Towards Understanding Inductive Bias in Transformers: A View From Infinity
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914814552440832 |
|---|---|
| author | Lavie, Itay Gur-Ari, Guy Ringel, Zohar |
| author_facet | Lavie, Itay Gur-Ari, Guy Ringel, Zohar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05173 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards Understanding Inductive Bias in Transformers: A View From Infinity Lavie, Itay Gur-Ari, Guy Ringel, Zohar Machine Learning Disordered Systems and Neural Networks 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. |
| title | Towards Understanding Inductive Bias in Transformers: A View From Infinity |
| topic | Machine Learning Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2402.05173 |