Kůrková Věra, Sanguineti Marcello
Institute of Computer Science, Czech Academy of Sciences, Pod Vodárenskou věží, 2 - 18207 Prague, Czech Republic.
DIBRIS, University of Genova, Via Opera Pia, 13 - 16145 Genova, Italy.
Neural Netw. 2017 Jul;91:34-41. doi: 10.1016/j.neunet.2017.04.003. Epub 2017 Apr 19.
Limitations of approximation capabilities of shallow perceptron networks are investigated. Lower bounds on approximation errors are derived for binary-valued functions on finite domains. It is proven that unless the number of network units is sufficiently large (larger than any polynomial of the logarithm of the size of the domain) a good approximation cannot be achieved for almost any uniformly randomly chosen function on a given domain. The results are obtained by combining probabilistic Chernoff-Hoeffding bounds with estimates of the sizes of sets of functions exactly computable by shallow networks with increasing numbers of units.
研究了浅层感知器网络逼近能力的局限性。推导了有限域上二值函数逼近误差的下界。证明了除非网络单元的数量足够大（大于域大小对数的任何多项式），否则对于给定域上几乎任何均匀随机选择的函数，都无法实现良好的逼近。这些结果是通过将概率切尔诺夫 - 霍夫丁界与具有不断增加单元数量的浅层网络可精确计算的函数集大小估计相结合而获得的。
