  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.
