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.

翻译：我们在无穷过参数化的高斯过程极限下研究Transformer的归纳偏好，并论证Transformer在序列空间上倾向于更置换对称的函数。我们展示了对称群表示论可用于在数据集对标记间置换具有对称性时给出定量分析预测。我们提出了一个简化版Transformer模块并在极限下求解模型，包括对学习曲线和网络输出的准确预测。我们证明，在常见设置下，可以推导出上下文长度作为可学习性函数的缩放定律形式下的紧界。最后，我们论证WikiText数据集确实具有一定程度的置换对称性。