  Neural networks find widespread use in scientific and technological
applications, yet their implementations in conventional computers have
encountered bottlenecks due to ever-expanding computational needs. Photonic
neuromorphic hardware, which manipulates information and represents data
continuously in the optical domain, is one of the promising platforms with
potential advantages of massive parallelism, ultralow latency, and reduced
energy consumption. While linear photonic neural networks are within reach,
photonic computing with large-scale optical nonlinear nodes remains largely
unexplored. Here, we demonstrate a large-scale, high-performance nonlinear
photonic neural system based on a disordered polycrystalline slab composed of
lithium niobate nanocrystals. Mediated by random quasi-phase-matching and
multiple scattering, linear and nonlinear optical speckle features are
generated as the interplay between the simultaneous linear random scattering
and the second-harmonic generation, defining a complex neural network in which
the second-order nonlinearity acts as internal nonlinear activation functions.
Benchmarked against linear random projection, such nonlinear mapping embedded
with rich physical computational operations shows improved performance across a
large collection of machine learning tasks in image classification, regression,
and graph classification with varying complexity. Demonstrating up to 27,648
input and 3,500 nonlinear output nodes, the combination of optical nonlinearity
and random scattering serves as a scalable computing engine for diverse
applications.
