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Reservoir computing based on delay-dynamical systems

dinsdag, 22 mei, 2012 - 10:30
Campus: Brussels Humanities, Sciences & Engineering campus
Lennert Appeltant

Walking down a street, we are constantly bombarded with sensory impressions. Seeing a vehicle or a
familiar face, hearing the ongoing traffic and conversations, smelling the food stalls … All these external
impulses instantly produce massive neural activity in our brain, so that we recognize the passing bus, a
good friend or a car horn, or that the smell of freshly baked waffles makes us hungry. We can see a blurry
photo and still recognize the scene in a fraction of a second, a task for which a computer might take
minutes or even hours. Today, except for mathematical operations, our brain functions much faster and
more efficient than any supercomputer. It is precisely this form of information processing in neural
networks that inspires researchers to create systems that mimic the brain's information processing
capabilities, in a way radically different from current computer based schemes.

In this thesis we propose a novel approach to implement these alternative information processing
architectures, based on delayed feedback. Time delays are intrinsic in many real systems. In engineering,
time delays often arise in feedback loops involving sensors and actuators. In photonic systems, time
delayed feedback plays an important role and arises due to unwanted external reflections. On the one
hand, time delays tend to destabilize systems such as lasers, but, on the other hand, the chaotic output
from e.g. a laser with feedback can put into use e.g. in chaotic communication systems. In general, one
an say that systems subject to time-delayed feedback present a rich variety of dynamical regimes.

We propose to exploit the rich dynamics of delayed feedback systems for information processing by using
the system’s transient response to an external input. We show that one single nonlinear node with
delayed feedback can replace a large network of nonlinear nodes. Our results demonstrate that this new
information processing architecture performs well in a variety of tasks, such as e.g. time series prediction
and speech recognition. We investigate whether applying this simple architecture in electronic, optoelectronic
or photonics systems could potentially be more resource-efficient as hundreds or even
thousands of neurons could be replaced by only one single hardware node in combination with a delay
line. Moreover, the fact that delay is easily implementable, sometimes even unavoidable, in photonic
systems may lead to the implementation of ultra-fast all-optical computational units. First, we numerically
investigate the architecture and performance of delayed feedback systems as information processing
units. Then we elaborate on electronic and opto-electronic implementations of the concept. Next to
evaluating their performance for standard benchmarks, we also study task independent properties of the
system, extracting information on how to further improve the initial scheme. Finally, some simple
modifications are suggested, yielding improvements in terms of speed, performance or power