# Tracing LLM Behavior to the Training Data with Empirical Next-Token Distributions

arXiv: https://arxiv.org/abs/2607.14306 · HTML: https://mlsanity.com/paper/2607.14306/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in SAE features and their applications, one of 13 directions in Mechanistic interpretability.
- Builds on 24 of its 31 references that are in the map.
- First posted on arXiv 15 Jul 2026.

## Placed in

- Mechanistic interpretability / [SAE features and their applications](https://mlsanity.com/mechinterp/sae-features-and-their-applications/)

## Builds on (most cited first, 24 of 24)

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- [Quantifying Memorization Across Neural Language Models](https://mlsanity.com/paper/2202.07646/) (2022)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
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- [Physics of Language Models: Part 3.1, Knowledge Storage and Extraction](https://mlsanity.com/paper/2309.14316/) (2023)
- [Data Mixing Laws: Optimizing Data Mixtures by Predicting Language Modeling Performance](https://mlsanity.com/paper/2403.16952/) (2024)
- [Stealing Part of a Production Language Model](https://mlsanity.com/paper/2403.06634/) (2024)
- [Infini-gram: Scaling Unbounded n-gram Language Models to a Trillion Tokens](https://mlsanity.com/paper/2401.17377/) (2024)
- [Breaking the Softmax Bottleneck: A High-Rank RNN Language Model](https://mlsanity.com/paper/1711.03953/) (2017)
- [Artificial Hivemind: The Open-Ended Homogeneity of Language Models (and Beyond)](https://mlsanity.com/paper/2510.22954/) (2025)
- [Language Contamination Helps Explain the Cross-lingual Capabilities of English Pretrained Models](https://mlsanity.com/paper/2204.08110/) (2022)
- [Generalization v.s. Memorization: Tracing Language Models' Capabilities Back to Pretraining Data](https://mlsanity.com/paper/2407.14985/) (2024)
- [Frequency Effects on Syntactic Rule Learning in Transformers](https://mlsanity.com/paper/2109.07020/) (2021)
- [Measuring Causal Effects of Data Statistics on Language Model's `Factual' Predictions](https://mlsanity.com/paper/2207.14251/) (2022)
- [PolyPythias: Stability and Outliers across Fifty Language Model Pre-Training Runs](https://mlsanity.com/paper/2503.09543/) (2025)
- [OLMoTrace: Tracing Language Model Outputs Back to Trillions of Training Tokens](https://mlsanity.com/paper/2504.07096/) (2025)
- [Understanding Transformers via N-gram Statistics](https://mlsanity.com/paper/2407.12034/) (2024)
- [Mechanistic Data Attribution: Tracing the Training Origins of Interpretable LLM Units](https://mlsanity.com/paper/2601.21996/) (2026)
- [Why Larger Models Learn More: Effects of Capacity, Interference, and Rare-Task Retention](https://mlsanity.com/paper/2605.29548/) (2026)
- [Quantitative Bounds for Length Generalization in Transformers](https://mlsanity.com/paper/2510.27015/) (2025)
- [How Do Transformers Learn to Associate Tokens: Gradient Leading Terms Bring Mechanistic Interpretability](https://mlsanity.com/paper/2601.19208/) (2026)

## Abstract (arXiv)

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 agreement generally 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.