Tanaka Gouhei, Aihara Kazuyuki
Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan.
IEEE Trans Neural Netw. 2009 Sep;20(9):1463-73. doi: 10.1109/TNN.2009.2025500. Epub 2009 Jul 28.
A widely used complex-valued activation function for complex-valued multistate Hopfield networks is revealed to be essentially based on a multilevel step function. By replacing the multilevel step function with other multilevel characteristics, we present two alternative complex-valued activation functions. One is based on a multilevel sigmoid function, while the other on a characteristic of a multistate bifurcating neuron. Numerical experiments show that both modifications to the complex-valued activation function bring about improvements in network performance for a multistate associative memory. The advantage of the proposed networks over the complex-valued Hopfield networks with the multilevel step function is more outstanding when a complex-valued neuron represents a larger number of multivalued states. Further, the performance of the proposed networks in reconstructing noisy 256 gray-level images is demonstrated in comparison with other recent associative memories to clarify their advantages and disadvantages.
一种广泛用于复值多状态霍普菲尔德网络的复值激活函数被揭示本质上基于多级阶跃函数。通过用其他多级特性替换多级阶跃函数，我们提出了两种替代的复值激活函数。一种基于多级Sigmoid函数，另一种基于多状态分叉神经元的特性。数值实验表明，对复值激活函数的这两种修改都能提高多状态联想记忆的网络性能。当复值神经元表示更多数量的多值状态时，所提出的网络相对于具有多级阶跃函数的复值霍普菲尔德网络的优势更为突出。此外，与其他近期的联想记忆相比，展示了所提出网络在重建有噪声的256灰度级图像方面的性能，以阐明它们的优缺点。
