Existing proofs of autoregressive Transformer Turing-completeness apply to scaling families of models rather than fixed systems with context management, so they do not establish Turing-completeness for real-world LLMs.
On the turing completeness of modern neural network architectures
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Position: The Turing-Completeness of Autoregressive Transformers Relies Heavily on Context Management
Existing proofs of autoregressive Transformer Turing-completeness apply to scaling families of models rather than fixed systems with context management, so they do not establish Turing-completeness for real-world LLMs.