{
  "abstract": "Reliable generalization in conditional latent variable models requires understanding both identifiability and extrapolation: how observed variation across attributes determines latent structure, and how that structure determines distributions at unseen attributes. However, existing identifiability and extrapolation guarantees are largely model-specific, with separate analyses in nonlinear ICA, causal representation learning, perturbation modeling, and related conditional latent variable models. We introduce concept modulation models (CMMs), an attribute-indexed class of conditional generative models with structure $A\\to Λ\\to C\\to X$, where attributes select modulators, modulators induce latent concept laws, and concepts generate observed features. CMMs lift transition-based identifiability to conditional settings by showing that feature agreement on observed attributes induces a latent concept transition constrained by the CMM class. We express these constraints through attribute potentials, log-density ratios between attribute-conditioned concept laws, separating the generic lifting step from model-specific rigidity arguments. The same potentials control extrapolation: agreement at unseen attributes holds exactly when the transported attribute-potential identities extend to those attributes. This yields algebraic extrapolation criteria, identifies the common potential-based proof objects behind several existing identifiability and extrapolation results, and, when combined with the model-specific rigidity arguments in those works, recovers their stated conclusions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.18509",
  "author_total": 4,
  "authors": [
    {
      "name": "Soheun Yi"
    },
    {
      "name": "Yizhou Lu"
    },
    {
      "name": "Chandler Squires"
    },
    {
      "name": "Pradeep Ravikumar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/83w1s3wn0jvgv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.18509",
  "fulltext_url": null,
  "id": "83w1s3wn0jvgv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.18509",
  "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.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Bayesian Modeling and Causal Inference"
    ]
  ],
  "openalex": "W7165205879",
  "pdf_url": "https://arxiv.org/pdf/2606.18509",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/83w1s3wn0jvgv.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:25Z",
      "native_id": "2606.18509",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.18509"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Concept Modulation Models: A Unified Framework for Identifiability and Extrapolation",
  "title_text": "Concept Modulation Models: A Unified Framework for Identifiability and Extrapolation",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/83w1s3wn0jvgv",
  "venue": "arXiv",
  "versions": []
}