{
  "abstract": "Kolmogorov-Arnold Networks (KANs) place learnable B-spline activations on network edges rather than fixed activations on nodes. The standard Cox-de Boor recursion evaluates these activations through $k$ sequential passes for degree-$k$ splines, consuming over 90% of forward-pass time. InKAN replaces this recursion with the truncated power form, a classical result from approximation theory that expresses each uniform cubic B-spline as five $(x)_+^3$ terms at shifted knot positions. The resulting expression computes exact B-spline basis values: the same mathematical function as the Cox-de Boor recursion, evaluated without sequential passes. This paper documents three contributions: (1) an implementation structured for torch . compile fusion, eliminating recursion, span lookup, and scatter-gather operations; (2) a bounded-coordinate evaluation that clamps the normalized input to $[0, k{+}1]$, preventing the growth of cancellation error at large off-support coordinates; and (3) an open-source package (pip install inkan). In the tested configurations, InKAN has 2.8--3.5$\\times$ lower forward-pass latency than the Cox-de Boor recursion. Partition-of-unity errors remain below $10^{-5}$ for grid sizes up to 200.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01956",
  "author_total": 1,
  "authors": [
    {
      "name": "Naveen Mysore"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3tk3t3q44hbd7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01956",
  "fulltext_url": null,
  "id": "3tk3t3q44hbd7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01956",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "1702|Neural Networks and Applications"
    ]
  ],
  "openalex": "W7207591737",
  "pdf_url": "https://arxiv.org/pdf/2609.01956",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3tk3t3q44hbd7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.01956",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01956"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "InKAN: B-Spline KANs via Truncated Power Form",
  "title_text": "InKAN: B-Spline KANs via Truncated Power Form",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/3tk3t3q44hbd7",
  "venue": "arXiv",
  "versions": []
}