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The paper discusses the architectural elements of neuromorphic systems on the example of behaviour control of robots. The basis of the work is new spiking neuron model, which allows describing the known biological network relying on macroscopic parameters of neurons - the size, the relative length of dendrites, etc. The model also allows no parametric setting but change synaptic and dendritic structures. This implies the possibility of a structural adjustment neuromorphic system. The paper gives examples of simulation results of the proposed elements neuromorphic systems.
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Procedia Computer Science 103 ( 2017 ) 190 197
1877-0509 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the scientific committee of the XIIth International Symposium “Intelligent Systems”
doi: 10.1016/j.procs.2017.01.057
ScienceDirect
Available online at www.sciencedirect.com
XIIth International Symposium «Intelligent Systems», INTELS’16, 5-7 October 2016, Moscow,
Russia
Application the spiking neuron model with structural adaptation to
describe neuromorphic systems
A.V. Bakhshiev*, F.V. Gundelakh
Computer Vision Laboratory, Russian State Scientific Center for Robotics and Technical Cybernetics (RTC), 21 Tikhoretskiy pr., Saint-
Petersburg 194064, Russia
Abstract
The paper discusses the architectural elements of neuromorphic systems on the example of behaviour control of robots. The basis
of the work is new spiking neuron model, which allows describing the known biological network relying on macroscopic
parameters of neurons - the size, the relative length of dendrites, etc. The model also allows no parametric setting but change
synaptic and dendritic structures. This implies the possibility of a structural adjustment neuromorphic system. The paper gives
examples of simulation results of the proposed elements neuromorphic systems.
© 2017 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the scientific committee of the XIIth International Symposium «Intelligent Systems».
Keywords: spiking neuron; neuromorphic system; structural adaptation; dendritic tree; motion control; behavior control.
1. Introduction
Currently, there are many poorly formalized tasks, which are badly solved by existing methods. One of the common
approaches to solving such problems are artificial neural networks.
However, artificial neural networks have a number of disadvantages:
x most modern artificial neural networks are used to solve a particular problem;
x in the case of changing of the context it is necessary to build and train a new network;
* Corresponding author.
E-mail address: alexab@rtc.ru
© 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the scientific committee of the XIIth International Symposium “Intelligent Systems”
191
A.V. Bakhshiev and F.V. Gundelakh / Procedia Computer Science 103 ( 2017 ) 190 – 197
x while solving common tasks, such as the behavior control of the robotic system, there is a problem of the
interaction between the individual neural networking subsystems (detection, recognition, etc.);
x the absence of structural adaptive capabilities.
To overcome these problems in artificial neural networks it seems promising to develop neuromorphic approach
which consists in the fact that data processing systems are formed based on models of biological neural networks
architecture, design of which are based on the features of the structure and principles of work of biological neural
structures of the brain.
2. The model of neuromorphic system
The feature of the modern approach on modeling neuromorphic systems1,2, and, particularly, the feature of large-
scale brain modeling projects is that they are focused on the modeling of the higher nervous activity. Namely, it means
that an attempt to understand how the higher cognitive activities are carried out is made by modeling of higher nervous
structures, the brain cortex and cerebellum functions.
However, we can offer a different approach - to go from the bottom, from the simplest neural structures. Since the
nervous system has appeared primarily as a response to the need to move, and movement (in the broad sense -
perception and active reaction to the environment) is the main function of all organisms on which the rest of the
functionality is built, so we can go towards the creation of the behavioral control systems for the technical systems in
the environment. In this case it need not necessarily be a physical robot that moves in space. The key moment here is
that neuromorphic system interacts with the environment, and the neural network carries all the information processing
cycle, from receiving it from the sensors to the impact on the environment through any effectors (figure 1, left).
The right side of the figure 1 shows the offered variant of an architecture of motor memory. It can be divided into
three levels:
1. Regulators' level - it provides basic functions to control effectors of the executive system and is based on the
networks of the spinal regulation level of muscle contraction3.
2. Level of memorization and reproduction of the executive system’s positions (states) provides the possibility to fix
in its neural network the target positions of the executive system in the state space, and it is based on the well-
known hypotheses about the similarities in the architecture of the motor and visual cortex of the brain4,5.
3. Level of memorization and reproduction of motion patterns, or in other words a dynamic activity, provides a
sequential transition of the execution system from one memorized position to another. It can be based on a
widespread neural ring structures with positive feedback, providing the nervous system with the centers of
activity.
One of the important properties of biological neural networks is their structural adaptation. It can be divided into
three stages:
1. Evolutionary. At this stage neural networks providing vital processes and the general form of the nervous
system's architecture were formed. In theory of artificial neural networks this stage can be associated with the
developer's choice of architecture of ANN, the number of layers, the number of neurons in the hidden layer, etc.
Also it can be associated with global optimization methods, such as genetic algorithms.
2. Primary development of the nervous system after birth. At this stage a detailed architecture of the visual and
motor cortex and higher levels are formed, according to the sensory information and the range of available
movements.
3. Continuous accumulation of experience in the structure of neuronal connections. It occurs during the entire time
of functioning of the body.
192 A.V. Bakhshiev and F.V. Gundelakh / Procedia Computer Science 103 ( 2017 ) 190 – 197
Fig. 1. The model of neuromorphic system.
Stages 2 and 3 in artificial neural networks are implemented by training algorithms that tunes weights of
connections between given number of neurons to achieve the best generalization/predictive ability on the training set.
An important practical difference of biological neural structures is their ability to carry out the adjustment (training)
online, i.e. without prior training stage. This feature allows it to adapt to changing conditions during the functioning,
and adaptation may even lead to a change in the architecture of the neural network (for example, the implementation
of a more complex analysis of the data from the acoustic analyzer in the visual cortex in the case of irreversible
damage). It is also known that at about a constant number of neurons in the brain, the number of connections between
them is actively changing. In addition, each connection provides not just the fact of data transfer from the output of
one neuron to the input of the other, but also performs other functions such as spatial and temporal generalization of
input data. The new model of a technical neuron with enhanced functionality has been developed for implementation
of the proposed architecture of neuromorphic systems.
3. The neuron's model
The model of the neuron is based on the concept of an equivalent electrical circuit of the membrane of a biological
neuron.
It is assumed that the inputs of the neuron's model receive spikes

