ABSTRACT The ultimate goal of neuroscience is to ultimately understand how the brain functions. The advancement of brain imaging shows us how the brain continuously alternates complex activity patterns and experimentally reveals how these patterns are responsible for memory, association, reasoning, and countless other tasks. Two fundamental parameters, dilution (the number of connections per node), and symmetry (the number of bidirectional connections of the same weight) characterise two fundamental features underlying the networks that connect the single neurons in the brain and generate these patterns. Mammalian brains show large variations of dilution, and mostly asymmetric connectivity, unfortunately the advantages which drove evolution to these state of network dilution and asymmetry are still unknown. Here, we studied the effects of symmetry and dilution on a discrete-time recurrent neural network with McCulloch–Pitts neurons. We use an exhaustive approach, in which we probe all possible inputs for several randomly connected neuron networks with different degrees of dilution and symmetry. We find an optimum value for the synaptic dilution and symmetry, which turns out to be in striking quantitative agreement with what previous researchers have found in the brain cortex, neocortex and hippocampus. The diluted asymmetric brain shows high memory capacity and pattern recognition speed, but most of all it is the less energy-consumptive with respect to fully connected and symmetric network topologies.

中文翻译：

---

高效大脑中的网络稀释和不对称

摘要 神经科学的最终目标是最终了解大脑的功能。大脑成像的进步向我们展示了大脑如何不断地交替复杂的活动模式，并通过实验揭示了这些模式如何负责记忆、联想、推理和无数其他任务。两个基本参数，稀释（每个节点的连接数）和对称性（相同权重的双向连接数）表征了连接大脑中单个神经元并生成这些模式的网络的两个基本特征。哺乳动物的大脑表现出很大的稀释变化，并且主要是不对称的连接，不幸的是，驱动进化到这些网络稀释和不对称状态的优势仍然未知。这里，我们研究了对称性和稀释对具有 McCulloch-Pitts 神经元的离散时间递归神经网络的影响。我们使用了一种详尽的方法，在该方法中，我们为几个具有不同稀释度和对称性的随机连接的神经元网络探测所有可能的输入。我们找到了突触稀释和对称性的最佳值，结果与之前研究人员在大脑皮层、新皮层和海马体中发现的结果具有惊人的定量一致。稀释的非对称大脑显示出较高的记忆容量和模式识别速度，但最重要的是，相对于完全连接和对称的网络拓扑，它的能量消耗较低。其中我们探测了几个具有不同稀释度和对称度的随机连接的神经元网络的所有可能输入。我们找到了突触稀释和对称性的最佳值，结果与之前研究人员在大脑皮层、新皮层和海马体中发现的结果具有惊人的定量一致。稀释的非对称大脑显示出较高的记忆容量和模式识别速度，但最重要的是，相对于完全连接和对称的网络拓扑，它的能量消耗较低。其中我们探测了几个具有不同稀释度和对称度的随机连接的神经元网络的所有可能输入。我们找到了突触稀释和对称性的最佳值，结果与之前研究人员在大脑皮层、新皮层和海马体中发现的结果具有惊人的定量一致。稀释的非对称大脑显示出较高的记忆容量和模式识别速度，但最重要的是，相对于完全连接和对称的网络拓扑，它的能量消耗较低。