Dynamical Stability Conditions for Recurrent Neural Networks with Unsaturating Piecewise Linear Transfer Functions
Dynamical Stability Conditions for Recurrent Neural Networks with Unsaturating Piecewise Linear Transfer Functions
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DOI：
10.1162/08997660152469350
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发表时间：
2001-08
影响因子：
2.9
通讯作者：
H. Wersing;W. Beyn;H. Ritter
中科院分区：
文献类型：
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作者：
H. Wersing;W. Beyn;H. Ritter
我们建立了两个条件，以确保不饱和的分段线性传递函数，也称为线性阈值或半线性传递函数的加性递归网络的非发散性。正如Hahn-loser、Sarpeshkar、Mahowald、道格拉斯和Seung（2000）所指出的，这种类型的网络可以有效地用硅来构建，并在单个电路中表现出数字选择和模拟放大的共存。为了获得这种行为，网络必须是多稳态和非发散的，我们的条件允许确定可以实现最大递归放大的制度。第一个条件可以应用于非对称网络，并且具有要求局部抑制的强度与聚集到神经元上的兴奋性权重之和相匹配的简单解释。第二个条件仅限于对称网络，但也可以考虑非局部抑制相互作用的稳定效果。我们演示了一个简单的例子和Ben-Yishai，Lev Bar-Or和Sompolinsky（1995）的取向选择性模型的条件的应用。我们表明，条件可以用来确定在其模型区域的最大取向选择性放大和对称性破缺。
We establish two conditions that ensure the nondivergence of additive recurrent networks with unsaturating piecewise linear transfer functions, also called linear threshold or semilinear transfer functions. As Hahn-loser, Sarpeshkar, Mahowald, Douglas, and Seung (2000) showed, networks of this type can be efficiently built in silicon and exhibit the coexistence of digital selection and analog amplification in a single circuit. To obtain this behavior, the network must be multistable and nondivergent, and our conditions allow determining the regimes where this can be achieved with maximal recurrent amplification. The first condition can be applied to nonsymmetric networks and has a simple interpretation of requiring that the strength of local inhibition match the sum over excitatory weights converging onto a neuron. The second condition is restricted to symmetric networks, but can also take into account the stabilizing effect of nonlocal inhibitory interactions. We demonstrate the application of the conditions on a simple example and the orientation-selectivity model of Ben-Yishai, Lev Bar-Or, and Sompolinsky (1995). We show that the conditions can be used to identify in their model regions of maximal orientation-selective amplification and symmetry breaking.