4,251 research outputs found
On computational power and the order-chaos phase transition in Reservoir Computing
Randomly connected recurrent neural circuits have proven to be very powerful models for online computations when a trained memoryless readout function is appended. Such Reservoir Computing (RC) systems are commonly used in two flavors: with analog or binary (spiking) neurons in the recurrent circuits. Previous work showed a fundamental difference between these two incarnations of the RC idea. The performance of a RC system built from binary neurons seems to depend strongly on the network connectivity structure. In networks of analog neurons such dependency has not been observed. In this article we investigate this apparent dichotomy in terms of the in-degree of the circuit nodes. Our analyses based amongst others on the Lyapunov exponent reveal that the phase transition between ordered and chaotic network behavior of binary circuits qualitatively differs from the one in analog circuits. This explains the observed decreased computational performance of binary circuits of high node in-degree. Furthermore, a novel mean-field predictor for computational performance is introduced and shown to accurately predict the numerically obtained results.
Delayed Dynamical Systems: Networks, Chimeras and Reservoir Computing
We present a systematic approach to reveal the correspondence between time
delay dynamics and networks of coupled oscillators. After early demonstrations
of the usefulness of spatio-temporal representations of time-delay system
dynamics, extensive research on optoelectronic feedback loops has revealed
their immense potential for realizing complex system dynamics such as chimeras
in rings of coupled oscillators and applications to reservoir computing.
Delayed dynamical systems have been enriched in recent years through the
application of digital signal processing techniques. Very recently, we have
showed that one can significantly extend the capabilities and implement
networks with arbitrary topologies through the use of field programmable gate
arrays (FPGAs). This architecture allows the design of appropriate filters and
multiple time delays which greatly extend the possibilities for exploring
synchronization patterns in arbitrary topological networks. This has enabled us
to explore complex dynamics on networks with nodes that can be perfectly
identical, introduce parameter heterogeneities and multiple time delays, as
well as change network topologies to control the formation and evolution of
patterns of synchrony
Can biological quantum networks solve NP-hard problems?
There is a widespread view that the human brain is so complex that it cannot
be efficiently simulated by universal Turing machines. During the last decades
the question has therefore been raised whether we need to consider quantum
effects to explain the imagined cognitive power of a conscious mind.
This paper presents a personal view of several fields of philosophy and
computational neurobiology in an attempt to suggest a realistic picture of how
the brain might work as a basis for perception, consciousness and cognition.
The purpose is to be able to identify and evaluate instances where quantum
effects might play a significant role in cognitive processes.
Not surprisingly, the conclusion is that quantum-enhanced cognition and
intelligence are very unlikely to be found in biological brains. Quantum
effects may certainly influence the functionality of various components and
signalling pathways at the molecular level in the brain network, like ion
ports, synapses, sensors, and enzymes. This might evidently influence the
functionality of some nodes and perhaps even the overall intelligence of the
brain network, but hardly give it any dramatically enhanced functionality. So,
the conclusion is that biological quantum networks can only approximately solve
small instances of NP-hard problems.
On the other hand, artificial intelligence and machine learning implemented
in complex dynamical systems based on genuine quantum networks can certainly be
expected to show enhanced performance and quantum advantage compared with
classical networks. Nevertheless, even quantum networks can only be expected to
efficiently solve NP-hard problems approximately. In the end it is a question
of precision - Nature is approximate.Comment: 38 page
Toward bio-inspired information processing with networks of nano-scale switching elements
Unconventional computing explores multi-scale platforms connecting
molecular-scale devices into networks for the development of scalable
neuromorphic architectures, often based on new materials and components with
new functionalities. We review some work investigating the functionalities of
locally connected networks of different types of switching elements as
computational substrates. In particular, we discuss reservoir computing with
networks of nonlinear nanoscale components. In usual neuromorphic paradigms,
the network synaptic weights are adjusted as a result of a training/learning
process. In reservoir computing, the non-linear network acts as a dynamical
system mixing and spreading the input signals over a large state space, and
only a readout layer is trained. We illustrate the most important concepts with
a few examples, featuring memristor networks with time-dependent and history
dependent resistances
A characterization of the Edge of Criticality in Binary Echo State Networks
Echo State Networks (ESNs) are simplified recurrent neural network models
composed of a reservoir and a linear, trainable readout layer. The reservoir is
tunable by some hyper-parameters that control the network behaviour. ESNs are
known to be effective in solving tasks when configured on a region in
(hyper-)parameter space called \emph{Edge of Criticality} (EoC), where the
system is maximally sensitive to perturbations hence affecting its behaviour.
In this paper, we propose binary ESNs, which are architecturally equivalent to
standard ESNs but consider binary activation functions and binary recurrent
weights. For these networks, we derive a closed-form expression for the EoC in
the autonomous case and perform simulations in order to assess their behavior
in the case of noisy neurons and in the presence of a signal. We propose a
theoretical explanation for the fact that the variance of the input plays a
major role in characterizing the EoC
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