In-situ training in programmable photonic frequency circuits.

Optical artificial neural networks (OANNs) leverage the advantages of photonic technologies including high processing speeds, low energy consumption, and mass production to establish a competitive and scalable platform for machine learning applications. While recent advancements have focused on harnessing spatial or temporal modes of light, the frequency domain attracts a lot of attention, with current implementations including spectral multiplexing, neural networks in nonlinear optical systems and extreme learning machines. Here, we present an experimental realization of a programmable photonic frequency circuit, realized with fiber-optical components, and implement the training with optical weight control of an OANN operating in the frequency domain. Input data is encoded into phases of frequency comb modes, and programmable phase and amplitude manipulations of the spectral modes enable training of the OANN, without employing a digital model of the device. The trained OANN achieves multiclass classification accuracies exceeding 90 %, comparable to conventional machine learning approaches. This proof-of-concept demonstrates the feasibility of a multilayer OANN in the frequency domain and can be extended to a scalable, integrated photonic platform with ultrafast weights updates, with potential applications to single-shot classification in spectroscopy.