# Do Large Language Models Capture the Diversity in their Training Data?

arXiv: https://arxiv.org/abs/2609.02275 · HTML: https://mlsanity.com/paper/2609.02275/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 54 of its 67 references that are in the map.
- First posted on arXiv 2 Sep 2026.

## Builds on (most cited first, 30 of 54)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://mlsanity.com/paper/2301.12597/) (2023)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [CIDEr: Consensus-based Image Description Evaluation](https://mlsanity.com/paper/1411.5726/) (2014)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [A Diversity-Promoting Objective Function for Neural Conversation Models](https://mlsanity.com/paper/1510.03055/) (2015)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [SPICE: Semantic Propositional Image Caption Evaluation](https://mlsanity.com/paper/1607.08822/) (2016)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [OLMo: Accelerating the Science of Language Models](https://mlsanity.com/paper/2402.00838/) (2024)
- [All are Worth Words: A ViT Backbone for Diffusion Models](https://mlsanity.com/paper/2209.12152/) (2022)
- [Texygen: A Benchmarking Platform for Text Generation Models](https://mlsanity.com/paper/1802.01886/) (2018)
- [Dolma: an Open Corpus of Three Trillion Tokens for Language Model Pretraining Research](https://mlsanity.com/paper/2402.00159/) (2024)
- [ColBERTv2: Effective and Efficient Retrieval via Lightweight Late Interaction](https://mlsanity.com/paper/2112.01488/) (2021)
- [MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers](https://mlsanity.com/paper/2102.01454/) (2021)
- [Regularizing Neural Networks by Penalizing Confident Output Distributions](https://mlsanity.com/paper/1701.06548/) (2017)

## Abstract (arXiv)

Large language models are trained to model conditional distributions over text, yet it remains inadequately understood whether they capture the full diversity of plausible outputs present in their training data. We study this question through an information-theoretic lens by comparing the conditional entropy of model-generated outputs with that of the corresponding training data. Given paired input-output samples, we use conditional entropy and its matrix-based analogue based on von Neumann entropy to measure output variability beyond what is explained by the conditioning input, without requiring multiple reference outputs for the same prompt. Across LLM families with publicly available training data, including OLMo, Pythia, and GPT-Neo, we consistently find that model-generated outputs exhibit lower conditional entropy than their training data, across different model scales, sequence lengths, and decoding strategies. We observe a similar conditional diversity gap beyond language modeling, including class-conditioned ImageNet generators and text-conditioned models trained on MS-COCO. To address this gap, we propose a post-hoc correction mechanism that generates multiple outputs for each input and reweights them through a matrix-entropy projection, increasing conditional diversity while remaining close to the original model distribution. We prove the concavity of the matrix-based conditional entropy functional, which makes the resulting entropy-constrained projection a convex optimization problem, and develop a scalable mirror-descent algorithm for its implementation. Our results reveal a systematic conditional diversity gap between modern generative models and their training data, and provide an information-theoretic framework for measuring and mitigating this gap.