{
  "abstract": "Evaluating text generation requires measuring how well the generated distribution matches the data distribution. For autoregressive models, this is done by the perplexity. Diffusion and flow-based language models can only provide a likelihood bound, whose tightness differs between model families. Sample-based substitutes such as generative perplexity with entropy do not consider the distribution fit. We propose SOL, a distance between text distributions. Each sequence is represented by the empirical measure of its hidden states under a fixed transformer and the distributions of these measures are compared by the double sliced Wasserstein distance. We prove that SOL is a metric if the transformer is injective. Experiments show that SOL detects distributional failures, recovers expected model trends, and provides stable sample-based estimates. We put forward SOL to fill the gap in the current evaluation protocol used for non auto-regressive models. As a first step we use SOL to re-evaluate a variety of models trained on OpenWebText.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06513",
  "author_total": 4,
  "authors": [
    {
      "name": "Gregor Kornhardt"
    },
    {
      "name": "Moritz Piening"
    },
    {
      "name": "Jannis Chemseddine"
    },
    {
      "name": "Gabriele Steidl"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/152gw6dzhat1s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06513",
  "fulltext_url": null,
  "id": "152gw6dzhat1s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06513",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CL"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Topic Modeling"
    ]
  ],
  "openalex": "W7220653121",
  "pdf_url": "https://arxiv.org/pdf/2610.06513",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/152gw6dzhat1s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:25Z",
      "native_id": "2610.06513",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06513"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "SOL: Measuring Gaps between Text Distributions by Double Sliced Wasserstein Metrics",
  "title_text": "SOL: Measuring Gaps between Text Distributions by Double Sliced Wasserstein Metrics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:25Z",
  "url": "https://research.draconitic.com/paper/152gw6dzhat1s",
  "venue": "arXiv",
  "versions": []
}