{
  "abstract": "Multimodal large language models often capture visual-linguistic correlations but struggle to predict how local visual interventions propagate and affect downstream answers. We introduce InfluenceField, an intervention-aware latent field inserted between the visual encoder and language decoder. It lifts patch features into a continuous spatial representation, propagates directed influence over multiple steps, and predicts local intervention effects through a shared transition operator. Training jointly optimizes language modeling, cross-environment invariance, counterfactual rollout supervision, and structural regularization. For a nonlinear finite-basis population model, we show that target-aligned interventional supervision, together with a one-step separation condition on the transition, restricts admissible representations to within-location reparameterizations, so that the directed dependency graph of the full transition is recovered exactly. A linear specialization gives an exact partial-coverage characterization and a finite-loss stability bound, and the field analysis derives the spatial profile of coefficient interventions together with a shared-channel calibration result. On CausalVQA, InfluenceField improves overall accuracy over its backbone by 13.1 percentage points, with the largest gains on the planning and hypothetical categories. Capacity-matched baselines and structural controls attribute the gains in robustness and factual-counterfactual consistency to the causal objectives rather than to added capacity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07874",
  "author_total": 3,
  "authors": [
    {
      "name": "Zihao Yang"
    },
    {
      "name": "Zijia Wang"
    },
    {
      "name": "Zhiqiu Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/11be39wv8748m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07874",
  "fulltext_url": null,
  "id": "11be39wv8748m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07874",
  "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",
      "1707|Multimodal Machine Learning Applications"
    ]
  ],
  "openalex": "W7212061951",
  "pdf_url": "https://arxiv.org/pdf/2609.07874",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/11be39wv8748m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:07Z",
      "native_id": "2609.07874",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07874"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "InfluenceField: A Differentiable Field with Interventionally Identifiable Causal Structure for Multimodal World Modeling",
  "title_text": "InfluenceField: A Differentiable Field with Interventionally Identifiable Causal Structure for Multimodal World Modeling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:07Z",
  "url": "https://research.draconitic.com/paper/11be39wv8748m",
  "venue": "arXiv",
  "versions": []
}