Autoregressive Large Language Models are Computationally Universal
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929527110762496 |
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| author | Schuurmans, Dale Dai, Hanjun Zanini, Francesco |
| author_facet | Schuurmans, Dale Dai, Hanjun Zanini, Francesco |
| contents | We show that autoregressive decoding of a transformer-based language model can realize universal computation, without external intervention or modification of the model's weights. Establishing this result requires understanding how a language model can process arbitrarily long inputs using a bounded context. For this purpose, we consider a generalization of autoregressive decoding where, given a long input, emitted tokens are appended to the end of the sequence as the context window advances. We first show that the resulting system corresponds to a classical model of computation, a Lag system, that has long been known to be computationally universal. By leveraging a new proof, we show that a universal Turing machine can be simulated by a Lag system with 2027 production rules. We then investigate whether an existing large language model can simulate the behaviour of such a universal Lag system. We give an affirmative answer by showing that a single system-prompt can be developed for gemini-1.5-pro-001 that drives the model, under deterministic (greedy) decoding, to correctly apply each of the 2027 production rules. We conclude that, by the Church-Turing thesis, prompted gemini-1.5-pro-001 with extended autoregressive (greedy) decoding is a general purpose computer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03170 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Autoregressive Large Language Models are Computationally Universal Schuurmans, Dale Dai, Hanjun Zanini, Francesco Computation and Language We show that autoregressive decoding of a transformer-based language model can realize universal computation, without external intervention or modification of the model's weights. Establishing this result requires understanding how a language model can process arbitrarily long inputs using a bounded context. For this purpose, we consider a generalization of autoregressive decoding where, given a long input, emitted tokens are appended to the end of the sequence as the context window advances. We first show that the resulting system corresponds to a classical model of computation, a Lag system, that has long been known to be computationally universal. By leveraging a new proof, we show that a universal Turing machine can be simulated by a Lag system with 2027 production rules. We then investigate whether an existing large language model can simulate the behaviour of such a universal Lag system. We give an affirmative answer by showing that a single system-prompt can be developed for gemini-1.5-pro-001 that drives the model, under deterministic (greedy) decoding, to correctly apply each of the 2027 production rules. We conclude that, by the Church-Turing thesis, prompted gemini-1.5-pro-001 with extended autoregressive (greedy) decoding is a general purpose computer. |
| title | Autoregressive Large Language Models are Computationally Universal |
| topic | Computation and Language |
| url | https://arxiv.org/abs/2410.03170 |