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 random subset of the waveguide channels, one can perform an embedding from a higher- to a lower-dimensional space that respects the Johnson–Lindenstrauss lemma and nearly preserves the Euclidean distances. The distance-preserving random projection through photonic lattices requires intermediate disorder levels that allow diffusive propagation of light. 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 computation stage.

© 2021 Optical Society of America

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