Abstract
Extreme learning machines explore nonlinear random projections to perform computing tasks on high-dimensional output spaces. Since training only occurs at the output layer, the approach has the potential to speed up the training process and the capacity to turn any physical system into a computing platform. Yet, requiring strong nonlinear dynamics, optical solutions operating at fast processing rates and low power can be hard to achieve with conventional nonlinear optical materials. In this context, this manuscript explores the possibility of using atomic gases in near-resonant conditions to implement an optical extreme learning machine leveraging their enhanced nonlinear optical properties. Our results suggest that these systems have the potential not only to work as an optical extreme learning machine but also to perform these computations at the few-photon level, paving opportunities for energy-efficient computing solutions.

Abstract
Exploring optical analogues with paraxial fluids of light has been a subject of great interest over the past years. Despite many optical analogues having been created and explored with these systems, they have some limitations that usually hinder the observation of the desired dynamics. Since these systems map the effective time onto the propagation direction, the fixed size of the nonlinear media limits the experimental effective time, and only the output state is accessible. In this work, we present a solution to overcome these problems in the form of an optical feedback loop, which consists of reconstructing the output state, by using the off-axis digital holography technique, and then re-injecting it again at the entrance of the medium through the utilization of Spatial Light Modulators. This technique enables access to intermediate states and an extension of the system effective time. Furthermore, the total control of the amplitude and phase of the beam at the input of the medium, also allows us to explore more exotic configurations that may be interesting in the context of optical analogues, that otherwise would be hard to create. To demonstrate the capabilities of the setup, we explore qualitatively some case studies, such as the dark soliton decay into vortices with the propagation of shock waves, and the collision dynamics between three flat-top states. The results presented in this work pave the way for probing new dynamics with paraxial fluids of light.

Abstract
This communication explores an optical extreme learning architecture to unravel the impact of using a nonlinear optical media as an activation layer. Our analysis encloses the evaluation of multiple parameters, with special emphasis on the efficiency of the training process, the dimensionality of the output space, and computing performance across tasks associated with the classification in low-dimensionality input feature spaces. The results enclosed provide evidence of the importance of the nonlinear media as a building block of an optical extreme learning machine, effectively increasing the size of the output space, the accuracy, and the generalization performances. These findings may constitute a step to support future research on the field, specifically targeting the development of robust general-purpose all-optical hardware to a full-stack integration with optical sensing devices toward edge computing solutions.

Abstract
Lately, the field of optical computing resurfaced with the demonstration of a series of novel photonic neuromorphic schemes for autonomous and inline data processing promising parallel and light-speed computing. We emphasize the Photonic Extreme Learning Machine (PELM) as a versatile configuration exploring the randomness of optical media and device production to bypass the training of the hidden layer. Nevertheless, the implementation of this framework is limited to having the output layer performed digitally. In this work, we extend the general PELM implementation to an all-optical configuration by exploring the amplitude modulation from a spatial light modulator (SLM) as an output linear layer with the main challenge residing in the training of the output weights. The proposed solution explores the package pyTorch to train a digital twin using gradient descent back-propagation. The trained model is then transposed to the SLM performing the linear output layer. We showcase this methodology by solving a two-class classification problem where the total intensity reaching the camera predicts the class of the input sample.

Abstract
Easily accessible through tabletop experiments, paraxial fluids of light are emerging as promising platforms for the simulation and exploration of quantumlike phenomena. In particular, the analogy builds on a formal equivalence between the governing model for a Bose-Einstein condensate under the mean-field approximation and the model of laser propagation inside nonlinear optical media under the paraxial approximation. Yet, the fact that the role of time is played by the propagation distance in the analog system imposes strong bounds on the range of accessible phenomena due to the limited length of the nonlinear medium. In this Letter, we present an experimental approach to solve this limitation in the form of a digital feedback loop, which consists of the reconstruction of the optical states at the end of the system followed by their subsequent reinjection exploiting wavefront shaping techniques. The results enclosed demonstrate the potential of this approach to access unprecedented dynamics, paving the way for the observation of novel phenomena in these systems.