Photonic Neural Networks with Kramers–Kronig Activation

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