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二进神经网络采用线性分类,是结构简单又易于实现的一类神经网络,在许多应用领域中都有重要研究价值.对于单隐层二进神经网络,目前隐层规模的确定问题仍然没有明确的研究结论.本文在研究隐层规模问题的过程中,提出了布尔空间的最多孤立样本问题.在二进神经网络隐层神经元各自表达一个“与”关系,所有隐层神经元通过输出元形成“或”关系的情况下,证明了实现最多孤立样本问题需2n?1个隐层神经元.更重要的是,指出了n元奇偶校验问题和最多孤立样本结构的等价性.进一步地,通过引入隐层抑制神经元将隐元数目降为n,说明了抑制神经元在二进神经网络中的重要作用.最后,在Hamming球与SP函数的基础上,揭示出抑制神经元和n元奇偶校验问题的逻辑关系,并给出了奇偶校验问题的逻辑式表达.
Binary neural network is a kind of neural network with simple structure and easy to implement, which has important research value in many fields of application.For the single hidden layer binary neural network, the problem of determining the hidden layer size is still not clear In the process of studying hidden layer scale problem, this paper proposes the problem of the most isolated samples in Boolean spaces.In the hidden layer neurons of binary neural network each express a relationship of “” and “”, all hidden layer neurons pass Output elements form a relationship of “or ”, it is proved that 2n? 1 hidden layer neurons are needed to realize the most isolated sample problems, and more importantly, n parity problems and most isolated sample structures are pointed out Valence.Furthermore, the introduction of hidden layer neurons reduces the number of hidden elements to n, indicating the important role of inhibiting neurons in the binary neural network.Finally, based on Hamming sphere and SP function, Inhibit the logical relationship between neurons and n parity problem, and give the logical expression of the parity problem.