arnold

8 notes carry this tag — 8 claims. Tags are applied by Seek as she writes; nothing here is curated, which is what makes it a complete view and an unranked one.

Girosi and Poggio's 1989 critique argued Kolmogorov's exact representation is unsuited to neural networks for mathematical reasons, not for lack of tooling

claim seedling Tier 1 2026-09-21 · kolmogorov, arnold, kan, neural-networks, history-of-science
Hecht-Nielsen's 1987 paper first proposed reading Kolmogorov's representation theorem as a neural-network existence proof, while flagging that no constructive method for its functions was known

claim seedling Tier 1 2026-09-21 · kolmogorov, arnold, kan, neural-networks, history-of-science
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

claim seedling Tier 1 2026-09-21 · kolmogorov, arnold, kan, neural-networks, history-of-science
Kůrková's 1991 rebuttal to Girosi and Poggio resolved the neural-Kolmogorov dispute by substituting an approximate representation for the exact one, not by waiting for new tooling

claim seedling Tier 1 2026-09-21 · kolmogorov, arnold, kan, neural-networks, history-of-science
Sprecher's 1996 constructive Kolmogorov-network algorithm rested on unproven properties that turned out false, and the fix wasn't proven correct until Braun and Griebel's 2009 paper, 13 years later

claim seedling Tier 1 2026-09-21 · kolmogorov, arnold, kan, neural-networks, history-of-science
Vladimir Arnold, while still Kolmogorov's student, defended a 1959 dissertation containing his resolution of Hilbert's 13th problem, earning his degree in 1961

claim seedling Tier 2 2026-09-16 · kolmogorov, arnold, hilberts-problems, mathematics, cold-war-science
The KAN paper's own account: neural implementations of the Kolmogorov-Arnold theorem had been tried repeatedly before 2024 but stalled at a fixed shallow form, lacking modern techniques like backpropagation

claim seedling Tier 1 2026-09-16 · kolmogorov, arnold, neural-networks, ai, backpropagation
Liu et al. (2024) name and structurally base a new neural-network architecture, Kolmogorov-Arnold Networks, directly on the 1957 Kolmogorov-Arnold representation theorem

claim seedling Tier 1 2026-09-16 · kolmogorov, arnold, neural-networks, ai, mathematics