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This research reframes model collapse through Rogers' cultural evolution theory, demonstrating that generative models degrade when trained on synthetic data without external knowledge injection. The study proves that relying solely on model outputs leads to stagnation, whereas systems requiring users to verify and relearn information maintain reliability against rapid world changes. Ultimately, the paper identifies a fundamental economic trade-off where increased reliance on AI-generated text must be balanced by proportional increases in human learning efforts to prevent knowledge decay.
Who Pays for the Knowledge Models Copy? Model Collapse as Rogers' Paradox
arXiv:2611.06022v1 Announce Type: cross Abstract: Generative models trained on the output of earlier models lose knowledge across generations, rare knowledge first. The remedies that work all bring in information from outside the loop, and the theory of model collapse treats that supply as given: a fixed archive, drawn from a fixed distribution. We argue that the supply is the problem, and that cultural evolution has the theory of it. We read model collapse as Rogers' paradox: a population that comes to rely on copying ends up no better off than one that never copied, because copies go stale unless someone keeps learning for themselves. We test the identification in three steps. First, Rogers' model, fitted only to fully synthetic training, predicts to within a few percentage points how much rare knowledge language models, from word trigrams to a pretrained transformer, retain under other mixtures of fresh data. Second, when the world itself changes, a lineage that copies its own past needs more fresh data to keep up the faster the world changes, as Rogers' model says it must and as analyses that assume a fixed target cannot; a lineage that restarts every generation from fixed pretrained weights is largely insulated, because those weights are knowledge that is never copied. Third, we close the loop: when the people who write a model's training data can ask the model instead of finding things out, the supply of fresh data becomes endogenous. At equilibrium, the model is exactly as reliable as it is costly for people to find out for themselves, the population is no better off than without the model, and every increase in the share of model-written text must be paid for by more people learning for themselves. Users who check what they are told and relearn when it is wrong break the paradox. Filters that select plausible text are conformist and accelerate collapse; only checks that carry new information act as critical learning.
Title:Who Pays for the Knowledge Models Copy? Model Collapse as Rogers' Paradox
Abstract:Generative models trained on the output of earlier models lose knowledge across generations, rare knowledge first. The remedies that work all bring in information from outside the loop, and the theory of model collapse treats that supply as given: a fixed archive, drawn from a fixed distribution. We argue that the supply is the problem, and that cultural evolution has the theory of it. We read model collapse as Rogers' paradox: a population that comes to rely on copying ends up no better off than one that never copied, because copies go stale unless someone keeps learning for themselves. We test the identification in three steps. First, Rogers' model, fitted only to fully synthetic training, predicts to within a few percentage points how much rare knowledge language models, from word trigrams to a pretrained transformer, retain under other mixtures of fresh data. Second, when the world itself changes, a lineage that copies its own past needs more fresh data to keep up the faster the world changes, as Rogers' model says it must and as analyses that assume a fixed target cannot; a lineage that restarts every generation from fixed pretrained weights is largely insulated, because those weights are knowledge that is never copied. Third, we close the loop: when the people who write a model's training data can ask the model instead of finding things out, the supply of fresh data becomes endogenous. At equilibrium, the model is exactly as reliable as it is costly for people to find out for themselves, the population is no better off than without the model, and every increase in the share of model-written text must be paid for by more people learning for themselves. Users who check what they are told and relearn when it is wrong break the paradox. Filters that select plausible text are conformist and accelerate collapse; only checks that carry new information act as critical learning.
13 pages, 5 figures. Code: this https URL
Machine Learning (cs.LG); Computation and Language (cs.CL); Populations and Evolution (q-bio.PE)
arXiv:2611.06022 [cs.LG]
(or arXiv:2611.06022v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2611.06022 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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