{
  "abstract": "As compute scales, models evolve, and training algorithms advance, our ability to explain the increasingly powerful AI systems they enable is eroding. To help safeguard interpretability, we introduce a specialized training algorithm (MACCHIATO) that jointly constructs (i) an explicitly structured $\\operatorname{ReLU}$-MLP from partial truth-table observations and (ii) an explicit Boolean circuit over signed literals with $\\{\\operatorname{AND},\\operatorname{OR},\\operatorname{XOR}\\}$ gates certifying what its subnetworks compute and how they compose. Intuitively, we iteratively project the residuals of a Boolean function onto low-dimensional $\\{\\operatorname{AND},\\operatorname{OR},\\operatorname{XOR}\\}$-circuit classes and exactly compile the resulting circuit into a $\\operatorname{ReLU}$-MLP; we combine $\\operatorname{ReLU}$-MLP circuit compilation, ESPRESSO logic minimization, and influence-based variable selection. Roughly speaking, our interpretability certificate is complemented by a statistical guarantee: under the theorem's influence-recovery conditions, if each of the $m$ stage-wise residuals depends on at most $\\log_2(B)$ bits, a sample-splitting variant of our algorithm trained on $T$ observations returns a six-layer $\\operatorname{ReLU}$-MLP (counting the input layer) of width $\\mathcal{O}(mB)$ with truth-table error $\\mathcal{O}\\bigl(\\sqrt{m(B+\\log(m/δ))/T}\\bigr)$. On synthetic random-junta tasks, our networks outperform depth- and hidden-width-matched Adam-trained MLPs in several data-sparse or projection-aligned regimes, while the trained ReLU-MLPs are stronger in others. Moreover, in our explicit PyEDA truth-table implementation, the iterative procedure completes in regimes where flat ambient-dimensional ESPRESSO exceeds the three-hour computational budget.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13439",
  "author_total": 2,
  "authors": [
    {
      "name": "Hrad Ghoukasian"
    },
    {
      "name": "Anastasis Kratsios"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/afrj05gdwmpnh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13439",
  "fulltext_url": null,
  "id": "afrj05gdwmpnh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13439",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Explainable Artificial Intelligence (XAI)"
    ]
  ],
  "openalex": "W7213294810",
  "pdf_url": "https://arxiv.org/pdf/2609.13439",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/afrj05gdwmpnh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:36Z",
      "native_id": "2609.13439",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13439"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Certifiably Interpretable Training of ReLU-MLPs for Boolean Tasks with Guaranteed Truth-Table Generalization",
  "title_text": "Certifiably Interpretable Training of ReLU-MLPs for Boolean Tasks with Guaranteed Truth-Table Generalization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:36Z",
  "url": "https://research.draconitic.com/paper/afrj05gdwmpnh",
  "venue": "arXiv",
  "versions": []
}