Maass W
Institute for Theoretical Computer Science, Technische Universitaet Graz, Austria.
Neural Comput. 1997 Feb 15;9(2):279-304. doi: 10.1162/neco.1997.9.2.279.
We show that networks of relatively realistic mathematical models for biological neurons in principle can simulate arbitrary feedforward sigmoidal neural nets in a way that has previously not been considered. This new approach is based on temporal coding by single spikes (respectively by the timing of synchronous firing in pools of neurons) rather than on the traditional interpretation of analog variables in terms of firing rates. The resulting new simulation is substantially faster and hence more consistent with experimental results about the maximal speed of information processing in cortical neural systems. As a consequence we can show that networks of noisy spiking neurons are "universal approximators" in the sense that they can approximate with regard to temporal coding any given continuous function of several variables. This result holds for a fairly large class of schemes for coding analog variables by firing times of spiking neurons. This new proposal for the possible organization of computations in networks of spiking neurons systems has some interesting consequences for the type of learning rules that would be needed to explain the self-organization of such networks. Finally, the fast and noise-robust implementation of sigmoidal neural nets by temporal coding points to possible new ways of implementing feedforward and recurrent sigmoidal neural nets with pulse stream VLSI.
我们表明，生物神经元相对现实的数学模型网络原则上能够以一种此前未被考虑的方式模拟任意前馈sigmoidal神经网络。这种新方法基于单个脉冲的时间编码（或神经元群体同步放电的时间），而非基于传统的以放电率来解释模拟变量。由此产生的新模拟速度大幅提高，因此与关于皮层神经系统中信息处理最大速度的实验结果更加一致。结果我们能够证明，有噪声的脉冲发放神经元网络是“通用逼近器”，即就时间编码而言，它们能够逼近几个变量的任何给定连续函数。对于相当多类通过脉冲发放神经元的发放时间来编码模拟变量的方案，这一结果都成立。这种关于脉冲发放神经元系统网络中计算可能组织方式的新提议，对于解释此类网络自组织所需的学习规则类型有一些有趣的影响。最后，通过时间编码实现sigmoidal神经网络的快速且抗噪声特性，为用脉冲流超大规模集成电路实现前馈和递归sigmoidal神经网络指出了可能的新途径。
