Photonic Neural Networks with Kramers–Kronig Activation

Abstract

Photonic neural networks (PNNs) are promising to replace conventional deep learning hardware due to their potentially higher energy efficiency and computational speed. Other than the fast progress on optical linear transformer, the nonlinear activators are much less mature. Usually, the optical activators employ the nonlinear mapping from input amplitude to output amplitude, which is limited by high threshold and loss, or rely on additional bias voltage and heterogeneous integration of external circuits. Herein, the activation induced by the Kramers–Kronig relationship is proposed, i.e., the connection between amplitude and phase of the light field, but not purely the light amplitude itself, namely, Kramers–Kronig activation (KKA). PNN with KKA exhibits learning capability apparently better than the activation‐free linear network and comparable to the network with popular activation functions like ReLU, Softplus, and so on. Moreover, PNN with KKA is highly programmable and cascadable supporting ultra‐deep networks. The essence of KKA is attributed to the learning of nonlinear features in relatively low‐dimensional RN × N space by linear features in high‐dimensional CN × N space. Considering besides the amplitude–phase coupling, several other parameters like wavelength, frequency, polarization, etc., can be also mutually linked. This approach may expand to new avenues for optical activations.