Nonlinear Processing with Linear Optics

Deep neural networks have achieved remarkable breakthroughs by leveraging multiple layers of data processing to extract hidden representations, albeit at the cost of large electronic computing power. To enhance energy efficiency and speed, the optical implementation of neural networks aims to harness the advantages of optical bandwidth and the energy efficiency of optical interconnections. In the absence of low-power optical nonlinearities, the challenge in the implementation of multilayer optical networks lies in realizing multiple optical layers without resorting to electronic components. In this study, we present a novel framework that uses multiple scattering that is capable of synthesizing programmable linear and nonlinear transformations concurrently at low optical power by leveraging the nonlinear relationship between the scattering potential, represented by data, and the scattered field. Theoretical and experimental investigations show that repeating the data by multiple scattering enables non-linear optical computing at low power continuous wave light.

Forward-Forward Training of an Optical Neural Network

Neural networks (NN) have demonstrated remarkable capabilities in various tasks, but their computation-intensive nature demands faster and more energy-efficient hardware implementations. Optics-based platforms, using technologies such as silicon photonics and spatial light modulators, offer promising avenues for achieving this goal. However, training multiple trainable layers in tandem with these physical systems poses challenges, as they are difficult to fully characterize and describe with differentiable functions, hindering the use of error backpropagation algorithm. The recently introduced Forward-Forward Algorithm (FFA) eliminates the need for perfect characterization of the learning system and shows promise for efficient training with large numbers of programmable parameters. The FFA does not require backpropagating an error signal to update the weights, rather the weights are updated by only sending information in one direction. The local loss function for each set of trainable weights enables low-power analog hardware implementations without resorting to metaheuristic algorithms or reinforcement learning. In this paper, we present an experiment utilizing multimode nonlinear wave propagation in an optical fiber demonstrating the feasibility of the FFA approach using an optical system. The results show that incorporating optical transforms in multilayer NN architectures trained with the FFA, can lead to performance improvements, even with a relatively small number of trainable weights. The proposed method offers a new path to the challenge of training optical NNs and provides insights into leveraging physical transformations for enhancing NN performance.

Nonlinear Optical Data Transformer for Machine Learning

Modern machine learning models use an ever-increasing number of parameters to train (175 billion parameters for GPT-3) with large datasets to obtain better performance. Bigger is better has been the norm. Optical computing has been reawakened as a potential solution to large-scale computing through optical accelerators that carry out linear operations while reducing electrical power. However, to achieve efficient computing with light, creating and controlling nonlinearity optically rather than electronically remains a challenge. This study explores a reservoir computing (RC) approach whereby a 14 mm long few-mode waveguide in LiNbO3 on insulator is used as a complex nonlinear optical processor. A dataset is encoded digitally on the spectrum of a femtosecond pulse which is then launched in the waveguide. The output spectrum depends nonlinearly on the input. We experimentally show that a simple digital linear classifier with 784 parameters using the output spectrum from the waveguide as input increased the classification accuracy of several databases compared to non-transformed data, approximately 10$\%$. In comparison, a deep digital neural network (NN) with 40000 parameters was necessary to achieve the same accuracy. Reducing the number of parameters by a factor of $\sim$50 illustrates that a compact optical RC approach can perform on par with a deep digital NN.