An improvement in the superposition theorem of Kolmogorov
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References
- 1.On the representation of continuous functions of several variables by superposition of continuous functions of one variable and addition(in Russian)Dokl. Akad. Nauk SSSR, 114 (1957), pp. 953-956On the representation of continuous functions of several variables by superposition of continuous functions of one variable and addition(in Russian)Dokl. Akad. Nauk MR 22, 114 (1957), pp. 953-956#2669Amer. Math. Soc. Transl., 2 (28) (1963), pp. 55-59
- 2.Improvement in the smoothness of functions in the Kolmogorov superposition theorem(in Russian)Dokl. Akad. Nauk SSSR, 177 (5) (1967), pp. 1019-1022Improvement in the smoothness of functions in the Kolmogorov superposition theorem(in Russian)Dokl. Akad. Nauk MR 38, 177 (5) (1967), pp. 1019-1022# 663Soviet Math. Dokl., 8 (6) (1967), pp. 1550-1553
- 3.On the structure of continuous functions of several variablesTrans. Amer. Math. Soc., 115 (1965), pp. 340-355On the structure of continuous functions of several variablesTrans. Amer. Math. Soc. MR 35, 115 (1965), pp. 340-355# 1737
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2021, Engineering Applications of Artificial IntelligenceCitation Excerpt :The further research of this representation can be conventionally divided into generic ways of model reduction (Sprecher, 1965; Lorentz, 1966; Sprecher, 1972; Lorentz et al., 1996) and practical ways of construction of the involved functions after picking one of the existing reduced forms (Igelnik and Parikh, 2003; Coppejans, 2004; Wasserman, 2006; Actor and Knepley, 2017; Actor, 2018).
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