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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.02040 |
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| _version_ | 1866912106554589184 |
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| author | Strobl, Lena Angluin, Dana Chiang, David Rawski, Jonathan Sabharwal, Ashish |
| author_facet | Strobl, Lena Angluin, Dana Chiang, David Rawski, Jonathan Sabharwal, Ashish |
| contents | We study the sequence-to-sequence mapping capacity of transformers by relating them to finite transducers, and find that they can express surprisingly large classes of transductions. We do so using variants of RASP, a programming language designed to help people "think like transformers," as an intermediate representation. We extend the existing Boolean variant B-RASP to sequence-to-sequence functions and show that it computes exactly the first-order rational functions (such as string rotation). Then, we introduce two new extensions. B-RASP[pos] enables calculations on positions (such as copying the first half of a string) and contains all first-order regular functions. S-RASP adds prefix sum, which enables additional arithmetic operations (such as squaring a string) and contains all first-order polyregular functions. Finally, we show that masked average-hard attention transformers can simulate S-RASP. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02040 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transformers as Transducers Strobl, Lena Angluin, Dana Chiang, David Rawski, Jonathan Sabharwal, Ashish Formal Languages and Automata Theory Machine Learning We study the sequence-to-sequence mapping capacity of transformers by relating them to finite transducers, and find that they can express surprisingly large classes of transductions. We do so using variants of RASP, a programming language designed to help people "think like transformers," as an intermediate representation. We extend the existing Boolean variant B-RASP to sequence-to-sequence functions and show that it computes exactly the first-order rational functions (such as string rotation). Then, we introduce two new extensions. B-RASP[pos] enables calculations on positions (such as copying the first half of a string) and contains all first-order regular functions. S-RASP adds prefix sum, which enables additional arithmetic operations (such as squaring a string) and contains all first-order polyregular functions. Finally, we show that masked average-hard attention transformers can simulate S-RASP. |
| title | Transformers as Transducers |
| topic | Formal Languages and Automata Theory Machine Learning |
| url | https://arxiv.org/abs/2404.02040 |