Found in varied contexts from neurons to ants to fish, binary decision-making is one of the simplest forms of collective computation. In this process, information collected by individuals about an uncertain environment is accumulated to guide behavior at the aggregate scale. We study binary decision-making dynamics in networks responding to inputs with small signal-to-noise ratios, looking for quantitative measures of collectivity that control performance in this task. We find that decision accuracy is directly correlated with the speed of collective dynamics, which is in turn controlled by three factors: the leading eigenvalue of the network adjacency matrix, the corresponding eigenvector’s participation ratio, and distance from the corresponding symmetry-breaking bifurcation. A novel approximation of the maximal attainable timescale near such a bifurcation allows us to predict how decision-making performance scales in large networks based solely on their spectral properties. Specifically, we explore the effects of localization caused by the hierarchical assortative structure of a “rich club” topology. This gives insight into the trade-offs involved in the higher-order structure found in living networks performing collective computations.

在从神经元到蚂蚁到鱼的各种环境中发现，二元决策是最简单的集体计算形式之一。在这个过程中，个人收集的关于不确定环境的信息被积累起来，以指导总体规模的行为。我们研究了响应具有小信噪比的输入的网络中的二元决策动态，寻找控制该任务性能的集体的定量测量。我们发现决策精度与集体动力学的速度直接相关，而集体动力学的速度又受三个因素控制：网络邻接矩阵的主要特征值、相应的特征向量的参与率以及与相应的对称破坏分岔的距离。在这种分叉附近的最大可达到时间尺度的新近似使我们能够预测决策性能如何在大型网络中仅基于它们的光谱特性进行扩展。具体来说，我们探讨了由“富俱乐部”拓扑的分层分类结构引起的本地化影响。这让我们深入了解在执行集体计算的活网络中发现的高阶结构所涉及的权衡。