On the Number of Solutions of a Class of Nonlinear Equations Related to Neural Networks with Tapered Connections
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概要
- 論文の詳細を見る
The number of solutions of a nonlinear equation x = sgn(Wx) is discussed. The equation is derived for the determination of equilibrium points of a kind of Hopfield neural networks. We impose some conditions on W. The conditions correspond to the case where a Hopfield neural network has n neurons arranged on a ring, each neuron has connections only from k preceding neurons and the magnitude of k connections decrease as the distance between two neurons increases. We show that the maximum number of solutions for the above case is extremely few and is independent of the number of neurons, n, if k is less than or equal to 4. We also show that the number of solutions generally increases exponentially with n by considering the case where k=n-1.
- 社団法人電子情報通信学会の論文
- 1995-10-25
著者
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Nishi T
Kyushu Univ. Fukuoka‐shi Jpn
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Nishi Tetsuo
Faculty Of Science And Engineering Waseda Univ.
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TAKAHASHI Norikazu
Faculty of Information Science and Electrical Eng.,Kyushu Univ.
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Takahashi N
Department Of Computer Science And Communication Engineering Kyushu Univ.
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Nishi Tetsuo
Faculty Of Engineering Kyushu University
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Takahashi Norikazu
Faculty Of Engineering Kyushu University
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