## 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.

Original language | English |
---|---|

Pages (from-to) | 26043-26069 |

Number of pages | 27 |

Journal | Proceedings of Machine Learning Research |

Volume | 235 |

State | Published - 2024 |

Event | 41st International Conference on Machine Learning, ICML 2024 - Vienna, Austria Duration: 21 Jul 2024 → 27 Jul 2024 |

### Bibliographical note

Publisher Copyright:Copyright 2024 by the author(s)