Principles and metrics of extreme learning machines using a highly nonlinear fiber.

Optical computing offers potential for ultra high-speed and low-latency computation by leveraging the intrinsic properties of light, such as parallelism and linear as well as nonlinear ultra-high bandwidth signal transformations. Here, we explore the use of highly nonlinear optical fibers (HNLFs) as platforms for optical computing based on the concept of extreme learning machines (ELMs). To evaluate the information processing potential of the system, we consider both task-independent and task-dependent performance metrics. The former focuses on intrinsic properties such as effective dimensionality, quantified via principal component analysis (PCA) on the system response to random inputs. The latter evaluates classification task accuracy on the MNIST digit dataset, highlighting how the system performs under different compression levels and nonlinear propagation regimes. We show that input power and fiber characteristics significantly influence the dimensionality of the computational system, with longer fibers and higher dispersion producing up to 100 principal components (PCs) at input power levels of 30 mW, where the PC corresponds to the linearly independent dimensions of the system. The spectral distribution of the PC's eigenvectors reveals that the high-dimensional dynamics facilitating computing through dimensionality expansion are located within 40 nm of the pump wavelength at 1,560 nm, providing general insight for computing with nonlinear Schrödinger equation systems. Task-dependent results demonstrate the effectiveness of HNLFs in classifying MNIST dataset images. Using input data compression through PC analysis, we inject MNIST images of various input dimensionality into the system and study the impact of input power upon classification accuracy. At optimized power levels, we achieve a classification test accuracy of 87 % ± 1.3 %, significantly surpassing the baseline of 83.7 % from linear systems. Noteworthy, we find that the best performance is not obtained at maximal input power, i.e., maximal system dimensionality, but at more than one order of magnitude lower. The same is confirmed regarding the MNIST image's compression, where accuracy is substantially improved when strongly compressing the image to less than 50 PCs. These are highly relevant findings for the dimensioning of future, ultrafast optical computing systems that can capture and process sequential input information on femtosecond timescales.