Characterizing the relation between weight structure and input/output statistics is fundamental for understanding the computational capabilities of neural circuits. In this work, I study the problem of storing associations between analog signals in the presence of correlations, using methods from statistical mechanics. I characterize the typical learning performance in terms of the power spectrum of random input and output processes. I show that optimal synaptic weight configurations reach a capacity of 0.5 for any fraction of excitatory to inhibitory weights and have a peculiar synaptic distribution with a finite fraction of silent synapses. I further provide a link between typical learning performance and principal components analysis in single cases. These results may shed light on the synaptic profile of brain circuits, such as cerebellar structures, that are thought to engage in processing time-dependent signals and performing on-line prediction.

表征权重结构与输入/输出统计数据之间的关系是了解神经电路计算能力的基础。在这项工作中，我研究了使用统计力学方法在存在相关性的情况下存储模拟信号之间的关联的问题。我根据随机输入和输出过程的功率谱来描述典型的学习表现。我表明，对于任何比例的兴奋性重量到抑制重量，最佳的突触权重配置均达到0.5的容量，并且具有有限比例的无声突触具有特殊的突触分布。在单个案例中，我进一步提供了典型学习成绩与主成分分析之间的联系。这些结果可能会阐明脑回路的突触特征，