平衡神经网络中的瞬态放大
Transient amplification in balanced neural networks
摘要：
瞬态放大不仅在神经科学中，而且在许多领域都被认为是一种重要的机制。尽管如此，没有明确的生物学合理机制来微调耦合矩阵或选择要放大的信号。在这项工作中，我们定量地研究瞬态动力学的Rajan-Abbott模型的递归神经网络[K。Rajan和L.F. Abbot PRL 97，188104（2006）]。我们发现一个弱或没有放大的瞬态和一个强放大的阶段，其中的平均轨迹被放大的阶段之间的二阶过渡。在后一阶段，戴尔原理和兴奋/抑制平衡的结合允许强权重，同时保持系统在混沌的边缘。此外，我们表明，放大与更大的动态变化齐头并进。通过数值研究平方范数的全概率密度，我们观察到随着权重强度的增加，分布的右尾变得更重，从高斯尾移动到指数尾。
英文摘要：
Transient amplification has been proposed as an important mechanism not only in neuroscience but in many areas modeled by dynamical systems. Despite that, there is no clear biologically plausible mechanism which fine-tunes the coupling matrix or selects signals to be amplified. In this work we quantitatively study transient dynamics in the Rajan-Abbott model of a recurrent neural network [K. Rajan and L.F. Abbot PRL 97, 188104 (2006)]. We find a second order transition between a phase of weakly or no amplified transients and a phase of strong amplification, where the average trajectory is amplified. In the latter phase the combination of Dale's principle and excitatory/inhibitory balance allows for strong weights, while maintaining the system at the edge of chaos. Moreover, we show that the amplification goes hand in hand with greater variability of the dynamics. By numerically studying the full probability density of the squared norm, we observe as the strength of weights grows, the right tail of the distribution becomes heavier, moving from the Gaussian to the exponential tail.
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