Sample Complexity and Representation Ability of Test-time Scaling Paradigms
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916791655071744 |
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| author | Huang, Baihe Li, Shanda Wu, Tianhao Yang, Yiming Talwalkar, Ameet Ramchandran, Kannan Jordan, Michael I. Jiao, Jiantao |
| author_facet | Huang, Baihe Li, Shanda Wu, Tianhao Yang, Yiming Talwalkar, Ameet Ramchandran, Kannan Jordan, Michael I. Jiao, Jiantao |
| contents | Test-time scaling paradigms have significantly advanced the capabilities of large language models (LLMs) on complex tasks. Despite their empirical success, theoretical understanding of the sample efficiency of various test-time strategies -- such as self-consistency, best-of-$n$, and self-correction -- remains limited. In this work, we first establish a separation result between two repeated sampling strategies: self-consistency requires $Θ(1/Δ^2)$ samples to produce the correct answer, while best-of-$n$ only needs $Θ(1/Δ)$, where $Δ< 1$ denotes the probability gap between the correct and second most likely answers. Next, we present an expressiveness result for the self-correction approach with verifier feedback: it enables Transformers to simulate online learning over a pool of experts at test time. Therefore, a single Transformer architecture can provably solve multiple tasks without prior knowledge of the specific task associated with a user query, extending the representation theory of Transformers from single-task to multi-task settings. Finally, we empirically validate our theoretical results, demonstrating the practical effectiveness of self-correction methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05295 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sample Complexity and Representation Ability of Test-time Scaling Paradigms Huang, Baihe Li, Shanda Wu, Tianhao Yang, Yiming Talwalkar, Ameet Ramchandran, Kannan Jordan, Michael I. Jiao, Jiantao Machine Learning Artificial Intelligence Test-time scaling paradigms have significantly advanced the capabilities of large language models (LLMs) on complex tasks. Despite their empirical success, theoretical understanding of the sample efficiency of various test-time strategies -- such as self-consistency, best-of-$n$, and self-correction -- remains limited. In this work, we first establish a separation result between two repeated sampling strategies: self-consistency requires $Θ(1/Δ^2)$ samples to produce the correct answer, while best-of-$n$ only needs $Θ(1/Δ)$, where $Δ< 1$ denotes the probability gap between the correct and second most likely answers. Next, we present an expressiveness result for the self-correction approach with verifier feedback: it enables Transformers to simulate online learning over a pool of experts at test time. Therefore, a single Transformer architecture can provably solve multiple tasks without prior knowledge of the specific task associated with a user query, extending the representation theory of Transformers from single-task to multi-task settings. Finally, we empirically validate our theoretical results, demonstrating the practical effectiveness of self-correction methods. |
| title | Sample Complexity and Representation Ability of Test-time Scaling Paradigms |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2506.05295 |