具有二阶突触基序的随机神经网络非线性动力学
Nonlinear dynamics of random neural networks with second-order synaptic motifs
- Interdisciplinary Graduate Program in Quantitative Biosciences, Georgia Institute of Technology（佐治亚理工学院定量生物科学跨学科研究生项目）
- School of Mathematics, Georgia Institute of Technology（佐治亚理工学院数学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究通过动态平均场理论揭示二阶突触基序（链式、互惠、汇聚、发散）共同重塑随机神经网络雅可比特征值谱，产生铁磁态、极限环及玻璃态等多稳态，并降低混沌活动的熵产生与吸引子维数，确立其为皮层回路动力学的基本结构机制。
AI中文摘要：
随机神经网络的经典理论通常假设连接是独立的，忽略了生物回路中普遍存在的局部基序结构。在此，我们研究了四种二阶突触基序（链式、互惠、汇聚和发散）如何塑造非线性发放率网络的动力学。虽然先前的研究已确定链式相关性会产生离群特征值，但我们证明这些基序还共同重塑了雅可比特征值谱的主体部分。利用路径积分形式，我们推导出一个动态平均场理论，该理论揭示链式基序通过响应核充当系综平均活动的延迟反馈，从而产生丰富的动力学状态谱系，包括铁磁态和极限环。当负链式相关性幅度足够大时，会产生一种玻璃态、多稳态状态，这种状态先前主要与部分对称网络相关联。我们的理论还区分了汇聚基序与发散基序：发散相关性主要重新标度时间噪声，而汇聚相关性通过将非零平均活动转化为淬火异质性来抑制时间混沌。最后，对李雅普诺夫谱和参与比维数的分析表明，基序结构改变了混沌活动的几何形状，即使在有效谱边缘保持固定的情况下，也降低了熵产生和吸引子维数。总之，这些发现确立了二阶基序作为控制局部皮层回路动力学状态的基本结构机制。
英文摘要：
Classical theories of random neural networks typically assume independent connectivity, overlooking the local motif structures prevalent in biological circuits. Here, we investigate how four second-order synaptic motifs (chain, reciprocal, convergent, and divergent) shape the dynamics of nonlinear firing-rate networks. While previous studies have established that chain correlations generate outlier eigenvalues, we demonstrate that these motifs also jointly reshape the Jacobian eigenvalue bulk. Using the path-integral formalism, we derive a dynamic mean-field theory which reveals that the chain motif acts as a retarded feedback of the ensemble-mean activity through the response kernel, producing a rich repertoire of dynamical regimes, including ferromagnetic states and limit cycles. At sufficiently large magnitude, negative chain correlations produce a glassy, multistable regime that was previously mainly associated with partially symmetric networks. Our theory also distinguishes convergent from divergent motifs: divergent correlations primarily rescale temporal noise, while convergent correlations suppress temporal chaos by converting nonzero mean activity into quenched heterogeneity. Finally, analyses of the Lyapunov spectrum and participation-ratio dimension show that motif structure changes the geometry of chaotic activity, reducing entropy production and attractor dimensionality even when the effective spectral edge is held fixed. Together, these findings establish second-order motifs as a fundamental structural mechanism governing the dynamical regimes of local cortical circuits.
