论文标题
HEBBIAN学习的神经突触网络的建模和合同
Modeling and Contractivity of Neural-Synaptic Networks with Hebbian Learning
论文作者
论文摘要
本文涉及对两个最常用的复发性神经网络模型（即Hopfield神经网络和点火率神经网络）的建模和分析，该模型涉及HEBBIAN学习规则的动态复发连接。为了捕获神经回路的突触稀疏性，我们提出了低维的表述。然后，我们表征某些关键动力学属性。首先，我们给出以生物学启发的远期不变性结果。然后，我们为模型的非欧国人合同提供了足够的条件。我们的收缩分析导致了时变轨迹的稳定性和稳健性 - 对于由Hebbian和Antibbian规则控制的具有兴奋性和抑制性突触的网络。对于每个模型，我们提出了基于生物学上有意义的数量（例如，神经和突触衰减率，最大程度和最大突触强度）的合并性测试。然后，我们表明这些模型满足了戴尔的原则。最后，我们通过数值示例说明了结果的有效性。
This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian learning rules. To capture the synaptic sparsity of neural circuits we propose a low dimensional formulation. We then characterize certain key dynamical properties. First, we give biologically-inspired forward invariance results. Then, we give sufficient conditions for the non-Euclidean contractivity of the models. Our contraction analysis leads to stability and robustness of time-varying trajectories -- for networks with both excitatory and inhibitory synapses governed by both Hebbian and anti-Hebbian rules. For each model, we propose a contractivity test based upon biologically meaningful quantities, e.g., neural and synaptic decay rate, maximum in-degree, and the maximum synaptic strength. Then, we show that the models satisfy Dale's Principle. Finally, we illustrate the effectiveness of our results via a numerical example.
