4,722 research outputs found
Integer Echo State Networks: Hyperdimensional Reservoir Computing
We propose an approximation of Echo State Networks (ESN) that can be
efficiently implemented on digital hardware based on the mathematics of
hyperdimensional computing. The reservoir of the proposed Integer Echo State
Network (intESN) is a vector containing only n-bits integers (where n<8 is
normally sufficient for a satisfactory performance). The recurrent matrix
multiplication is replaced with an efficient cyclic shift operation. The intESN
architecture is verified with typical tasks in reservoir computing: memorizing
of a sequence of inputs; classifying time-series; learning dynamic processes.
Such an architecture results in dramatic improvements in memory footprint and
computational efficiency, with minimal performance loss.Comment: 10 pages, 10 figures, 1 tabl
Simply modified GKL density classifiers that reach consensus faster
The two-state Gacs-Kurdyumov-Levin (GKL) cellular automaton has been a staple
model in the study of complex systems due to its ability to classify binary
arrays of symbols according to their initial density. We show that a class of
modified GKL models over extended neighborhoods, but still involving only three
cells at a time, achieves comparable density classification performance but in
some cases reach consensus more than twice as fast. Our results suggest the
time to consensus (relative to the length of the CA) as a complementary measure
of density classification performance.Comment: Short note, 3 pages, 1 table, 2 composite figures, 18 reference
Sensitivity to noise and ergodicity of an assembly line of cellular automata that classifies density
We investigate the sensitivity of the composite cellular automaton of H.
Fuk\'{s} [Phys. Rev. E 55, R2081 (1997)] to noise and assess the density
classification performance of the resulting probabilistic cellular automaton
(PCA) numerically. We conclude that the composite PCA performs the density
classification task reliably only up to very small levels of noise. In
particular, it cannot outperform the noisy Gacs-Kurdyumov-Levin automaton, an
imperfect classifier, for any level of noise. While the original composite CA
is nonergodic, analyses of relaxation times indicate that its noisy version is
an ergodic automaton, with the relaxation times decaying algebraically over an
extended range of parameters with an exponent very close (possibly equal) to
the mean-field value.Comment: Typeset in REVTeX 4.1, 5 pages, 5 figures, 2 tables, 1 appendix.
Version v2 corresponds to the published version of the manuscrip
A guided tour of asynchronous cellular automata
Research on asynchronous cellular automata has received a great amount of
attention these last years and has turned to a thriving field. We survey the
recent research that has been carried out on this topic and present a wide
state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat
Density Classification Quality of the Traffic-majority Rules
The density classification task is a famous problem in the theory of cellular
automata. It is unsolvable for deterministic automata, but recently solutions
for stochastic cellular automata have been found. One of them is a set of
stochastic transition rules depending on a parameter , the
traffic-majority rules.
Here I derive a simplified model for these cellular automata. It is valid for
a subset of the initial configurations and uses random walks and generating
functions. I compare its prediction with computer simulations and show that it
expresses recognition quality and time correctly for a large range of
values.Comment: 40 pages, 9 figures. Accepted by the Journal of Cellular Automata.
(Some typos corrected; the numbers for theorems, lemmas and definitions have
changed with respect to version 1.
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