Small-scale photonic Kolmogorov-Arnold networks using standard telecom nonlinear modules

Photonic neural networks promise inference at the speed of light, yet most architectures combine linear optical meshes with electronic nonlinearities, reintroducing optical-electrical-optical bottlenecks. Kolmogorov-Arnold networks place trainable nonlinear functions on network edges, concentrating expressivity into a few structured modules. Each edge here is a single module built from a Mach-Zehnder interferometer, a semiconductor optical amplifier, and variable optical attenuators, giving a four-parameter transfer function set by gain saturation and interferometric mixing. A four-module network attains 94.3% accuracy (±3.9% s.d. over ten seeds) on nonlinear classification, and a seven-module network reaches R² = 0.986 ± 0.015 on six-input regression, remaining robust to 6-bit inputs and 14 dB signal-to-noise ratio. Here, we show that a fully differentiable physics model enables end-to-end optimization of these standard telecom modules, giving a practical route from simulation toward experimental demonstration of photonic Kolmogorov-Arnold networks.