Nonlinear optical extreme learner via data reverberation with incoherent light.

Artificial neural networks have revolutionized fields from computer vision to natural language processing, yet their growing energy and computational demands threaten future progress. Optical neural networks promise greater speed, bandwidth, and energy efficiency but suffer from weak optical nonlinearities. Here, we demonstrate a low-power, incoherent-light-compatible optical extreme learner that leverages "data nonlinearity" from optical pattern reverberations, eliminating reliance on intrinsic nonlinear materials. By encoding input data in the spatial polarization distribution of a tailored optical cavity and allowing light to pass through it multiple times, we achieve nonlinear transformations at extremely low optical power. Coupled with a simple trainable readout, our optical learner consistently outperforms linear digital networks in standard image classification tasks and XOR benchmarks, delivering accuracy matching fully nonlinear digital models. Our compact, energy-efficient approach substantially reduces complexity, cost, and energy consumption, paving the way for practical, scalable all-optical machine learning platforms.