# A Penalty Goes a Long Way: Measuring Lexical Diversity in Synthetic Texts Under Prompt-Influenced Length Variations

arXiv: https://arxiv.org/abs/2507.15092 · HTML: https://mlsanity.com/paper/2507.15092/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 20 Jul 2025.

## Builds on (most cited first, 17 of 17)

- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Scaling Synthetic Data Creation with 1,000,000,000 Personas](https://mlsanity.com/paper/2406.20094/) (2024)
- [Understanding the Effects of RLHF on LLM Generalisation and Diversity](https://mlsanity.com/paper/2310.06452/) (2023)
- [Magpie: Alignment Data Synthesis from Scratch by Prompting Aligned LLMs with Nothing](https://mlsanity.com/paper/2406.08464/) (2024)
- [On LLMs-Driven Synthetic Data Generation, Curation, and Evaluation: A Survey](https://mlsanity.com/paper/2406.15126/) (2024)
- [Does Writing with Language Models Reduce Content Diversity?](https://mlsanity.com/paper/2309.05196/) (2023)
- [Generative artificial intelligence enhances creativity but reduces the diversity of novel content](https://mlsanity.com/paper/2312.00506/) (2023)
- [The Curious Decline of Linguistic Diversity: Training Language Models on Synthetic Text](https://mlsanity.com/paper/2311.09807/) (2023)
- [A Confederacy of Models: a Comprehensive Evaluation of LLMs on Creative Writing](https://mlsanity.com/paper/2310.08433/) (2023)
- [How Bad is Training on Synthetic Data? A Statistical Analysis of Language Model Collapse](https://mlsanity.com/paper/2404.05090/) (2024)
- [Data Diversity Matters for Robust Instruction Tuning](https://mlsanity.com/paper/2311.14736/) (2023)
- [Standardizing the Measurement of Text Diversity: A Tool and a Comparative Analysis of Scores](https://mlsanity.com/paper/2403.00553/) (2024)
- [Can AI writing be salvaged? Mitigating Idiosyncrasies and Improving Human-AI Alignment in the Writing Process through Edits](https://mlsanity.com/paper/2409.14509/) (2024)
- [Detection and Measurement of Syntactic Templates in Generated Text](https://mlsanity.com/paper/2407.00211/) (2024)
- [Creativity Support in the Age of Large Language Models: An Empirical Study Involving Emerging Writers](https://mlsanity.com/paper/2309.12570/) (2023)
- [Diversify and Conquer: Diversity-Centric Data Selection with Iterative Refinement](https://mlsanity.com/paper/2409.11378/) (2024)

## Abstract (arXiv)

Synthetic text generated by Large Language Models (LLMs) is increasingly used for further training and improvement of LLMs. Diversity is crucial for the effectiveness of synthetic data, and researchers rely on prompt engineering to improve diversity. However, the impact of prompt variations on response text length, and, more importantly, the consequential effect on lexical diversity measurements, remain underexplored. In this work, we propose Penalty-Adjusted Type-Token Ratio (PATTR), a diversity metric robust to length variations. We generate a large synthetic corpus of over 20M words using seven models from the LLaMA, OLMo, and Phi families, focusing on a creative writing task of video script generation, where diversity is crucial. We evaluate per-response lexical diversity using PATTR and compare it against existing metrics of Moving-Average TTR (MATTR) and Compression Ratio (CR). Our analysis highlights how text length variations introduce biases favoring shorter responses. Unlike existing metrics, PATTR explicitly considers the task-specific target response length (LT) to effectively mitigate length biases. We further demonstrate the utility of PATTR in filtering the top-10/100/1,000 most lexically diverse responses, showing that it consistently outperforms MATTR and CR by yielding on par or better diversity with high adherence to LT.