Towards Understanding Inductive Bias in Transformers: A View From Infinity

Itay Lavie, Guy Gur-Ari, Zohar Ringel
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:26043-26069, 2024.

Abstract

We study inductive bias in Transformers in the infinitely over-parameterized Gaussian process limit and argue transformers tend to be biased towards more permutation symmetric functions in sequence space. We show that the representation theory of the symmetric group can be used to give quantitative analytical predictions when the dataset is symmetric to permutations between tokens. We present a simplified transformer block and solve the model at the limit, including accurate predictions for the learning curves and network outputs. We show that in common setups, one can derive tight bounds in the form of a scaling law for the learnability as a function of the context length. Finally, we argue WikiText dataset, does indeed possess a degree of permutation symmetry.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-lavie24a, title = {Towards Understanding Inductive Bias in Transformers: A View From Infinity}, author = {Lavie, Itay and Gur-Ari, Guy and Ringel, Zohar}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {26043--26069}, 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/lavie24a/lavie24a.pdf}, url = {https://proceedings.mlr.press/v235/lavie24a.html}, abstract = {We study inductive bias in Transformers in the infinitely over-parameterized Gaussian process limit and argue transformers tend to be biased towards more permutation symmetric functions in sequence space. We show that the representation theory of the symmetric group can be used to give quantitative analytical predictions when the dataset is symmetric to permutations between tokens. We present a simplified transformer block and solve the model at the limit, including accurate predictions for the learning curves and network outputs. We show that in common setups, one can derive tight bounds in the form of a scaling law for the learnability as a function of the context length. Finally, we argue WikiText dataset, does indeed possess a degree of permutation symmetry.} }
Endnote
%0 Conference Paper %T Towards Understanding Inductive Bias in Transformers: A View From Infinity %A Itay Lavie %A Guy Gur-Ari %A Zohar Ringel %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-lavie24a %I PMLR %P 26043--26069 %U https://proceedings.mlr.press/v235/lavie24a.html %V 235 %X We study inductive bias in Transformers in the infinitely over-parameterized Gaussian process limit and argue transformers tend to be biased towards more permutation symmetric functions in sequence space. We show that the representation theory of the symmetric group can be used to give quantitative analytical predictions when the dataset is symmetric to permutations between tokens. We present a simplified transformer block and solve the model at the limit, including accurate predictions for the learning curves and network outputs. We show that in common setups, one can derive tight bounds in the form of a scaling law for the learnability as a function of the context length. Finally, we argue WikiText dataset, does indeed possess a degree of permutation symmetry.
APA
Lavie, I., Gur-Ari, G. & Ringel, Z.. (2024). Towards Understanding Inductive Bias in Transformers: A View From Infinity. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:26043-26069 Available from https://proceedings.mlr.press/v235/lavie24a.html.

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