Turing Complete Transformers: Two Transformers Are More Powerful Than One

24 Sept 2023 (modified: 11 Feb 2024)Submitted to ICLR 2024EveryoneRevisionsBibTeX
Primary Area: general machine learning (i.e., none of the above)
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Keywords: transformers, computational complexity, computation, generalization, agents, multi-model
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TL;DR: We prove transformers are not Turing complete, propose a new architecture that is Turing complete, and empirically demonstrate that the new architecture can generalize more effectively than transformers.
Abstract: This paper presents Find+Replace transformers, a family of multi-transformer architectures that can provably do things no single transformer can, and which outperforms GPT-4 on several challenging tasks. We first establish that traditional transformers and similar architectures are not Turing Complete, while Find+Replace transformers are. Using this fact, we show how arbitrary programs can be compiled into Find+Replace transformers, potentially aiding interpretability research. We also demonstrate the superior performance of Find+Replace transformers over GPT-4 on a set of composition challenge problems. This work aims to provide a theoretical basis for multi-transformer architectures, and to encourage their further exploration.
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Submission Number: 8781