We introduce frequency propagation, a learning algorithm for nonlinear physical networks. In a resistive electrical circuit with variable resistors, an activation current is applied at a set of input nodes at one frequency, and an error current is applied at a set of output nodes at another frequency. The voltage response of the circuit to these boundary currents is the superposition of an `activation signal' and an `error signal' whose coefficients can be read in different frequencies of the frequency domain. Each conductance is updated proportionally to the product of the two coefficients. The learning rule is local and proved to perform gradient descent on a loss function. We argue that frequency propagation is an instance of a multi-mechanism learning strategy for physical networks, be it resistive, elastic, or flow networks. Multi-mechanism learning strategies incorporate at least two physical quantities, potentially governed by independent physical mechanisms, to act as activation and error signals in the training process. Locally available information about these two signals is then used to update the trainable parameters to perform gradient descent. We demonstrate how earlier work implementing learning via chemical signaling in flow networks also falls under the rubric of multi-mechanism learning.

翻译：我们引入频率传播,这是非线性物理网络的学习算法。在一个带变量阻力的抗电电路中,在一个频率的一组输入节点上应用激活电流,另一个频率的一组输出节点上应用错误流。电路对这些边界流的电压反应是“激活信号”和“传感器信号”的叠加,其系数可以在频率域的不同频率中读取。每种电路都与两个系数的产物成比例的更新。学习规则是局部性的,并证明可以对损失函数进行梯度下降。我们争辩说,频率传播是物理网络多机械学习战略的例子,可以是抗力的,是弹性的,也可以是流网络。多机械学习战略至少包含两个物理量,可能由独立的物理机制管理,作为培训过程中的激活和错误信号。关于这两个信号的当地现有信息随后被用来更新可训练参数,以进行梯度下降。我们证明,频率传播是物理网络中化学信号学习的多式学习的早期工作也在图象学习之下。