Center for Theoretical Neuroscience, Department of Neuroscience, and Kavli Institute for Brain Science, College of Physicians and Surgeons, Columbia University, New York, NY 10032, USA.
Neural Comput. 2013 Aug;25(8):1994-2037. doi: 10.1162/NECO_a_00472. Epub 2013 May 10.
We study a rate-model neural network composed of excitatory and inhibitory neurons in which neuronal input-output functions are power laws with a power greater than 1, as observed in primary visual cortex. This supralinear input-output function leads to supralinear summation of network responses to multiple inputs for weak inputs. We show that for stronger inputs, which would drive the excitatory subnetwork to instability, the network will dynamically stabilize provided feedback inhibition is sufficiently strong. For a wide range of network and stimulus parameters, this dynamic stabilization yields a transition from supralinear to sublinear summation of network responses to multiple inputs. We compare this to the dynamic stabilization in the balanced network, which yields only linear behavior. We more exhaustively analyze the two-dimensional case of one excitatory and one inhibitory population. We show that in this case, dynamic stabilization will occur whenever the determinant of the weight matrix is positive and the inhibitory time constant is sufficiently small, and analyze the conditions for supersaturation, or decrease of firing rates with increasing stimulus contrast (which represents increasing input firing rates). In work to be presented elsewhere, we have found that this transition from supralinear to sublinear summation can explain a wide variety of nonlinearities in cerebral cortical processing.
我们研究了一种由兴奋性和抑制性神经元组成的率型神经网络，其中神经元的输入-输出函数是幂律关系，幂次大于 1，这与初级视觉皮层中的观察结果一致。这种超线性的输入-输出函数导致网络对多个弱输入的响应进行超线性求和。我们表明，对于更强的输入，即会使兴奋性子网不稳定的输入，只要反馈抑制足够强，网络就会动态稳定。对于广泛的网络和刺激参数，这种动态稳定导致网络对多个输入的响应从超线性求和到亚线性求和的转变。我们将其与平衡网络中的动态稳定进行了比较，后者只产生线性行为。我们更详尽地分析了一个兴奋性和一个抑制性群体的二维情况。我们表明，在这种情况下，只要权重矩阵的行列式为正且抑制时间常数足够小，就会发生动态稳定，并分析了超饱和或随着刺激对比度增加（表示输入放电率增加）而放电率降低的条件（这代表大脑皮层处理中的各种非线性）。在其他地方将要展示的工作中，我们发现这种从超线性到亚线性求和的转变可以解释大脑皮层处理中的各种非线性。
