Tiago David Ferreira

Abstract
Extreme Learning Machines (ELMs) are a versatile Machine Learning (ML) algorithm that features as the main advantage the possibility of a seamless implementation with physical systems. Yet, despite the success of the physical implementations of ELMs, there is still a lack of fundamental understanding in regard to their optical implementations. In this context, this work makes use of an optical complex media and wavefront shaping techniques to implement a versatile optical ELM playground to gain a deeper insight into these machines. In particular, we present experimental evidences on the correlation between the effective dimensionality of the hidden space and its generalization capability, thus bringing the inner workings of optical ELMs under a new light and opening paths toward future technological implementations of similar principles.

Abstract
Light propagating in nonlinear optical materials opens the possibility to emulate quantum fluids of light with accessible tabletop experiments by taking advantage of the hydrodynamical interpretation. In this context, various optical materials have been studied in recent years, with nematic liquid crystals appearing as one of the most promising ones due to their controllable properties. Indeed, the application of an external electric field can tune their nonlocal response, and this mechanism may be useful for producing fluids of light and developing optical analogues. In this work, we extend the applicability of nematic liquid crystal to support optical analogues and study the possibility of emulating turbulent phenomena by using two fluids of light. These fluids interact with each other through the nonlinearity of the medium and generate instabilities that will lead to turbulent regimes. We also explore the possibility of exciting turbulent regimes through the decay of dark soliton stripes. The preliminary results are presented.

Abstract
Abstract The propagation of light in nonlinear optical media has been widely used as a tabletop platform for emulating quantum-like phenomena due to their similar theoretical description to quantum fluids. These fluids of light are often used to study 2-dimensional phenomena involving superfluid-like flows, yet turbulent regimes still remain underexplored. In this work, we study the possibility of creating 2-dimensional turbulent phenomena and probing their signatures in the kinetic energy spectrum. To that end, we emulate and disturb a fluid of light with an all-optical defect using the propagation of two beams in a photorefractive crystal. Our experimental results show that the superfluid regime of the fluid of light breaks down at a critical velocity at which the defect starts to exert a drag force on the fluid, in accordance with the theoretical and numerical predictions. Furthermore, in this dissipative regime, nonlinear perturbations are excited on the fluid that can decay into vortex structures and thus precede a turbulent state. Using the off-axis digital holographic method, we reconstructed the complex description of the output fluids and calculated the incompressible component of the kinetic energy. With these states, we observed the expected power law that characterizes the generated turbulent vortex dipole structures. The findings enclosed in this manuscript align with the theoretical predictions for the vortex structures of 2-dimensional quantum fluids and thus may pave the way to the observation of other distinct hallmarks of turbulent phenomena, such as distinct turbulent regimes and their associated power laws and energy cascades.

Abstract
Extreme learning machines (ELMs) are a versatile machine learning technique that can be seamlessly implemented with optical systems. In short, they can be described as a network of hidden neurons with random fixed weights and biases, that generate a complex behaviour in response to an input. Yet, despite the success of the physical implementations of ELMs, there is still a lack of fundamental understanding about their optical implementations. This work makes use of an optical complex media to implement an ELM and introduce an ab-initio theoretical framework to support the experimental implementation. We validate the proposed framework, in particular, by exploring the correlation between the rank of the outputs, H, and its generalization capability, thus shedding new light into the inner workings of optical ELMs and opening paths towards future technological implementations of similar principles.

Abstract
Reservoir computing is a versatile approach for implementing physically Recurrent Neural networks which take advantage of a reservoir, consisting of a set of interconnected neurons with temporal dynamics, whose weights and biases are fixed and do not need to be optimized. Instead, the training takes place only at the output layer towards a specific task. One important requirement for these systems to work is nonlinearity, which in optical setups is usually obtained via the saturation of the detection device. In this work, we explore a distinct approach using a photorefractive crystal as the source of the nonlinearity in the reservoir. Furthermore, by leveraging on the time response of the photorefractive media, one can also have the temporal interaction required for such architecture. If we space out in time the propagation of different states, the temporal interaction is lost, and the system can work as an extreme learning machine. This corresponds to a physical implementation of a Feed-Forward Neural Network with a single hidden layer and fixed random weights and biases. Some preliminary results are presented and discussed. © Published under licence by IOP Publishing Ltd.