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Do Large Language Models Capture the Diversity in their Training Data? — arXiv:2609.02275

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.02275
License (as archived): CC0-1.0
Archived: 2026-10-17T03:37:37.332Z
SHA-256 of the archived text: dc6a316ac7ba41f705dcd8d7ae85b2b36ae03c6ec29d0b346b278fb18ca8ac15
Stable URL of this page: https://metraipolis.com/documento/dc_ee3ef7d86dec

How to cite

Do Large Language Models Capture the Diversity in their Training Data? — arXiv:2609.02275 — arXiv (en), https://arxiv.org/abs/2609.02275 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ee3ef7d86dec (Metraipolis archive dc_ee3ef7d86dec, sha256 dc6a316ac7ba41f705dcd8d7ae85b2b36ae03c6ec29d0b346b278fb18ca8ac15)

BibTeX

@misc{dcee3ef7d86dec,
  title = {Do Large Language Models Capture the Diversity in their Training Data? — arXiv:2609.02275},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.02275},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ee3ef7d86dec; sha256 dc6a316ac7ba41f705dcd8d7ae85b2b36ae03c6ec29d0b346b278fb18ca8ac15},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.02275. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-03 in cs.AI).
Categorie arXiv: Computation and Language (cs.CL) ; Artificial Intelligence (cs.AI); Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.02275 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T03:13:12.527Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-09-03?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).