Entropic Limits of Iterative Computation in Generative AI: Model Collapse Explained by the Data Processing Inequality and the AI Theorem

Generative AI systems trained on synthetic data exhibit progressive degradation known as model collapse. This paper provides a theoretical explanation of this phenomenon using Shannon’s Data Processing Inequality (DPI), modeling iterative synthetic-data training as a Markov chain of lossy transformations. We show that mutual information with respect to the original data distribution must decrease monotonically, yielding quantitative predictions for exponential decay rates and identifying architectural constraints as the dominant source of information loss.Building on this analysis, we introduce the AI conceptual theorem, a generalized stability limit for computable systems. The theorem states that any purely computational system that generates outputs iteratively under finite precision, bounded capacity, and without external low-entropy input must experience cumulative information degradation after a finite number of steps. DPI-based collapse emerges as a special case of this broader principle. We emphasize that the AI Theorem is introduced as a conceptual stability principle rather than a formal mathematical theorem.Together, DPI and the AI Theorem provide a unified information-theoretic framework for understanding degradation in synthetic training, long-horizon inference, and other iterative computational processes. The resulting predictions are quantitatively falsifiable and offer guidance for designing more stable and information-preserving AI systems.