Xt
, which are transformed into analog values

gt
, in artificial synapses, approximately describing the release and decay processes of the neurotransmitter in the
synaptic cleft and characterizing the influence of the input data on the segment of the neuron's membrane. Within the
model we assume that the input and output signals of the neuron are equal to zero in the absence of a spike and they
are equal to the
Ey
constant during the spike. The spike duration is determined by the temporal parameters of the
neuron membrane. The membrane of the neuron's body and dendrites is represented by a set of pairs of ionic
mechanisms' models, describing the features of excitation and inhibition mechanisms respectively. The outputs of the
ionic mechanisms models represent generalized contribution
  
^`
,Ut Uat Ust
to the intracellular potential

Ut6
from the excitation and inhibition processes occurring in the segment of the membrane (hereinafter, the
subscripts s and a distinguish variables corresponding to the excitatory and inhibitory effects). The signals from the
synapses are used to change the activity of the ionic mechanisms towards the weakening of their functions that
simulates the change in the concentration of ions inside the cell under the external influences. The output signal

Yt
of the neuron is a sequence of spikes, similar to the input signals.
It is proposed to distinguish between the types of ionic mechanisms by the sign of the output signal. A positive
output value represents the excitatory influence, while negative represents the inhibitory influence. Thus, the total
193
A.V. Bakhshiev and F.V. Gundelakh / Procedia Computer Science 103 ( 2017 ) 190 – 197
Fig. 2. The organization of the structure of the neuron's membrane.
value of the outputs will characterize the membrane's segment contribution to the total value of the neuron's potential.
The role of the artificial synaptic apparatus in the model is the primary processing of the input signals. It should be
noted that the models of the excitatory and inhibitory synapses are also identical to each other, and the difference in
their effect on membrane's segment is determined by which of the ionic mechanisms a particular synapse is connected
to. Each synapse of the model describes a group of synapses in the natural neuron.
The structure of the neuron's membrane, which can be described with the model is presented in figure 2.
The body of the neuron conventionally defined as those parts of the membrane that are covered by feedback from
the generator of the action potential (
UF
).
It should also be noted that the closer the membrane's segment is to the generating zone, the more effective is
contribution of its inputs to the overall picture of neuronal excitation.
Thus, artificial dendrites carry out spatial and temporal summation of signals at considerable time intervals (small
contribution to the excitation of neuron from each input) and the accumulation of potential is independent of neuron's
discharges.
The body of the neuron carries out the summation of signals over short intervals of time (a great contribution to
the excitation of the neuron from each input) and accumulated potential is lost when the neuron discharges.
The generator of the action potential performs the spike formation

