  The recent progress of artificial intelligence (AI) has boosted the
computational possibilities in fields where standard computers are not able to
perform. The AI paradigm is to emulate human intelligence and therefore breaks
the familiar architecture on which digital computers are based. In particular,
neuromorphic computing, artificial neural networks (ANN) and deep learning
models mimic how the brain computes. Large networks of interconnected neurons
whose synapsis are individually strengthened or weakened during the learning
phase find many applications. With this respect, photonics is a suitable
platform to implement ANN hardware thanks to its speed, low power dissipation
and multi-wavelength opportunities. One photonic device candidate to perform as
an optical neuron is the optical microring resonator. Indeed microring
resonators show both a nonlinear response and a capability of optical energy
storage, which can be interpreted as a fading memory. Moreover, by using
silicon photonics, the photonic integrated circuits can be fabricated in volume
and with integrated electronics on board. For these reasons, here, we describe
the physics of silicon microring resonators and of arrays of microring
resonators for application in neuromorphic computing. We describe different
types of ANNs from feed-forward networks to photonics extreme learning machines
and reservoir computing. In addition, we discuss also hybrid systems where
silicon microresonators are coupled to other active materials. this review aims
to introduce the basics and to discuss the most recent developments in the
field.
