General-Purpose Nonlinear Function Approximation via Linear Integrated Photonics
2026-06-22 • Emerging Technologies
Emerging Technologies
AI summaryⓘ
The authors developed a new way to do complex math operations on light-based computer chips, which are good at simple, fast calculations but struggle with complicated ones. They use a trick called optical random Fourier feature mapping to turn difficult nonlinear functions into easier linear ones, making the computations simpler. This method works with standard silicon photonics without needing special materials and can handle many kinds of complex functions. Their experiments show it can do a wide range of nonlinear tasks, helping make future light-based computers more powerful and versatile.
photonic computingnonlinear functionsrandom Fourier featuresvector-matrix multiplicationsilicon photonicsoptical computingLegendre polynomialsactivation functionssoftmaxFresnel functions
Authors
Ayana Mizuno, Isamu Takai, Makoto Nakai, Atsutaka Miyamichi, Ryuichi Konishi, Satoshi Sunada
Abstract
Photonic computing has emerged as a promising platform for accelerating artificial intelligence workloads by enabling low-latency and energy-efficient linear operations such as vector-matrix multiplication. However, scalable on-chip high-order nonlinear processing remains challenging, limiting the functional versatility of current photonic hardware. Here, we present an optoelectronic approach for approximating high-order and high-dimensional nonlinear functions. The key to this approach lies in optical random Fourier feature mapping, which transforms nonlinear function evaluation into an equivalent linear computation. This approach enables nonlinear computing within a linear photonic framework, eliminating the need for complex optical nonlinear or active materials while preserving scalability and computational throughput in a simple silicon photonic circuit. We experimentally demonstrate a broad class of nonlinear functions, including tenth-order Legendre polynomials, computationally demanding special functions (Voigt, Fermi-Dirac, and Fresnel), neural-network activation functions, two-dimensional nonlinear functions, and a 10-dimensional softmax layer. This work establishes a general and scalable strategy for nonlinear computing in photonic integrated hardware and opens a pathway toward fully functional optical accelerators for next-generation computing systems.