{
  "abstract": "Amortized neural likelihoods enable computationally expensive inference for models with analytically intractable or unspecified likelihoods, but their black-box nature limits interpretability. We introduce a symbolic distillation pipeline that converts trained neural likelihoods into explicit, interpretable expressions optimized for efficient parameter estimation. Our approach uses a recovery-directed objective to guide symbolic regression toward expressions that preserve parameter-recovery accuracy rather than merely approximating the likelihood function. Candidate expressions are evaluated on held-out datasets and selected using a criterion that jointly accounts for expression complexity, parameter-recovery performance, and distributional distance from the learned likelihood. We evaluate the pipeline on the diffusion decision model, a classical cognitive model, whose analytically tractable likelihood provides ground truth for controlled evaluation. The proposed recovery-directed objective improves parameter recovery over standard symbolic-regression objectives. The resulting symbolic likelihoods enable over 100 times faster parameter evaluation than both neural likelihoods and, when available, the exact likelihood, while maintaining a manageable loss in precision. We further demonstrate these computational benefits in Bayesian hierarchical inference on empirical data. Our pipeline provides a lightweight interface for integrating symbolic distillation with existing neural-likelihood estimation methods and can be adapted to a range of simulation-based inference settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32409",
  "author_total": 2,
  "authors": [
    {
      "name": "Kianté Fernandez"
    },
    {
      "name": "Xinwei Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dvh319cyhmbb3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32409",
  "fulltext_url": null,
  "id": "dvh319cyhmbb3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32409",
  "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",
      "q-bio.NC"
    ],
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7214723379",
  "pdf_url": "https://arxiv.org/pdf/2609.32409",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dvh319cyhmbb3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:21Z",
      "native_id": "2609.32409",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32409"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.NC",
      "subfield": "neuroscience"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "Recovery-Directed Symbolic Distillation of Neural Likelihoods",
  "title_text": "Recovery-Directed Symbolic Distillation of Neural Likelihoods",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/dvh319cyhmbb3",
  "venue": "arXiv",
  "versions": []
}