标题： 离散吸引子神经网络中密集模式的动力稳定性 显示英文标题

标题： Dynamical stability for dense patterns in discrete attractor neural networks

摘要： 神经网络存储多个离散吸引子是生物记忆的经典模型。 以前，这类网络的动力学稳定性只能在高度限制的条件下得到保证。 在这里，我们推导了一个关于具有分级神经活动的广泛网络中离散固定点局部稳定性的理论，并且在存在噪声的情况下。 通过直接分析雅可比谱的主体和异常值，我们表明所有固定点在临界负载以下都是稳定的，该临界负载与经典的\textit{临界容量}不同，并且取决于固定点中神经活动的统计特性以及单个神经元的激活函数。 我们的分析突出了阈值线性激活和稀疏模式的计算优势。 显示英文摘要

摘要： Neural networks storing multiple discrete attractors are canonical models of biological memory. Previously, the dynamical stability of such networks could only be guaranteed under highly restrictive conditions. Here, we derive a theory of the local stability of discrete fixed points in a broad class of networks with graded neural activities and in the presence of noise. By directly analyzing the bulk and outliers of the Jacobian spectrum, we show that all fixed points are stable below a critical load that is distinct from the classical \textit{critical capacity} and depends on the statistics of neural activities in the fixed points as well as the single-neuron activation function. Our analysis highlights the computational benefits of threshold-linear activation and sparse-like patterns.