Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan.
Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.
Phys Rev Lett. 2020 Jul 10;125(2):028101. doi: 10.1103/PhysRevLett.125.028101.
We propose an analytically tractable neural connectivity model with power-law distributed synaptic strengths. When threshold neurons with biologically plausible number of incoming connections are considered, our model features a continuous transition to chaos and can reproduce biologically relevant low activity levels and scale-free avalanches, i.e., bursts of activity with power-law distributions of sizes and lifetimes. In contrast, the Gaussian counterpart exhibits a discontinuous transition to chaos and thus cannot be poised near the edge of chaos. We validate our predictions in simulations of networks of binary as well as leaky integrate-and-fire neurons. Our results suggest that heavy-tailed synaptic distribution may form a weakly informative sparse-connectivity prior that can be useful in biological and artificial adaptive systems.
我们提出了一种具有幂律分布突触强度的可分析处理的神经连接模型。当考虑具有生物上合理数量传入连接的阈值神经元时，我们的模型具有连续向混沌的转变，并能够再现生物相关的低活动水平和无标度的级联，即具有幂律分布大小和寿命的活动爆发。相比之下，高斯对应物表现出不连续向混沌的转变，因此不能在混沌边缘附近保持平衡。我们在二进制和漏积分和放电神经元网络的模拟中验证了我们的预测。我们的结果表明，重尾突触分布可能形成一种弱信息稀疏连接先验，这在生物和人工自适应系统中可能是有用的。
