An Information-Theoretic Analysis of In-Context Learning

Hong Jun Jeon, Jason D. Lee, Qi Lei, Benjamin Van Roy
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:21522-21554, 2024.

Abstract

Previous theoretical results pertaining to meta-learning on sequences build on contrived and convoluted mixing time assumptions. We introduce new information-theoretic tools that lead to a concise yet general decomposition of error for a Bayes optimal predictor into two components: 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 and corroborate existing results a simple linear setting. Our theoretical results characterize 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-jeon24a, title = {An Information-Theoretic Analysis of In-Context Learning}, author = {Jeon, Hong Jun and Lee, Jason D. and Lei, Qi and Van Roy, Benjamin}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {21522--21554}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/jeon24a/jeon24a.pdf}, url = {https://proceedings.mlr.press/v235/jeon24a.html}, abstract = {Previous theoretical results pertaining to meta-learning on sequences build on contrived and convoluted mixing time assumptions. We introduce new information-theoretic tools that lead to a concise yet general decomposition of error for a Bayes optimal predictor into two components: 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 and corroborate existing results a simple linear setting. Our theoretical results characterize 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.} }
Endnote
%0 Conference Paper %T An Information-Theoretic Analysis of In-Context Learning %A Hong Jun Jeon %A Jason D. Lee %A Qi Lei %A Benjamin Van Roy %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-jeon24a %I PMLR %P 21522--21554 %U https://proceedings.mlr.press/v235/jeon24a.html %V 235 %X Previous theoretical results pertaining to meta-learning on sequences build on contrived and convoluted mixing time assumptions. We introduce new information-theoretic tools that lead to a concise yet general decomposition of error for a Bayes optimal predictor into two components: 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 and corroborate existing results a simple linear setting. Our theoretical results characterize 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.
APA
Jeon, H.J., Lee, J.D., Lei, Q. & Van Roy, B.. (2024). An Information-Theoretic Analysis of In-Context Learning. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:21522-21554 Available from https://proceedings.mlr.press/v235/jeon24a.html.

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