.03, 0.07], pre-registered) so all configurations face the same alert budget. Neither tested standard comparators nor Loopzero's pre-registered quantile detector achieved an accepted operating point. Directional witness alignment held on both canonical benchmarks, with adjacent-horizon and row-level limitations disclosed. Digitized Shumailov et al. (2024) LLM training-loop trajectories are directionally consistent with the pattern; matched-FP evaluation in that domain is deferred. The contribution is a reproducible, falsifiable benchmark framework for evaluating recursive-collapse warning claims under an explicit alert-budget contract -- non-acceptance reported as a first-class scientific outcome.

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 ($R^2 = 0.94$). These results reframe model collapse as a cultural transmission phenomenon and yield concrete principles for self-training pipeline design.