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Almost Linear VC-Dimension Bounds for Piecewise Polynomial Networks

机译:分段多项式网络的几乎线性VC维边界

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摘要

We compute upper and lower bounds on the VC dimension and pseudodimension of feedforward neural networks composed of piecewise polynomial activation functions. We show that if the number of layers is fixed, then the VC dimension and pseudo-dimension grow as W log W, where W is the number of parameters in the network. This result stands in opposition to the case where the number of layers is unbounded, in which case the VC dimension and pseudo-dimension grow as W2. We combine our results with recently established approximation error rates and determine error bounds for the problem of regression estimation by piecewise polynomial networks with unbounded weights.
机译:我们计算由分段多项式激活函数组成的前馈神经网络的VC维和伪维的上界和下界。我们表明,如果层数固定,则VC维度和伪维将随着W log W增长,其中W是网络中参数的数量。该结果与层数不受限制的情况相反,在这种情况下,VC维和伪维随W2增长。我们将我们的结果与最近建立的近似误差率相结合,并通过具有无穷大权重的分段多项式网络来确定回归估计问题的误差范围。

著录项

  • 来源
    《Neural computation》 |1998年第8期|2159-2173|共15页
  • 作者

    Bartlett P; Maiorov V; Meir R;

  • 作者单位

    Department of System Engineering, Australian National University, Canberra, ACT 0200, Australia;

  • 收录信息 美国《科学引文索引》(SCI);美国《化学文摘》(CA);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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