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Convolutions are one of the most relevant operations in artificialintelligence (AI) systems. High computational complexity scaling posessignificant challenges, especially in fast-responding network-edge AIapplications. Fortunately, the convolution theorem can be executed on-the-flyin the optical domain via a joint transform correlator (JTC) offering tofundamentally reduce the computational complexity. Nonetheless, the iterativetwo-step process of a classical JTC renders them unpractical. Here we introducea novel implementation of an optical convolution-processor capable of near-zerolatency by utilizing all-optical nonlinearity inside a JTC, thus minimizingelectronic signal or conversion delay. Fundamentally we show how this nonlinearauto-correlator enables reducing the high $O(n^4)$ scaling complexity ofprocessing two-dimensional data to only $O(n^2)$. Moreover, this optical JTCprocesses millions of channels in time-parallel, ideal for large-matrix machinelearning tasks. Exemplary utilizing the nonlinear process of four-wave mixing,we show light processing performing a full convolution that is temporallylimited only by geometric features of the lens and the nonlinear material'sresponse time. We further discuss that the all-optical nonlinearity exhibitsgain in excess of $>10^{3}$ when enhanced by slow-light effects such asepsilon-near-zero. Such novel implementation for a machine learning acceleratorfeaturing low-latency and non-iterative massive data parallelism enabled byfundamental reduced complexity scaling bears significant promise fornetwork-edge, and cloud AI systems.

Nonlinear Optical Joint Transform Correlator for Low Latency Convolution Operations