Towards Trainable Media: Using Waves for Neural Network-Style Training
In this paper we study the concept of using the interaction between waves and
a trainable medium in order to construct a matrix-vector multiplier. In
particular we study such a device in the context of the backpropagation
algorithm, which is commonly used for training neural networks. Here, the
weights of the connections between neurons are trained by multiplying a
forward' signal with a backwards propagating error' signal. We show that this
concept can be extended to trainable media, where the gradient for the local
wave number is given by multiplying signal waves and error waves. We provide a
numerical example of such a system with waves traveling freely in a trainable
medium, and we discuss a potential way to build such a device in an integrated
photonics chip.
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