The Link between Artificial Neural Networks and Propagation in Random Media

Random media (RM) with tailored optical properties are attractive for their many applications. Transmission channels (TCs) in RM can be effectively controlled, and their rich behavior is due to the multitude of interacting optical modes. We demonstrate that TCs in RM act as an untrained artificial neural network (ANN), as deep as the amount of perturbations. This lets us obtain a random optical machine (ROM), able to do computation by reservoir computing (RC).

TCs in RM can be modulated by tuning the transmission matrix (TM) through iterative algorithms that modify the input until a designed output is obtained. This approach treats RM as black boxes, i.e., it treats the TM as an ANN hidden layer of a reservoir computing (RC) strategy, a machine learning technique that left untrained the ANN internal part and optimizes weights only at input and readout.

By electromagnetic perturbation theory, we prove that weakly tampering the medium generates a new TM, given by the product between the previous TM and the perturbative one. We then design the ANN depth of our ROM by optimizing the amount of perturbations, moving from an extreme learning machine (unperturbed system) to untrained deep learning (many perturbations).