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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.02393 |
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| _version_ | 1866913938669568000 |
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| author | Amiri, Alireza Huang, Xinting Rofin, Mark Hahn, Michael |
| author_facet | Amiri, Alireza Huang, Xinting Rofin, Mark Hahn, Michael |
| contents | Chain-of-thought reasoning and scratchpads have emerged as critical tools for enhancing the computational capabilities of transformers. While theoretical results show that polynomial-length scratchpads can extend transformers' expressivity from $TC^0$ to $PTIME$, their required length remains poorly understood. Empirical evidence even suggests that transformers need scratchpads even for many problems in $TC^0$, such as Parity or Multiplication, challenging optimistic bounds derived from circuit complexity. In this work, we initiate the study of systematic lower bounds for the number of chain-of-thought steps across different algorithmic problems, in the hard-attention regime. We study a variety of algorithmic problems, and provide bounds that are tight up to logarithmic factors. Overall, these results contribute to emerging understanding of the power and limitations of chain-of-thought reasoning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02393 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lower Bounds for Chain-of-Thought Reasoning in Hard-Attention Transformers Amiri, Alireza Huang, Xinting Rofin, Mark Hahn, Michael Machine Learning Computational Complexity Chain-of-thought reasoning and scratchpads have emerged as critical tools for enhancing the computational capabilities of transformers. While theoretical results show that polynomial-length scratchpads can extend transformers' expressivity from $TC^0$ to $PTIME$, their required length remains poorly understood. Empirical evidence even suggests that transformers need scratchpads even for many problems in $TC^0$, such as Parity or Multiplication, challenging optimistic bounds derived from circuit complexity. In this work, we initiate the study of systematic lower bounds for the number of chain-of-thought steps across different algorithmic problems, in the hard-attention regime. We study a variety of algorithmic problems, and provide bounds that are tight up to logarithmic factors. Overall, these results contribute to emerging understanding of the power and limitations of chain-of-thought reasoning. |
| title | Lower Bounds for Chain-of-Thought Reasoning in Hard-Attention Transformers |
| topic | Machine Learning Computational Complexity |
| url | https://arxiv.org/abs/2502.02393 |