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随机神经网络中的活动维度

David G Clark¹, L F Abbott¹, Ashok Litwin-Kumar¹

¹Zuckerman Institute, Department of Neuroscience, Columbia University, New York, New York 10027, USA.

Physical review letters

|September 29, 2023

概括

研究人员使用动态平均场理论 (DMFT) 计算了随机神经网络中的交叉共差. 这揭示了这些复杂系统中神经活动协调的有效维度和时间范围的洞察力.

科学领域:

计算神经科学是一种神经科学.
机器学习理论机器学习理论
复杂的系统复杂的系统.

背景情况:

神经网络是复杂的动态系统,对信息处理至关重要.
了解协调活动,如交叉共变量,是解读网络功能和学习的关键.
动态平均场理论 (DMFT) 解释了混乱活动,但缺乏交叉协方差计算.

研究的目的:

开发和应用一个自相一致的动态平均场理论 (DMFT) 来计算随机神经网络中的交叉共变性.
在正规的随机网络模型中研究时空活动协调.
将理论框架概括为非独立且相同分布的 (non-i.i.d.) 连接器. 连接器. 连接器.

主要方法:

采用双位腔动态平均场理论 (DMFT) 方法进行自我一致的交叉共变率计算.
分析了一个经典的随机神经网络模型,具有独立且相同分布的 (i.i.d.) 连接器. 连接器. 连接器.
将分析扩展到具有部分对称性,非i.i.d.的网络. 连接器. 连接器. 连接器.

主要成果:

证明神经活动具有广泛但微小的有效维度.
确定了长时间的人口层面的时间尺度,控制了活动动态.
提供了适用于各种单元动态和合结构的通用理论框架.

结论:

开发的DMFT方法成功量化了交叉协差,为神经网络动态提供了新的分析工具.
这些发现揭示了随机网络中协调活动的基本特性,这些特性与生物和人工系统相关.
理论框架的灵活性允许研究更具生物学和计算现实的网络结构.

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