Yt
when the threshold is exceeded and the
signal of the membrane's overcharging
UF
.
The system of equations describing the model of a neuron contains
N
first-order differential equations, where
N
is calculated by the formula
11
1.
i
LL
ii
l
il
NLN
§·
¨¸
©¹
¦¦
(1)
Detailed description of the functional elements of the neuron’s model is presented in the paper6.
4. Software for modeling systems with structural adjustment
Modern modeling tools, such as Matlab/Simulink7, are unsuitable for modeling neuromorphic systems, the
structure of which can be changed at runtime. The reason is the inability to change the structure of the model during
194 A.V. Bakhshiev and F.V. Gundelakh / Procedia Computer Science 103 ( 2017 ) 190 – 197
the calculation. Therefore, our own CAD system “Neuro Modeler Software Developer Kit (NMSDK)” has been
developed, to provide the required functionality.
The problem of the development of software for modeling neural networks with the structure changing at runtime
can be generalized to the problem of development of software system, which allows to calculate the algorithm at each
step consisting of a chain of modules, each of which solves a separate local subtask. In addition, each module has
input and output data, parameters and state variables. Each module may also be connected to other modules via inputs
and outputs, the structure of connections can be arbitrary.
Since the task is to provide the possibility of rapid changes in the structure of the modeled system, it imposes the
following requirements for architecture:
x it is necessary to have an option to load an d save the structure of the algorithm’s modules;
x to provide unified access to parameters, state variables, input and output data of the modules;
x to have an option to add new modules to the algorithm (from the list of existing ones), remove existing ones,
change the order of calculation.
This approach also makes it possible to unify:
x performance estimation for modules;
x testing tools for modules (since there is unified access to all input and output of the module, universal testing
tools can be implemented);
x tools for exchanging data between algorithm and external to it software structural elements, such as user
interface.
Such unification simplifies creation of applications improves reliability through the code reusing. The software
which satisfies the requirements formulated above must have a two-level architecture:
x the core level with a universal programming interface;
x the level of the final software that uses the library, including a collection of algorithms and user interface.
Figure 3(a) shows the scheme of interaction between basic software core modules and user applications.
The developed software tools have the following advantages:
x cross-platform core that allows you to create applications for all systems that support the C ++ standard and with
the implementation of boost library;
x quick creation of new algorithmic solutions based on the already existing library component;
x unification of descriptions of inputs, outputs, and parameters of each algorithm;
x simplicity of creation of testing tools for the individual algorithms and complex testing;
x easy creation of new components and collections;
x small overhead on the interaction between the components that implement some algorithms to create flexible
systems operating in real-time;
x user interface that allows you to monitor and control system.
5. Modeling of basic elements of the neuromorphic systems
5.1. Selection of modeling objects
An application of of a neuron model to describe the ring structures of the two neurons with positive and negative
feedback as elements neuromorphic systems was considered.
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A.V. Bakhshiev and F.V. Gundelakh / Procedia Computer Science 103 ( 2017 ) 190 – 197
196 A.V. Bakhshiev and F.V. Gundelakh / Procedia Computer Science 103 ( 2017 ) 190 – 197
5.2. Ring structures with negative feedback
As the ring structure with negative feedback, consider circuit element, which is a widespread in the nervous system
connection of excitatory and inhibitory neurons, first studied in neurophysiological experiments, as the motoneuron
interaction, providing a contraction in muscle fibers and Renshaw cells (Figure 3(b)).
There are two mechanisms to increase muscle contraction force. The first is to increase the spiking frequency at
the output of motoneuron. The second is to increase in the number active motoneurons, the axons of which are
connected to the muscle fibers of the current muscle. Specialized inhibition neuron in the circuit of recurrent inhibition
- Renshaw cell - limits and stabilizes the frequency of motoneuron discharge.
The developed model of the neuron allows to model the elements of neuromorphic systems based on easily
observable parameters of biological prototypes.
So Renshaw cell is a small size neuron, which generates a specific burst in response to the one spike that comes on
its input through the recurrent inhibition circuit from the motoneuron. In the modeled structure the body of the neuron
consists of one membrane’s segment
1
M
. Motoneuron is a large neuron (Figure 4(a)). Motoneuron’s body consists
of three membrane’s segments
13
MM
. In this experiment, the neuron’s body size was chosen empirically.
The behavior of such neural structure according to the neurophysiologic data is shown at Figure 4(b).
The graphs show that the frequency of motoneuron stimulation enhances the inhibitory effect on Renshaw cells
with motoneuron, causing, in turn, decrease the frequency of motoneuron discharges.
Thus by increasing the frequency of motoneuron stimulation, the spiking frequency at the output in the first
moments increases and then stabilizes at a low level with a duration of interpulse intervals determined by the duration
of Renshaw cell discharges. It is essential that this limit depends on if the motoneuron is influenced by recurrent
inhibition of Renshaw cells, or not. Computer modeling has allowed to investigate the interaction of neurons in more
detail. The results of experiment on the model is presented in Figure 5(a).
It can be seen that there is a qualitative and a quantitative relationship in experimental data.
5.3. Ring structures with positive feedback
Figure 5(b) shows structural diagram of connections of pair neurons with positive feedback. Such a structure within
neuromorphic system can describe, for example, motion trajectory element.
A single excitation of such a structure brings it to a stable state of generation. At a signal from the lowest level,
confirming achievement of the target position, acting simultaneously on both the neuron in the ring structure, it can
be inhibited. In more detail trajectory element is shown in Figure 6(a).
To the only exciting connection, which are connected in series such ring structures, does not lead to the
simultaneous launch of all trajectory elements, connections between the trajectory elements are using features of the
structural organization of the membrane in the neuron model. At the input of the ring structure

