Shannon Entropy Helps Optimize the Performance of a Frequency-Multiplexed Extreme Learning Machine

Abstract

Knowing the dynamics of neuromorphic photonic schemes would allow their optimization for controlled data-processing capability in possibly simplified designs and minimized energy consumption levels. In nonlinear substrates such as optical fibers or semiconductors, these dynamics can widely vary depending on the encoded inputs, even for a single set of physical parameters. Thus, other approaches are required to optimize the schemes. Here, I consider a frequency-multiplexed Extreme Learning Machine (ELM) that encodes information in the line amplitudes of a frequency comb and processes this information in a single-mode fiber subject to Kerr nonlinearity. Its performance is evaluated with Iris and Breast Cancer Wisconsin classification datasets. I introduce the notions of Shannon entropy of optical power, phase, and spectrum and numerically show that the optimization of system parameters (continuous-wave laser optical power and the modulation depth of the subsequent phase modulator as well as the fiber group-velocity dispersion and length) yields the ELM performance that places this neuromorphic scheme among the top-performing state-of-the-art computer-based machine-learning models. I show that the ELM's performance is robust against initial noise, paving the way for cost-effective designs. Using Soliton Radiation Beat Analysis, I show that information encoding symmetric in frequency-comb lines yields the formation of input-power-dependent Akhmediev-breather-like structures and Peregrine solitons, whereas asymmetric encoding of the comb exhibits an additional regime of soliton crystals. Also, I discuss that asymmetric encoding supports the theory of Four-Wave Mixing as a data processing mechanism, whereas symmetric encoding underlines the theory of soliton-mediated information processing. The findings advance the toolbox and knowledge of Neuromorphic Photonics and general Nonlinear Optics.