{
  "abstract": "Many probabilistic predictors must satisfy exact structure in every stochastic realization, yet common hard-constraint approaches form predictions in ambient coordinates and then correct or project them. We introduce SLP-ProbHard, a cross-family, representation-centered framework for probabilistic hard-constrained learning when explicit structural parameterizations are available. Its core object, a Structural Feasible Latent Parameterization (SFLP), combines a structural latent law $Z \\sim P^Z_θ(\\cdot\\mid x)$ with a feasible map $Y=h_ϕ(x,Z)$ that satisfies the constraint for every latent realization. Together these components define the predictive law itself, including its support and boundary probabilities, rather than serving as a final feasibility wrapper. We study how feasible coordinates and maps affect stochastic dimension, dependence, calibration, expressiveness, and computation. Experiments use Gaussian latent laws and fixed geometry-derived maps across affine equalities, ordering and simplex constraints, nonlinear manifolds, and three structural representations of seven-basin hydrological flow-duration-curve (FDC) data. In an official-source affine comparison with ProbHardE2E/DPPL, both methods achieve zero practical constraint violations. SLP-ProbHard uses 8 instead of 11 stochastic coordinates and improves MSE/MAE, while DPPL yields better marginal CRPS and closer-to-nominal coverage; a paired test detects no Energy Score difference across ten seeds. Real-world affine and nonlinear FDC representations reduce 13 to 7 and 14 to 8 ambient versus computational coordinates, respectively. Exact feasibility alone thus does not determine a predictive law, motivating direct structural generation when meaningful feasible coordinates are available.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33515",
  "author_total": 2,
  "authors": [
    {
      "name": "Wondesen Teshome Bekele"
    },
    {
      "name": "Marco D'Oria"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9entkt1vxy71h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33515",
  "fulltext_url": null,
  "id": "9entkt1vxy71h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33515",
  "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|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7214793613",
  "pdf_url": "https://arxiv.org/pdf/2609.33515",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9entkt1vxy71h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:26Z",
      "native_id": "2609.33515",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33515"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "SLP-ProbHard: Probabilistic Hard-Constrained Learning via Structural Latent Parameterization",
  "title_text": "SLP-ProbHard: Probabilistic Hard-Constrained Learning via Structural Latent Parameterization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/9entkt1vxy71h",
  "venue": "arXiv",
  "versions": []
}