{
  "abstract": "Deep ReLU networks are piecewise-affine mappings that partition the input space into cells, each characterized by a distinct activation pattern. This structure motivates fitting a local linear model within each cell to preserve predictive accuracy while improving interpretability. The challenge is to identify regimes that are stable, data-adaptive, and easy to explain. We propose REALM, a mixture of linear models whose regimes are induced by neural activation patterns. Because the number of activation cells in a deep neural network (DNN) can grow rapidly with depth, we first distill a deep teacher into a wide, shallow student network (WSSN), then binarize and cluster its hidden-layer activations to define the regimes and fit a linear model within each regime. Since the regimes are discovered from internal structure, the router does not carry the predictive burden. To make regime assignment interpretable, we train a multiclass logistic regression, the explanatory gate, to reproduce the regime assignments. The two-level structure is interpretable at both stages in terms of raw tabular or learned convolutional features: the gate identifies features that determine regime assignments, while the linear models identify features that drive predictions within each regime. We analyze an idealized setting that illustrates a trade-off between partition complexity and stability: as the number of regimes grows, finer partitions can improve approximation but may reduce regime-assignment stability. Experiments on tabular and image datasets show that REALM achieves competitive predictive performance relative to other DNN-guided mixture surrogates and inherently interpretable models while producing stable regime-level explanations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32141",
  "author_total": 3,
  "authors": [
    {
      "name": "Xiaoran Cheng"
    },
    {
      "name": "Sen Na"
    },
    {
      "name": "Jia Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5zg11bm6819xp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32141",
  "fulltext_url": null,
  "id": "5zg11bm6819xp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32141",
  "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.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Explainable Artificial Intelligence (XAI)"
    ]
  ],
  "openalex": "W7214707813",
  "pdf_url": "https://arxiv.org/pdf/2609.32141",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5zg11bm6819xp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:26Z",
      "native_id": "2609.32141",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32141"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "REALM: Regime-Switching, Explainable, and Activation-Induced Linear Models",
  "title_text": "REALM: Regime-Switching, Explainable, and Activation-Induced Linear Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/5zg11bm6819xp",
  "venue": "arXiv",
  "versions": []
}