提出神经网络存储模式的动态稳定性新理论，突破传统限制。
Dynamical stability for dense patterns in discrete attractor neural networks
- 基于雅可比谱分析，建立广义神经网络局部稳定性的理论框架。
- 发现稳定阈值与经典容量不同，受神经活动统计和激活函数影响。
- 揭示阈值线性激活与稀疏模式的计算优势，适合记忆系统研究者。
存储多个离散吸引子的神经网络是生物记忆的经典模型。以往，这类网络的动态稳定性仅在极严格条件下成立。本文推导出一类具有连续神经活动的网络在噪声存在下的离散不动点局部稳定性理论。通过直接分析雅可比矩阵的主体与异常值，我们证明所有不动点在低于一个临界负载时均稳定，该负载不同于经典的临界容量，取决于不动点中神经活动的统计特性以及单神经元激活函数。分析表明，阈值线性激活函数和类似稀疏的模式具有显著的计算优势。
原文摘要 · Abstract (English)
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 the 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.
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