76 research outputs found
Exploring Transfer Function Nonlinearity in Echo State Networks
Supralinear and sublinear pre-synaptic and dendritic integration is
considered to be responsible for nonlinear computation power of biological
neurons, emphasizing the role of nonlinear integration as opposed to nonlinear
output thresholding. How, why, and to what degree the transfer function
nonlinearity helps biologically inspired neural network models is not fully
understood. Here, we study these questions in the context of echo state
networks (ESN). ESN is a simple neural network architecture in which a fixed
recurrent network is driven with an input signal, and the output is generated
by a readout layer from the measurements of the network states. ESN
architecture enjoys efficient training and good performance on certain
signal-processing tasks, such as system identification and time series
prediction. ESN performance has been analyzed with respect to the connectivity
pattern in the network structure and the input bias. However, the effects of
the transfer function in the network have not been studied systematically.
Here, we use an approach tanh on the Taylor expansion of a frequently used
transfer function, the hyperbolic tangent function, to systematically study the
effect of increasing nonlinearity of the transfer function on the memory,
nonlinear capacity, and signal processing performance of ESN. Interestingly, we
find that a quadratic approximation is enough to capture the computational
power of ESN with tanh function. The results of this study apply to both
software and hardware implementation of ESN.Comment: arXiv admin note: text overlap with arXiv:1502.0071
Product Reservoir Computing: Time-Series Computation with Multiplicative Neurons
Echo state networks (ESN), a type of reservoir computing (RC) architecture,
are efficient and accurate artificial neural systems for time series processing
and learning. An ESN consists of a core of recurrent neural networks, called a
reservoir, with a small number of tunable parameters to generate a
high-dimensional representation of an input, and a readout layer which is
easily trained using regression to produce a desired output from the reservoir
states. Certain computational tasks involve real-time calculation of high-order
time correlations, which requires nonlinear transformation either in the
reservoir or the readout layer. Traditional ESN employs a reservoir with
sigmoid or tanh function neurons. In contrast, some types of biological neurons
obey response curves that can be described as a product unit rather than a sum
and threshold. Inspired by this class of neurons, we introduce a RC
architecture with a reservoir of product nodes for time series computation. We
find that the product RC shows many properties of standard ESN such as
short-term memory and nonlinear capacity. On standard benchmarks for chaotic
prediction tasks, the product RC maintains the performance of a standard
nonlinear ESN while being more amenable to mathematical analysis. Our study
provides evidence that such networks are powerful in highly nonlinear tasks
owing to high-order statistics generated by the recurrent product node
reservoir
Vanishing quantum discord is necessary and sufficient for completely positive maps
Two long standing open problems in quantum theory are to characterize the
class of initial system-bath states for which quantum dynamics is equivalent to
(1) a map between the initial and final system states, and (2) a completely
positive (CP) map. The CP map problem is especially important, due to the
widespread use of such maps in quantum information processing and open quantum
systems theory. Here we settle both these questions by showing that the answer
to the first is "all", with the resulting map being Hermitian, and that the
answer to the second is that CP maps arise exclusively from the class of
separable states with vanishing quantum discord.Comment: 4 pages, no figures. v2: Accepted for publication in Phys. Rev. Let
Quantum filter for a non-Markovian single qubit system
In this paper, a quantum filter for estimating the states of a non-Markovian
qubit system is presented in an augmented Markovian system framework including
both the qubit system of interest and multi-ancillary systems for representing
the internal modes of the non-Markovian environment. The colored noise
generated by the multi-ancillary systems disturbs the qubit system via a direct
interaction. The resulting non-Markovian dynamics of the qubit is determined by
a memory kernel function arising from the dynamics of the ancillary system. In
principle, colored noise with arbitrary power spectrum can be generated by a
combination of Lorentzian noises. Hence, the quantum filter can be constructed
for the qubit disturbed by arbitrary colored noise and the conditional state of
the qubit system can be obtained by tracing out the multi-ancillary systems. An
illustrative example is given to show the non-Markovian dynamics of the qubit
system with Lorentzian noise.Comment: arXiv admin note: text overlap with arXiv:1503.0799
Quantum Autoencoders for Learning Quantum Channel Codes
This work investigates the application of quantum machine learning techniques
for classical and quantum communication across different qubit channel models.
By employing parameterized quantum circuits and a flexible channel noise model,
we develop a machine learning framework to generate quantum channel codes and
evaluate their effectiveness. We explore classical, entanglement-assisted, and
quantum communication scenarios within our framework. Applying it to various
quantum channel models as proof of concept, we demonstrate strong performance
in each case. Our results highlight the potential of quantum machine learning
in advancing research on quantum communication systems, enabling a better
understanding of capacity bounds under modulation constraints, various
communication settings, and diverse channel models.Comment: Submitted to IEEE GLOBECOM 2023 and is subject to licence chang
Quantum filter for a class of non-Markovian quantum systems
In this paper we present a Markovian representation approach to constructing
quantum filters for a class of non-Markovian quantum systems disturbed by
Lorenztian noise. An ancillary system is introduced to convert white noise into
Lorentzian noise which is injected into a principal system via a direct
interaction. The resulting dynamics of the principal system are non-Markovian,
which are driven by the Lorentzian noise. By probing the principal system, a
quantum filter for the augmented system can be derived from standard theory,
where the conditional state of the principal system can be obtained by tracing
out the ancillary system. An example is provided to illustrate the
non-Markovian dynamics of the principal system.Comment: 8 pages, 7 figure
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