Kernel computations from large-scale random features obtained by Optical Processing Units

TL;DR

This paper explores how optical processing units (OPUs) can efficiently compute large-scale random features for kernel approximation, enabling faster and more energy-efficient machine learning applications like image classification.

Contribution

It introduces a new method for kernel computation using OPUs, connecting the OPU operation to polynomial kernels and extending to arbitrary powers of the feature map.

Findings

OPU-based kernels are competitive in kernel ridge regression.

The method achieves significant time and energy savings.

Extensions to arbitrary powers improve flexibility.

Abstract

Approximating kernel functions with random features (RFs)has been a successful application of random projections for nonparametric estimation. However, performing random projections presents computational challenges for large-scale problems. Recently, a new optical hardware called Optical Processing Unit (OPU) has been developed for fast and energy-efficient computation of large-scale RFs in the analog domain. More specifically, the OPU performs the multiplication of input vectors by a large random matrix with complex-valued i.i.d. Gaussian entries, followed by the application of an element-wise squared absolute value operation - this last nonlinearity being intrinsic to the sensing process. In this paper, we show that this operation results in a dot-product kernel that has connections to the polynomial kernel, and we extend this computation to arbitrary powers of the feature map. Experiments demonstrate that the OPU kernel and its RF approximation achieve competitive performance in applications using kernel ridge regression and transfer learning for image classification. Crucially, thanks to the use of the OPU, these results are obtained with time and energy savings.