In this paper, we study the connection between an LLM's output distribution and the data used to train it. Specifically, we study the degree to which an LLM's next-token distribution agrees with the empirical next-token distribution (ENTD) given the context in the training data. The ENTD is an appealing target because it is the unrestricted global minimizer of the next-token cross entropy loss used for pretraining, as well as an easily interpretable function of the pretraining corpus. We find that for a significant fraction of inputs, the LLM's distribution agrees with the ENTD almost perfectly, and the average agreement increases with model scale and training compute. Nevertheless, there is a long tail of input sequences where the LLM and ENTD differ significantly, and we examine several possible sources of this discrepancy across the transformer architecture, training procedure, and finite-sample noise in the ENTD estimate itself. More broadly, we hope our findings will encourage more work on ``data-centric mechanistic interpretability,'' a complement to standard mechanistic interpretability that opens the black box of how model behaviors arise from the data, rather than how they are encoded in the learned weights.

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