We study multifrequency Hebbian plasticity by analyzing phenomenological models of weakly connected neural networks. We start with an analysis of a model for single-frequency networks previously shown to learn and memorize phase differences between component oscillators. We then study a model for gradient frequency neural networks (GrFNNs) which extends the single-frequency model by introducing frequency detuning and nonlinear coupling terms for multifrequency interactions. Our analysis focuses on models of two coupled oscillators and examines the dynamics of steady-state behaviors in multiple parameter regimes available to the models. We find that the model for two distinct frequencies shares essential dynamical properties with the single-frequency model and that Hebbian learning results in stronger connections for simple frequency ratios than for complex ratios. We then compare the analysis of the two-frequency model with numerical simulations of the GrFNN model and show that Hebbian plasticity in the latter is locally dominated by a nonlinear resonance captured by the two-frequency model.

我们通过分析弱连接神经网络的现象学模型来研究多频赫布可塑性。我们首先分析先前显示的单频网络模型，该模型用于学习和记忆组件振荡器之间的相位差。然后，我们研究了梯度频率神经网络 (GrFNN) 模型，该模型通过为多频交互引入频率失谐和非线性耦合项来扩展单频模型。我们的分析侧重于两个耦合振荡器的模型，并检查模型可用的多个参数范围内稳态行为的动力学。我们发现两个不同频率的模型与单频模型共享基本的动力学特性，并且 Hebbian 学习导致简单频率比的连接比复杂比更强。然后，我们将双频模型的分析与 GrFNN 模型的数值模拟进行比较，并表明后者的赫布塑性在局部由双频模型捕获的非线性共振主导。