STABILITY OF ANALOG NEURAL NETWORKS WITH DELAY
STABILITY OF ANALOG NEURAL NETWORKS WITH DELAY
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DOI：
10.1103/physreva.39.347
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发表时间：
1989-01-01
影响因子：
2.9
通讯作者：
WESTERVELT, RM
中科院分区：
文献类型：
--
作者：
MARCUS, CM;WESTERVELT, RM
具有对称连接的连续时间模拟神经网络，当神经元具有无限快的响应时，总是收敛于不动点，但当存在小的时间延迟时，会出现振荡。由时间延迟引起的持续振荡与神经网络的硬件实现有关，其中由放大器的有限切换速度引起的延迟与网络松弛时间相比是可以感知的。我们分析了具有延迟的连续时间模拟网络的动力学，并证明存在一个临界延迟，超过该延迟，对称连接的网络将产生振荡。给出了低神经元增益和高神经元增益两种不同的稳定性分析。研究结果可作为构建快速稳定的电子网络的设计准则。我们发现，对于某些连接拓扑，远小于松弛时间的延迟会导致振荡，而对于其他拓扑，包括联想记忆网络，即使长时间的延迟也不会产生振荡。最容易振荡的网络结构是全抑制性网络；在这种结构中，振荡的临界延迟比网络松弛时间小N倍，即网络的大小。理论结果与实验结果进行了比较，在一个小（8个神经元）的可控延迟电子网络上进行了实验。
Continuous-time analog neural networks with symmetric connections will always converge to fixed points when the neurons have infinitely fast response, but can oscillate when a small time delay is present. Sustained oscillation resulting from time delay is relevant to hardware implementations of neural networks where delay due to the finite switching speed of amplifiers can be appreciable compared to the network relaxation time. We analyze the dynamics of continuous-time analog networks with delay, and show that there is a critical delay above which a symmetrically connected network will oscillate. Two different stability analyses are presented for low and high neuron gain. The results are useful as design criteria for building fast but stable electronic networks. We find that for some connection topologies, a delay much smaller than the relaxation time can lead to oscillation, whereas for other topologies, including associative memory networks, even long delays will not produce oscillation. The most oscillation-prone network configuration is the all-inhibitory network; in this configuration, the critical delay for oscillation is smaller than the network relaxation time by a factor of N, the size of the network. Theoretical results are compared with numerical simulations and with experiments performed on a small (eight neurons) electronic network with controllable delay.