---
title: "Adam's Law: Textual Frequency Law on Large Language Models"
description: "The authors propose the Textual Frequency Law (TFL): among paraphrases with identical meaning… 45 references, cited by 2 papers here."
authors: ["Hongyuan Lu", "Zixuan Li", "Zefan Zhang", "Bowen Cao", "Wai Lam"]
year: 2026
venue: "Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)"
source: "https://aclanthology.org/2026.acl-long.188/"
doi: "10.18653/v1/2026.acl-long.188"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/lu-2026-adam-s-law-textual-frequency/"
---
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# Adam's Law: Textual Frequency Law on Large Language Models

**Authors:** [Hongyuan Lu](https://md.research.elamur.ai/free/en/authors/hongyuan-adam-lu/), [Zixuan Li](https://md.research.elamur.ai/free/en/authors/zixuan-li/), Zefan Zhang, Bowen Cao and [Wai Lam](https://md.research.elamur.ai/free/en/authors/wai-lam/) · **Year:** 2026 · **Venue:** [Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)](https://md.research.elamur.ai/free/en/venues/acl/) ([ACL 2026](https://md.research.elamur.ai/free/en/venues/acl/2026/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2026.acl-long.188/) · [PDF](https://aclanthology.org/2026.acl-long.188.pdf) · [DOI 10.18653/v1/2026.acl-long.188](https://doi.org/10.18653/v1/2026.acl-long.188) · [OpenAlex](https://openalex.org/W7166887580)

**Citations:** 0 citations (OpenAlex, 2026-10-14) · [2](https://md.research.elamur.ai/free/en/papers/lu-2026-adam-s-law-textual-frequency/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary

The paper asks whether an LLM performs better when it receives a more common wording of the same content. The authors propose the Textual Frequency Law (TFL): among paraphrases with identical meaning, choose the one with the highest sentence-level frequency, both when prompting and when fine-tuning. Training corpora of most LLMs are not public, so frequency is estimated from openly available text as a normalised product of word-level frequencies. Textual Frequency Distillation (TFD), an optional and more expensive step, refines this estimate by having the target LLM extend dataset sentences into stories and recounting frequencies on that output. Curriculum Textual Frequency Training (CTFT) then orders fine-tuning data from low to high frequency. The authors build the Textual Frequency Paired Dataset (TFPD) with human-checked high/low-frequency paraphrase pairs. Its tasks include math reasoning, translation between numerous language combinations, commonsense questions, and tool use by agents. High-frequency inputs, TFD and CTFT each yield gains, which shows that cheap rephrasing and data ordering can help, including for low-resource translation.

## Key points

- **TFPD paired instances per task:** math reasoning 738, MT 526, commonsense reasoning 575, tool calling 114. Average lengths of the high- and low-frequency sides are similar.
- **Effect of CTFT on MT fine-tuning:** fine-tuning on the high-frequency partition with CTFT raised BLEU on pag_Latn from 3.7781 to 4.9102 (+29.96%). It gave the best score on 8 of 8 metrics.
- **Effect of TFPD fine-tuning:** on kea_Latn, BLEU rose from 4.6772 to 5.2466 (+12.17%).
- **TFD ablation:** removing TFD hurts results. With DeepSeek-V3, every language pair scored higher on COMET when TFD was used, and more distillation data gave larger gains.
- **Frequency vs. complexity:** frequency correlates only weakly with complexity measures (dependency tree depth, dependency distance, Flesch-Kincaid), so TFL differs from classic difficulty-based curricula. When syntactic depth is matched, high-frequency prompts still win in nearly all bins, by +4.78 BLEU overall.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Chinese University of Hong Kong](https://md.research.elamur.ai/free/en/universities/chinese-university-of-hong-kong/) — University, Hong Kong, China · 126 works · 14,073 citations

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## Cite

Cite as: Hongyuan Lu, Zixuan Li, Zefan Zhang, Bowen Cao and Wai Lam. 2026. Adam's Law: Textual Frequency Law on Large Language Models. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{lu2026adam,
  title = {{Adam's Law: Textual Frequency Law on Large Language Models}},
  author = {Hongyuan Lu, Zixuan Li, Zefan Zhang, Bowen Cao and Wai Lam},
  booktitle = {Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2026},
  doi = {10.18653/v1/2026.acl-long.188},
  url = {https://doi.org/10.18653/v1/2026.acl-long.188}
}
```

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*Updated 31 October 2026*