### Speaker

Simone Borlenghi Garoia
(KTH)

### Description

Oscillator networks are ubiquitous in Physics.Very different
systems, From Bose-Einstein condensates to mechanical
oscillators, spin systems and electrical power grids, can be
described using the language of the discrete Nonlinear
Schrödinger equation (DNLS). In this talk, I will show how
the DNLS can be used to model a neural network for pattern
recognition.
An input is passed through the network, that reaches a
off-equilibrium steady state and produces an output in the
form of energy currents that flow between the oscillators.
Different inputs are used to encode simple images (typically
black and white digits), and the output is trained using
standard machine learning techniques in order to
discriminate between the various digits, with a recognition
rate of more than 90%. This computational paradigm is called
reservoir computing, where the term "reservoir" indicates
any complex system able to perform information processing.
The advantage of reservoir computing is that one can chose
as network any nonlinear complex system, and the training is
performed only at the output level, without modifying the
network. This has huge advantages in terms of computational
cost, so that a simple recognition problem can be performed
on a laptop. The generality of the DNLS model suggests that
a large class of microscopic and macroscopic systems can be
used for this purpose, and the techinque employed is
somewhat universal.
References:
Simone Borlenghi, Magnus Boman and Anna Delin, "Modelling
reservoir computing with the discrete nonlinear Schrödinger
equation", Phys. Rev. E 98, 052101 (2018)
Stefano Iubini, Stefano Lepri and Antonio Politi,
"Nonequilibrium discrete Nonlinear Schrödinger Equation",
Phys. Rev. E, 86, 011108 (2012)
Stefano Iubini, Stefano Lepri, Roberto Livi and Antonio
Politi, "Off equilibrium Langevin dynamics of the discrete
nonlinear Schrödinger chain", J. Stat. Mech, 2013 (2013)
Mantas Lukosevicius and Herbert Jaeger, "Reservoir computing
approaches to recurrent neural network training", Computer
science reviews 3, 127 (2009)