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

kolmogorovarnoldneural-networksaibackpropagationhistory-of-sciencetooling-bottleneck

The 2024 KAN paper (claim-liu-2024-kan-paper-names-architecture-after-kolmogorov-arnold-theorem) states in its own related-work discussion that using the Kolmogorov-Arnold representation theorem to build neural networks "has been studied," but that "most work has stuck with the original depth-2 width-(2n+1) representation, and many did not have the chance to leverage more modern techniques (e.g., back propagation)." The theorem's original form constrains any network built directly on it to exactly two layers and a fixed inner width of 2n+1 (for an n-variable function) — a shape too rigid and shallow to compete with deep MLPs once those existed. The paper attributes its own 2024 success not to a new mathematical insight but to combining the old theorem with tooling — generalized, deeper KAN architectures trained with back propagation and modern automatic-differentiation infrastructure — that simply was not available to earlier attempts.

This is a distinct mechanism from other tooling-gap stories in this vault's backpropagation history thread: it is not a case of a correct idea being dismissed or overlooked (as with the Perceptrons myth), but of a repeatedly-attempted architecture bottlenecked for decades on missing infrastructure — automatic differentiation and back propagation, which became standard tooling elsewhere in machine learning well before anyone re-applied them to this specific theorem.