An Information-Theoretic Analysis of In-Context Learning
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913213074898944 |
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| author | Jeon, Hong Jun Lee, Jason D. Lei, Qi Van Roy, Benjamin |
| author_facet | Jeon, Hong Jun Lee, Jason D. Lei, Qi Van Roy, Benjamin |
| contents | Previous theoretical results pertaining to meta-learning on sequences build on contrived assumptions and are somewhat convoluted. We introduce new information-theoretic tools that lead to an elegant and very general decomposition of error into three components: irreducible error, meta-learning error, and intra-task error. These tools unify analyses across many meta-learning challenges. To illustrate, we apply them to establish new results about in-context learning with transformers. Our theoretical results characterizes how error decays in both the number of training sequences and sequence lengths. Our results are very general; for example, they avoid contrived mixing time assumptions made by all prior results that establish decay of error with sequence length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15530 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Information-Theoretic Analysis of In-Context Learning Jeon, Hong Jun Lee, Jason D. Lei, Qi Van Roy, Benjamin Machine Learning Information Theory Previous theoretical results pertaining to meta-learning on sequences build on contrived assumptions and are somewhat convoluted. We introduce new information-theoretic tools that lead to an elegant and very general decomposition of error into three components: irreducible error, meta-learning error, and intra-task error. These tools unify analyses across many meta-learning challenges. To illustrate, we apply them to establish new results about in-context learning with transformers. Our theoretical results characterizes how error decays in both the number of training sequences and sequence lengths. Our results are very general; for example, they avoid contrived mixing time assumptions made by all prior results that establish decay of error with sequence length. |
| title | An Information-Theoretic Analysis of In-Context Learning |
| topic | Machine Learning Information Theory |
| url | https://arxiv.org/abs/2401.15530 |