Who Pays for the Knowledge Models Copy? Model Collapse as Rogers' Paradox

Nam H. Le

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…