# Parallel Extreme Learning Machines Based on Frequency Multiplexing
## 5 Conclusions  
In this work we explored the parallelization capabilities of a photonic ELM based on frequency multiplexing, which had been hypothesized in our previous work [19]. We proved that propagating multiple light sources in the same setup allows both for an increase in the number of available neurons and for the execution of multiple non-interacting tasks. This parallelized scheme is expected to remain compatible with the optical weighting scheme proposed in [19], even if no experiment has been run in this sense yet. Figure 4: Results of single operation mode tests. The left panel contains results from the mushroom classification task. We report experimental results compared with the numerical simulation of our system, the score obtained by another photonic ELM reported in [8], and a software ELM with a number of neurons comparable to our experiment. The right panel contains results from the MNIST classification task. We report the results obtained by a numerical simulation featuring 10 combs (\(\sim\)300 neurons), a numerical simulation featuring 15 combs (\(\sim\)450 neurons), and a software ELM reported in [32] (\(\sim\)800 neurons). When present, error bars represent the standard deviation of the score over 100 random repartitions of training and testing data (more information in Section 4.2). When compared with an identical experiment run with a single light source, the current scheme displayed a slight decrease in performance. We expected this effect to be completely avoidable by increasing the SNR of data encoded in the combs, which can be obtained by increasing the light source power, by introducing optical amplification, or by reducing the losses at the laser source combiners. Our ELM performed similarly to a photonic one based on free-space propagation [8] when both were tested on the same task (mushroom classification). Numerical simulations also suggest that our scheme would perform similarly to a software ELM on tasks requiring hundreds of neurons such as MNIST digit classification. We tested the system with a maximum of \(N_{S}=3\) sources, but this number could be significantly increased. The \(C\)-band spans 4.4 THz and can hence accommodate approximately 300 neurons at the current spacing of \(\Omega\approx 16\) GHz, which means approximately 10 different combs similar to the ones employed in the current experiment. Moreover, \(\Omega\) could be decreased, which would lead to a more dense frequency multiplexing, provided that the employed spectral filters have enough resolution. We also note that the broadness of the comb itself could be increased or decreased, modifying the RF power driving PM\({}_{1}\) and PM\({}_{2}\) (hence, acting on the values \(m_{1}\) and \(m_{2}\)). In principle, a lower \(m_{1}\) value would generate smaller combs, allowing for even more operations in parallel to be executed at the expense of the number of neurons available for each operation. The main drawback of the current scheme is the information processing speed, limited by the programmable spectral filters whose maximum update rate is 2 Hz. Nevertheless, this speed can, in principle, be increased considerably. For instance, an integrated photonic version of this scheme may rely on a programmable spectral filter realized by a combination of WDM filters and electroptical absorption modulators, which should theoretically allow GHz rates to be reached. The present work further demonstrates the potential of photonic information processing in the frequency domain, particularly for ELMs. Conceptualization, A.L. and S.M. ; data curation, A.L. ; funding acquisition, S.M. ; investigation, A.L. ; methodology, A.L. and S.M. ; project administration, S.M. ; software, A.L. ; supervision, S.M. ; visualization, A.L. ; writing--original draft, A.L. ; writing--review and editing, S.M. All authors have read and agreed to the published version of the manuscript.