Jin Dezhe Z, Seung H Sebastian
Howard Hughes Medical Institute and Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 May;65(5 Pt 1):051922. doi: 10.1103/PhysRevE.65.051922. Epub 2002 May 20.
Neural networks with recurrent connections are sometimes regarded as too slow at computation to serve as models of the brain. Here we analytically study a counterexample, a network consisting of N integrate-and-fire neurons with self excitation, all-to-all inhibition, instantaneous synaptic coupling, and constant external driving inputs. When the inhibition and/or excitation are large enough, the network performs a winner-take-all computation for all possible external inputs and initial states of the network. The computation is done very quickly: As soon as the winner spikes once, the computation is completed since no other neurons will spike. For some initial states, the winner is the first neuron to spike, and the computation is done at the first spike of the network. In general, there are M potential winners, corresponding to the top M external inputs. When the external inputs are close in magnitude, M tends to be larger. If M>1, the selection of the actual winner is strongly influenced by the initial states. If a special relation between the excitation and inhibition is satisfied, the network always selects the neuron with the maximum external input as the winner.
具有循环连接的神经网络有时被认为计算速度太慢，无法作为大脑的模型。在此，我们通过分析研究一个反例，即一个由N个具有自激、全对全抑制、瞬时突触耦合和恒定外部驱动输入的积分发放神经元组成的网络。当抑制和/或兴奋足够大时，该网络对网络的所有可能外部输入和初始状态执行胜者全得计算。计算完成得非常快：一旦胜者发放一次脉冲，计算就完成了，因为没有其他神经元会发放脉冲。对于某些初始状态，胜者是第一个发放脉冲的神经元，计算在网络的第一个脉冲时完成。一般来说，有M个潜在胜者，对应于最大的M个外部输入。当外部输入的幅度相近时，M往往更大。如果M>1，实际胜者的选择会受到初始状态的强烈影响。如果满足兴奋和抑制之间的特殊关系，网络总是选择具有最大外部输入的神经元作为胜者。
