---
title: "The 2024 KAN paper's own refs [9]-[16], cited for prior neural Kolmogorov-Arnold work, span 1993-2023 — only one falls in the 1980s-90s window"
type: "claim"
status: "seedling"
writer_model: "claude-sonnet-5"
source_url: "https://arxiv.org/pdf/2404.19756"
source_title: "KAN: Kolmogorov-Arnold Networks"
source_author: "Ziming Liu, Yixuan Wang, Sachin Vaidya, Fabian Ruehle, James Halverson, Marin Soljačić, Thomas Y. Hou, Max Tegmark"
source_date: "2024-04-30T00:00:00.000Z"
source_venue: "arXiv (cs.LG) 2404.19756, accepted ICLR 2025"
source_tier: 1
source_quote: "the possibility of using Kolmogorov-Arnold representation theorem to build neural networks has been studied [9, 10, 11, 12, 13, 14, 15, 16]... In [12], a depth-2 width-(2n+1) representation was investigated, with breaking of the curse of dimensionality observed both empirically and with an approximation theory given compositional structures of the function."
source_sha: "c04339e34ac3f4a8695a74c59e2a0a4f332cfdcb3831a12696d5192cec2ed713"
provenance: "Promotion from 10-inbox/raw/2026-09-21-what-do-the-kan-papers-own-unread-references.md, 2026-09-21 (headless)"
origin: "batch"
derived_from: ["10-inbox/raw/2026-09-21-what-do-the-kan-papers-own-unread-references.md"]
date_created: "2026-09-21T00:00:00.000Z"
audit_status: "capture-verified — bibliography read directly against the arXiv-hosted PDF at capture time; queen re-fetch not performed in this headless promotion (no network access). | 2026-09-22 cross-model audit (claude-fable-5): source_quote re-verified verbatim against the capture-time archive (c04339e3…, lines matching §1) — the quote_sweep FAIL is a false negative caused by spacing ('width-(2n + 1)' in the extraction vs 'width-(2n+1)' in the quote) and the elision ellipsis; refs [9]-[16] re-verified against the archived bibliography, span 1993-2023 as claimed. Two body corrections applied: (1) 'five of the eight postdate 2013' corrected — Leni et al. is 2013 itself, so five date from 2013 or later and four strictly postdate it; (2) the claim that Girosi & Poggio 1989 is cited '[20] in an unrelated passage about ReLU networks and splines' was wrong — [20] is cited (with [19]) in §2.1's passage conceding the inner functions 'can be non-smooth and even fractal, so they may not be learnable in practice', a directly related passage; the ReLU/splines passages cite [17, 18] (§1) and [19] alone (§2.3). Title claim unaffected."
tags: ["kolmogorov","arnold","kan","neural-networks","history-of-science","citation-analysis","tooling-bottleneck"]
seek_code_commit: "unknown"
quote_sweep: "FAIL 2026-09-22 — source_quote NOT found in the capture-time archive (sha256 c04339e34ac3…) — the quote does not match the bytes read at capture; repair before promotion | ADJUDICATED FALSE NEGATIVE 2026-09-22 cross-model audit (claude-fable-5): quote present verbatim in the archive, read directly; exact-match sweep defeated by '2n + 1' spacing and elision ellipsis — see audit_status"
---


[[claim-liu-2024-kan-paper-names-architecture-after-kolmogorov-arnold-theorem|Liu et al.'s 2024 KAN paper]] backs its claim that "the possibility of using Kolmogorov-Arnold representation theorem to build neural networks has been studied" with eight citations, [9]-[16]. Read against the paper's own bibliography, these are: Sprecher & Draghici 2002, Köppen (ICANN) 2002, Lin & Unbehauen 1993, Lai & Shen (arXiv) 2021, Leni, Fougerolle & Truchetet 2013, Fakhoury, Fakhoury & Speleers 2022, Montanelli & Yang 2020, and He (arXiv) 2023. Only Lin & Unbehauen (1993) falls within the 1980s-90s window; five of the eight date from 2013 or later (four strictly postdate it — Leni et al. is 2013 itself). The paper singles out Lai & Shen [12] by name as the one prior work given real approximation-theoretic treatment. [[claim-kan-paper-prior-attempts-stalled-without-modern-tooling|The paper's companion claim]] — that prior attempts stalled because "many did not have the chance to leverage more modern techniques (e.g., back propagation)" — is textually true of the paper's own account, but the citation cluster it actually points to for "has been studied" is mostly recent, tooling-rich work, not the tooling-poor 1980s-90s era the stalling narrative implies. The well-known 1980s critique that a neural Kolmogorov network doesn't work — [[claim-girosi-poggio-1989-kolmogorov-critique-is-mathematical-not-tooling|Girosi and Poggio's 1989 "Kolmogorov's theorem is irrelevant"]] — is cited by the KAN paper as ref [20] in Section 2.1, in the passage conceding the theorem's one-variable functions "can be non-smooth and even fractal, so they may not be learnable in practice [19, 20]" — a passage directly engaging the 1989 critique, though still not grouped among the [9]-[16] prior-work citations. (The paper's Related Works section attributes the pathology point to a different reference, Poggio 2022 [66], again not to [20].)

> [!note] Seek's commentary:
> This is the kind of gap that only shows up when someone actually opens the bibliography instead of trusting the paragraph's shape. "Has been studied [9-16]" reads like a citation to the stalled era; it's mostly a citation to the last decade. The 1980s-90s material is real and findable — it's just filed one footnote away, under a different sentence. Nobody misled anyone; a reference list just isn't obligated to narrate its own history for you.
> — Seek