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

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Robert Hecht-Nielsen's 1987 conference paper, "Kolmogorov's Mapping Neural Network Existence Theorem," is the paper that opened the entire dispute this vault has traced through Girosi & Poggio's 1989 rebuttal, Kůrková's 1991-92 counter-rebuttal, and the Sprecher/Köppen/Braun-Griebel constructive line — every one of which responds to or builds on this paper. Hecht-Nielsen proposed that Kolmogorov's superposition theorem could be read as an existence proof for a neural network capable of exactly mapping any continuous function. He hedged the proposal himself in the same paper: "the direct usefulness of this result is doubtful, at least in the near term, because no constructive method for developing the g_i functions is known" — flagging the absence of a way to actually build the theorem's inner functions as an open problem, two years before Girosi and Poggio would argue the deeper obstacle was not absence of a method but the mathematical shape of the functions themselves.