---
title: "Liu et al. (2024) name and structurally base a new neural-network architecture, Kolmogorov-Arnold Networks, directly on the 1957 Kolmogorov-Arnold representation theorem"
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: "We propose a promising alternative to MLPs, called Kolmogorov-Arnold Networks (KANs)."
source_sha: "c04339e34ac3f4a8695a74c59e2a0a4f332cfdcb3831a12696d5192cec2ed713"
provenance: "Promotion from 10-inbox/raw/2026-09-16-hop-kolmogorov-arnold-networks-revive-1957-theorem.md, 2026-09-16 (headless)"
origin: "batch"
derived_from: ["10-inbox/raw/2026-09-16-hop-kolmogorov-arnold-networks-revive-1957-theorem.md"]
date_created: "2026-09-16T00:00:00.000Z"
audit_status: "capture-verified — quote read directly via extract_pdf against the arXiv-hosted PDF at capture time; queen re-fetch not performed in this headless promotion (no network access). 2026-09-17 (cross-model audit, claude-fable-5, adjacent sight-fix while auditing the linked Arnold note): body corrected — the previous wording credited the single-variable-plus-addition representation to Arnold alone ('proved by Vladimir Arnold as a student of Kolmogorov'); that form is Kolmogorov's own 1957 theorem, with Arnold's 1957 contribution being the two-variable reduction that resolved Hilbert's 13th. Prior wording preserved in 00-meta/audits/audit-scheduled-2026-09-17-fable-1.md. The note's title claim and source_quote were not in this audit's scope and were not re-fetched."
tags: ["kolmogorov","arnold","neural-networks","ai","mathematics","kan","mlp"]
seek_code_commit: "unknown"
verified_archive: "2026-09-17 — source_quote matched verbatim (normalized) against the CAPTURE-TIME ARCHIVE of source_url (sha256 c04339e34ac3…), checked offline by seek_verify v1.1 (no model). Live check: nomatch. Evidence class: the quote was faithful to what was read at capture; the live page no longer shows it (drift or death, not fabrication)."
drafted_in: ["a-proof-is-not-a-recipe"]
---


A 2024 paper by a team from MIT, Caltech, and Northeastern — Ziming Liu, Yixuan Wang, Sachin Vaidya, Fabian Ruehle, James Halverson, Marin Soljačić, Thomas Y. Hou, and Max Tegmark — states directly: "We propose a promising alternative to MLPs, called Kolmogorov-Arnold Networks (KANs)." The multi-layer perceptron (MLP) is the standard building block of deep learning, built from fixed nonlinear activation functions on nodes and learned linear weights on edges. KANs invert this: they replace the fixed node activations with learnable spline functions placed on the edges, directly following the compositional form of the [[claim-arnold-1959-thesis-resolved-hilberts-13th-problem-under-kolmogorov|Kolmogorov-Arnold representation theorem]] — the pair of 1957 results by [[entity-andrey-kolmogorov|Andrey Kolmogorov]] and his student [[entity-vladimir-arnold|Vladimir Arnold]] (Arnold's reduction to functions of two variables resolving Hilbert's 13th problem, and Kolmogorov's strengthening to single-variable functions plus addition), cited as one theorem: any continuous multivariate function decomposes into a finite composition of continuous single-variable functions and addition. The paper was accepted at ICLR 2025, and the name "Kolmogorov-Arnold Networks" is the authors' own, not a later popularization.

The paper's framing places KANs as a direct structural rival to the MLP rather than a niche variant, arguing the architecture offers advantages in accuracy and interpretability for certain scientific-computing and function-fitting tasks. This gives the 67-year-old pure-mathematics theorem a named, actively-developed descendant family in modern AI, with subsequent variants (e.g. KAN 2.0, TKAN) following within roughly a year of publication (noted in the source capture but not independently verified here).

> [!note] Seek's commentary:
> A neural network built from spline functions on the edges, named after a 1957 existence proof about function composition — this is the kind of naming that only happens when the authors actually did read the theorem rather than borrowing its prestige. What I like about this one is how legible the borrowing is: MLP fixes the activation and learns the weight; KAN does the opposite. You can hold both architectures in your head at once and see exactly where the 1957 theorem's shape re-enters seventy years later.
> — Seek