{
  "abstract": "Causal representation learning (CRL) aims to recover latent causal variables and their structural relations from high-dimensional observations. Existing CRL methods typically assume that all environments are defined over the same latent variables, or at least share a common latent representation space. We study a fragmented multi-client setting, where multiple clients interact with the same global latent causal system but each client only accesses and intervenes on a subset of the latent variables. In this regime, marginalizing unused latent variables induces bidirected edges, so a single client no longer admits a node-wise latent causal graph, and the global latent causal order must be recovered by assembling client-specific structural fragments. We propose \\textbf{Jigsaw-CRL}, a framework for recovering global latent causal order from such fragmented interventions. Under soft interventions, differences between precision matrices across environments exhibit a low-rank structure governed by latent ancestor relations. This enables recovery, for each client, of a block partition, the corresponding block-level ancestral order, and latent subspaces, and then assembly of these fragments into the global node-level latent causal order. We establish identifiability guarantees, develop practical algorithms, and validate the framework on synthetic data. Our codes are available on https://anonymous.4open.science/r/code-for-Jigsaw-CRL-7B26",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28991",
  "author_total": 2,
  "authors": [
    {
      "name": "Haijie Xu"
    },
    {
      "name": "Chen Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/agvybvjkgtv5b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28991",
  "fulltext_url": null,
  "id": "agvybvjkgtv5b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28991",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Bayesian Modeling and Causal Inference"
    ]
  ],
  "openalex": "W7204908392",
  "pdf_url": "https://arxiv.org/pdf/2608.28991",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/agvybvjkgtv5b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:54Z",
      "native_id": "2608.28991",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28991"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Jigsaw-CRL: Recovering Global Latent Causal Order from Fragmented Multi-Client Interventions",
  "title_text": "Jigsaw-CRL: Recovering Global Latent Causal Order from Fragmented Multi-Client Interventions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:54Z",
  "url": "https://research.draconitic.com/paper/agvybvjkgtv5b",
  "venue": "arXiv",
  "versions": []
}