  Photonic neural networks offer a promising alternative to traditional
electronic systems for machine learning accelerators due to their low latency
and energy efficiency. However, the challenge of implementing the
backpropagation algorithm during training has limited their development. To
address this, alternative machine learning schemes, such as extreme learning
machines (ELMs), have been proposed. ELMs use a random hidden layer to increase
the feature space dimensionality, requiring only the output layer to be trained
through linear regression, thus reducing training complexity. Here, we
experimentally demonstrate a programmable photonic extreme learning machine
(PPELM) using a hexagonal waveguide mesh, and which enables to program directly
on chip the input feature vector and the random hidden layer. Our system also
permits to apply the nonlinearity directly on-chip by using the systems
integrated photodetecting elements. Using the PPELM we solved successfully
three different complex classification tasks. Additioanlly, we also propose and
demonstrate two techniques to increase the accuracy of the models and reduce
their variability using an evolutionary algorithm and a wavelength division
multiplexing approach, obtaining excellent performance. Our results show that
programmable photonic processors may become a feasible way to train competitive
machine learning models on a versatile and compact platform.
