Nonlinear Optical Joint Transform Correlator for Low Latency Convolution Operations (2202.06444v2)

Abstract: Convolutions are one of the most relevant operations in AI systems. High computational complexity scaling poses significant challenges, especially in fast-responding network-edge AI applications. Fortunately, the convolution theorem can be executed on-the-fly in the optical domain via a joint transform correlator (JTC) offering to fundamentally reduce the computational complexity. Nonetheless, the iterative two-step process of a classical JTC renders them unpractical. Here we introduce a novel implementation of an optical convolution-processor capable of near-zero latency by utilizing all-optical nonlinearity inside a JTC, thus minimizing electronic signal or conversion delay. Fundamentally we show how this nonlinear auto-correlator enables reducing the high $O(n^4)$ scaling complexity of processing two-dimensional data to only $O(n^2)$. Moreover, this optical JTC processes millions of channels in time-parallel, ideal for large-matrix machine learning tasks. Exemplary utilizing the nonlinear process of four-wave mixing, we show light processing performing a full convolution that is temporally limited only by geometric features of the lens and the nonlinear material's response time. We further discuss that the all-optical nonlinearity exhibits gain in excess of $>10^{3}$ when enhanced by slow-light effects such as epsilon-near-zero. Such novel implementation for a machine learning accelerator featuring low-latency and non-iterative massive data parallelism enabled by fundamental reduced complexity scaling bears significant promise for network-edge, and cloud AI systems.