Integrated Random Projection and Dimensionality Reduction by Propagating Light in Photonic Lattices

TL;DR

This paper demonstrates that disordered photonic lattices can perform efficient, distance-preserving random projections for dimensionality reduction, leveraging light propagation to facilitate neural network processing.

Contribution

It introduces a novel method of using light propagation in disordered photonic lattices as a physical implementation of random projection for dimensionality reduction.

Findings

Photonic lattices can implement Johnson-Lindenstrauss embeddings.

Intermediate disorder levels enable diffusive light spreading for effective projection.

The scheme offers a simple, integrated approach to reduce data dimensionality.

Abstract

It is proposed that the propagation of light in disordered photonic lattices can be harnessed as a random projection that preserves distances between a set of projected vectors. This mapping is enabled by the complex evolution matrix of a photonic lattice with diagonal disorder, which turns out to be a random complex Gaussian matrix. Thus, by collecting the output light from a subset of the waveguide channels, one can perform an embedding from a higher-dimension to a lower-dimension space that respects the Johnson-Lindenstrauss lemma and nearly preserves the Euclidean distances. It is discussed that distance-preserving random projection through photonic lattices requires intermediate disorder levels that allow diffusive spreading of light from a single channel excitation, as opposed to strong disorder which initiates the localization regime. The proposed scheme can be utilized as a simple and powerful integrated dimension reduction stage that can greatly reduce the burden of a subsequent neural computing stage.