On the approximation capability of recurrent neural networks
On the approximation capability of recurrent neural networks
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DOI：
10.1016/s0925-2312(99)00174-5
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发表时间：
2000-03-01
期刊：
影响因子：
6
通讯作者：
Hammer, B
中科院分区：
文献类型：
--
作者：
Hammer, B
研究了递归神经网络将函数从实向量列表逼近到实向量空间的能力。任何可测量的函数都可以用概率来近似。此外，在一些有趣的情况下，可以推导出资源的边界，使其足以近似。相反，符号数据上存在不能在最大范数中逼近的可计算映射。在输入长度受限的情况下，实值序列上的某些连续函数需要神经元数量随输入长度至少线性增加。在一元序列上，任何范围有界的映射都可以近似于最大范数。因此，标准s型网络可以作为计算模型在离线输入上计算任何映射。(C) 2000 Elsevier Science B.V.版权所有
The capability of recurrent neural networks of approximating functions from lists of real vectors to a real vector space is examined. Any measurable function can be approximated in probability. Additionally, bounds on the resources sufficient for an approximation can be derived in interesting cases. On the contrary, there exist computable mappings on symbolic data which cannot be approximated in the maximum norm. For restricted input length, some continuous functions on real-valued sequences need a number of neurons increasing at least linearly in the input length. On unary sequences, any mapping with bounded range can be approximated in the maximum norm. Consequently, standard sigmoidal networks can compute any mapping on offline inputs as a computational model. (C) 2000 Elsevier Science B.V. All rights reserved.