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Java CNN Simulator
by Martin Haenggi (ETHZ - Zurich)
Cellular Neural Networks (CNN)
is a massive parallel computing
paradigm defined in discrete N-dimensional spaces.
Following the Chua-Yang definition:
- A CNN is an N-dimensional regular array of elements ( cells);
- The cell grid can be for example a planar array with rectangular,
triangular or hexagonal geometry, a 2-D or 3-D torus, a 3-D finite
array, or a 3-D sequence of 2-D arrays ( layers );
- Cells are multiple input-single output processors, all described by
one or just some few parametric functionals ;
- A cell is characterized by an internal state variable ,
sometimes not directly observable from outside the cell itself;
- More than one connection network can be present, with different
neighborhood sizes;
- A CNN dynamical system can operate both
in continuous (CT-CNN) or discrete time (DT-CNN);
- CNN data and parameters are typically continuous values;
- CNN operate typically with more than one iteration, i.e. they are
recurrent networks.
CNN main characteristic is the locality of the
connections between the units: in fact the main difference between
CNN and other
Neural Networks
paradigms is the fact that
informations are directly exchanged just between neighboring units.
Of course this characteristic allows also to obtain global processing.
Communications between non directly ( remote )
connected units are
obtained passing through other units.
It is possible to consider the CNN paradigm as an evolution
of
Cellular Automata paradigm.
Moreover it has been demonstrated
that CNN paradigm
is universal, being equivalent to the Turing Machine.
A mathematical formal description of the discrete time case
is contained in the following equations.
x(t+1) = g(x(t)) + I(t) +
SUM( A(yk(t),PA(j)) ) +
SUM( B(uk(t),PB(j)) )
y(t) = f (x(t))
where
x is the internal state of a cell, y its output, u its
external input and I a local value called bias .
A and B are two generic
parametric functionals, PA(j) and PB(j) are the
parameters arrays (typically the inter-cell connection weights).
The neighbor yk and uk values
are collected from the cells present in the
two neighborhood Nr , for the feedback functional A ,
and Ns ,
for the control functional B .
The two neighborhoods are potentially different.
The functionals A and B are also called templates .
The instantaneous local feedback function g express the possibility
of an immediate feedback effect.
This function is typically not used.
f is the function that gives cell output from the internal state.
Generally is used the chessboard distance convention,
expressed by the equation
d(i,j) = max(|x(i) - x(j)|,|y(i)-y(j)|)
In most of cases the system is non-markovian ,
i.e. the future internal
state depends also from the past history of the system.
In the special case of time-variant CNN all the above functions,
neighborhoods and parameters can be also function of time.
In figure is depicted a block-scheme of a generical CNN iteration.
Internet resources:
- Ftp site manager:
- Roberto Battiti
- battiti@itnvax.science.unitn.it (130.186.34.2)
Internet Pointers (Papers):
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