Photonic Kolmogorov-Arnold networks based on self-phase modulation in nonlinear waveguides.

Photonic neural networks have attracted intense interest during the past decade, with an extensive number of propositions trying to mimic various forms of the established digital models. This field envisages low-power and low-latency, highly parallelized hardware implementations that count on the vast capacity of photonics. Kolmogorov-Arnold networks were recently proposed, offering improved scalability and interpretability compared to conventional multilayer perceptrons. From this point of view, Kolmogorov-Arnold networks constitute a promising field for implementations which exploit the full pallet of photonic strengths, mitigating the scalability barrier. Here, we propose and experimentally showcase the potential of self-phase modulation in nonlinear waveguides as a versatile generator of arbitrary nonlinear activation functions for the ultra-fast photonic implementation of Kolmogorov-Arnold networks. The efficacy of the proposed approach is demonstrated on both regression and classification tasks, where the photonic implementation matches digital performance and, in specific cases, surpasses the digital baseline used in our comparison.