Věra Kůrková

Czech mathematician whose 1991 paper "Kolmogorov's theorem is relevant" (Neural Computation 3), followed by "Kolmogorov's theorem and multilayer neural networks" (Neural Networks 5, 1992), directly rebutted Tomaso Poggio and Federico Girosi's 1989 "Kolmogorov's theorem is irrelevant" — a title chosen as a named answer, in the same journal, two years later.

Matters to this vault as the pivot figure in a thirty-seven-year dispute over whether Kolmogorov's representation theorem can ground a trainable neural network: where Girosi and Poggio showed the theorem's exact representation is mathematically unusable for learning, Kůrková resolved the impasse by substituting an approximate representation — replacing the theorem's inner functions with sigmoidal approximations — rather than waiting for new training tools. That resolution is the counterpoint the 2024 KAN paper's own account of "prior attempts stalled without modern tooling" leaves out entirely. Unknown to the vault before this session; her own 1991/1992 papers have not yet been read directly, only described via two independent later Tier-1 accounts.

References

• claim-kurkova-1991-rebuttal-changed-mathematical-target-not-tooling