How Powerful are Decoder-Only Transformer Neural Models?
This work provides foundational theoretical validation for the computational capabilities of widely used AI models, addressing a gap in prior research focused on more expressive architectures.
The paper proves that decoder-only transformer models, which underlie modern large language models like GPT, are Turing complete under reasonable assumptions, establishing their theoretical computational power. It also identifies sparsity in word embeddings as a key factor for this completeness and links transformers to B machines studied by Hao Wang.
In this article we prove that the general transformer neural model undergirding modern large language models (LLMs) is Turing complete under reasonable assumptions. This is the first work to directly address the Turing completeness of the underlying technology employed in GPT-x as past work has focused on the more expressive, full auto-encoder transformer architecture. From this theoretical analysis, we show that the sparsity/compressibility of the word embedding is an important consideration for Turing completeness to hold. We also show that Transformers are are a variant of B machines studied by Hao Wang.