IEEE Circuits and Systems Magazine - Q2 2018 - 78

j
xij - State/yij - Output
A

i
zij - Bias

B

uij - Input
(b)

(a)

ing feature compared to the fully connected feedforward
and feedback neural networks.
The state of the original CNN is discrete in space and
continuous in time and value. The state equations of the
CNN consists of m # n pieces of coupled ordinary differential equation system (one for each cell):
xo ij (t ) = - 1 x i, j (t ) +
x

+

/

/

A ij; kl y kl (t )

k, l ! S r (i, j )

B ij; kl u kl (t ) + z ij

(1)

k, l ! S r (i, j )

Figure 1. the architecture of the original CNN with 3 x 3
interconnection pattern.

yij

1

-1

1

xij

-1

Figure 2. the output nonlinearity of a cellular neural network.

motivations are described in Section III. After this, an
overview of the CNN development system components
(software simulator, emulators, template designers, chip
development systems) are coming in Section IV and V.
Then, in Section VI the analog implementation domain
of CNN devices are extended to the digital CNN domain.
The programming method of the CNN devices are introduced in Section VIII via a few explains from the Template Library. The paper is closed by a summary of the
current research trends in Section IX.
II. Definition of the CNN and the CNN-UM
A. Single Layer CNN
The original CNN cell has an input, a state and an output
and the cells are arranged to an m # n rectangular grid.
Each cell can communicate with its neighbors within a
small radius. Fig. 1 shows a situation, when the radius of
the interconnections is one. The communication weight
pattern is translation invariant, therefore, the dynamic
behavior of the CNN can be described with a very limited number of variables (19 number only in the simplest
case as it is shown in Fig. 1). This is a strong distinguish-

where u ij is the input, x ij is the state, y ij (t ) is the output, and z ij is the bias. A and B are the space invariant
template matrices. x is the time constant. The output
transfer function is as follow:
1 if x ij (t ) > 1
y ij (t) = f ^ x ij (t) h = * x ij (t ) if x ij (t ) # 1 4
- 1 if x ij (t ) 1 - 1

(2)

The original CNN was extended with different architectural ideas (e.g. 1D CNN, multi-layer CNN, non-linear
CNN, delay-type CNN, discrete time CNN, full signal
range model, CNN on trigonal or hexagonal grids, CNN
with space variant templates, CNN with different densities, chaotic CNN etc.) These variants are described
in [4] and [5]. As a result, the CNN was redefined as a
2.5 dimensional (the number of the layers are significantly smaller than m or n) dynamic neural networks
with local interconnection pattern with arbitrary transfer functions.
B. CNN Universal Machine
When proposed in 1988, the CNN was a subclass of the
Hopfield type neural networks with a number of practical architectural constraints, which made analog VLSI
implementations easy, supported early vision processing and enabled direct programming. However, it quickly turned out, that one instruction primitive (one CNN
template) cannot solve complex processing problems,
therefore operation sequences were assembled from the
instruction primitives. This generated the need of the efficient implementation of these sequences, which led to
the invention of the CNN Universal Machine (CNN-UM).
This great theoretical step ahead meant the conversion
of a neural network to a many-core microprocessor,
which handles arrays of continuous-time dynamic signals
as variables and applies sequences of spatial-temporal

Ákos Zarándy is with the Institute for Computer Science and Control of the Hungarian Academy of Sciences (MTA-SZTAKI) Budapest, Hungary.
András Horváth and Péter Szolgay are with the Pázmány Péter Catholic University, The Faculty of Information Technology and Bionics, Budapest,
Hungary.

78

IEEE CIrCuItS aND SyStEmS magazINE

SECOND quartEr 2018



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