kramaker

arXiv.org

On the Limits of Self-Improving in Large Language Models: The Singularity Is Not Near Without Symbolic Model Synthesis

We formalise recursive self-training in Large Language Models (LLMs) and Generative AI as a discrete-time dynamical system. We prove that if the proportion of exogenous, externally grounded signal $α_t$ vanishes asymptotically ($α_t \to 0$), the system undergoes degenerative dynamics. We derive two fundamental failure modes: (1) \textit{Entropy Decay}, where finite sampling effects induce monotonic loss of distributional diversity, and (2) \textit{Variance Amplification}, where the absence of pe

1630301168645268

framasoft.org

Framasoft

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