Given a sequence of tokens, such as words, the task of next-token prediction is to predict the next-token conditional probability distribution. Decoder-only transformers have become effective models for this task, but their properties are still not fully understood. In particular, the largest number of distinct context sequences that a decoder-only transformer can interpolate next-token distributions for has not been established. To fill this gap, we prove upper and lower bounds on this number, which are equal up to a multiplicative constant. We prove these bounds in the general setting where next-token distributions can be arbitrary as well as the empirical setting where they are calculated from a finite number of document sequences. Our lower bounds are for one-layer transformers and our proofs highlight an important injectivity property satisfied by self-attention. Furthermore, we provide numerical evidence that the minimal number of parameters for memorization is sufficient for being able to train the model to the entropy lower bound.

给定一个令牌序列，如单词，下一个令牌预测的任务是预测下一个令牌的条件概率分布。我们针对仅编码器的transformer模型的性质进行了研究，并证明了该模型可以插值下一个令牌分布的最大上下文序列的上下界，其中下界只需最小的参数数量即可实现。

Transformer模型在下一个Token预测中的上限和下限记忆容量