  Convolutions are one of the most relevant operations in artificial
intelligence (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.