1
tcn
j
u
several inhibitory
and excitatory synapses are formed. In this case inhibitory synapses on the dendrite are located closer to the body of
the neuron and thus carry more weight, but less time impact on the contribution to the neuron excitation. And
excitatory synapses are formed on the distant segments of dendrites and, consequently, have less weight, but a longer
influence in time. Thus at the moment when activity

1
tcn
j
u
appears, neuron
1
N
of the next

1i
trajectory element
is inhibited by a "strong" inhibitory synapse, but when activity disappears, the inhibitory effect disappears faster than
the remaining excitation on dendrites, which launches the next ring structure.
Figure 6(b) shows the output of the circuit of three sequentially connected trajectory elements.
The oscillator is used as a top-level control. Lower levels of simulated by delays. It can be seen that a single
activation of the first trajectory element leads to consecutive starts of the remaining elements after receiving
confirmation from the lowest level that the transition in position, given by the previous trajectory element, is over.
6. Conclusion
The paper presents models of some basic elements of neuromorphic systems, based on the new technical model of
a neuron with a structural adaptation.
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A.V. Bakhshiev and F.V. Gundelakh / Procedia Computer Science 103 ( 2017 ) 190 – 197
(a) (b)
Fig. 5. (a) Reactions of structure “motoneuron-Renshaw cell” upon excitation of motoneurons pulsed stream at 50 Hz: 1 - input pulsed stream; 2
motoneuron’s reaction with enabled FB; 3 - Renshaw cell responses with enabled FB; 4 motoneur on’s r eaction without FB; 5 - Renshaw cell
responses without FB.; (b) Structural diagram of the trajectory element.
(a) (b)
Fig. 6. (a) Detailed structural diagram of a trajectory element; (b) an example of the functioning of sequential activation of ring structures,
responsible for the working off the three elements trajectory (0 - exciting pulse from the upper level; 1 - activity of the first element 2 - activity of
the second trajectory element, and 3 - activity of the third trajectory element. The horizontal axis indicates the time in seconds).
On the basis of the developed software, which allows to model systems, the structure of which can be changed at
runtime, a number of experiments, confirming the adequacy of the functions of the developed models, were made.
The developed models, provide unique structural adaptation abilities of neural networks and allow to synthesize
neuromorphic systems based on known biological neural structures and the principles of their formation in nature.
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... The main requirement for creating a computer analog of a biological neuron was to preserve the principles of transmitting and converting signals in the form of pulse streams. Figure 5 shows a block diagram of the afferent neuron model developed on the basis of the compartment spike model described in [5,6]. This is a model of a neuron whose input is direct depolarizing effects from the sensor (analog signal) E . ...
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... One of the promising options for implementing the model of an element of neuro- morphic systems is the phenomenological model of a dynamic spike neuron with the ability to describe the spatial structure of the dendritic apparatus [40]. This model allows us to describe the variable topology of a neural network, based on the principles of neural structure formation known from neurophysiology [41]. ...
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Structural rationale of the nervous system functions as an automatic regulator
  • Sp Romanov
Romanov SP. Structural rationale of the nervous system functions as an automatic regulator. Neurocomputers: development, application 2006;7:54-63.
Information and the brain: sight of the neurophysiologist. Neurocomputers: development, application
  • G S Voronkov
Voronkov GS. Information and the brain: sight of the neurophysiologist. Neurocomputers: development, application 2002:1-2:79-88.
  • S P Romanov
Romanov SP. Structural rationale of the nervous system functions as an automatic regulator. Neurocomputers: development, application 2006;7:54-63.