Towards Understanding Inductive Bias in Transformers: A View From Infinity
This work provides theoretical insights into Transformer behavior for researchers in machine learning, though it is incremental as it builds on existing over-parameterization studies.
The authors tackled the problem of understanding inductive bias in Transformers by analyzing them in the infinitely over-parameterized Gaussian process limit, showing they tend to favor permutation symmetric functions and deriving scaling laws for learnability based on context length.
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.