Random Projections through multiple optical scattering: Approximating kernels at the speed of light

TL;DR

This paper introduces an optical device that performs random projections at the speed of light using multiple scattering, enabling fast, memory-efficient kernel approximations for large-scale machine learning tasks.

Contribution

The authors propose a novel optical system for random projections that eliminates the need for storing large matrices, significantly accelerating kernel computations.

Findings

Experimental results on MNIST match theoretical kernel performance.

Device enables real-time, memory-efficient kernel approximations.

Framework applicable to large datasets and various kernel types.

Abstract

Random projections have proven extremely useful in many signal processing and machine learning applications. However, they often require either to store a very large random matrix, or to use a different, structured matrix to reduce the computational and memory costs. Here, we overcome this difficulty by proposing an analog, optical device, that performs the random projections literally at the speed of light without having to store any matrix in memory. This is achieved using the physical properties of multiple coherent scattering of coherent light in random media. We use this device on a simple task of classification with a kernel machine, and we show that, on the MNIST database, the experimental results closely match the theoretical performance of the corresponding kernel. This framework can help make kernel methods practical for applications that have large training sets and/or require real-time prediction. We discuss possible extensions of the method in terms of a class of kernels, speed, memory consumption and different problems.