论文标题
gâteaux-hopfield神经网络方法
The Gâteaux-Hopfield Neural Network method
论文作者
论文摘要
在目前的工作中，通过线性扩展Gateaux derivative（LEGD）建立了Hopfield神经网络（HNN）方法的新的微分方程。这种新方法将被称为Gâteaux-Hopfiel神经网络（GHNN）。如果与HNN整数阶微分方程相比，使用一阶Fredholm积分问题来测试这种新方法，则发现它比α> 1的精确溶液更快地收敛。通过分析不同α值的结果，可以观察到学习时间的限制。将指出这种新方法的鲁棒性和优势。
In the present work a new set of differential equations for the Hopfield Neural Network (HNN) method were established by means of the Linear Extended Gateaux Derivative (LEGD). This new approach will be referred to as Gâteaux-Hopfiel Neural Network (GHNN). A first order Fredholm integral problem was used to test this new method and it was found to converge 22 times faster to the exact solutions for α > 1 if compared with the HNN integer order differential equations. Also a limit to the learning time is observed by analysing the results for different values of α. The robustness and advantages of this new method will be pointed out.
