=Paper=
{{Paper
|id=Vol-3137/paper8
|storemode=property
|title=Neuroevolutionary Mechanisms in the Synthesis of Spiking Neural Networks
|pdfUrl=https://ceur-ws.org/Vol-3137/paper8.pdf
|volume=Vol-3137
|authors=Serhii Leoshchenko,Andrii Oliinyk,Sergey Subbotin,Matviy Ilyashenko,Artem Borovikov
|dblpUrl=https://dblp.org/rec/conf/cmis/LeoshchenkoOSIB22
}}
==Neuroevolutionary Mechanisms in the Synthesis of Spiking Neural Networks==
https://ceur-ws.org/Vol-3137/paper8.pdf
Neuroevolutionary mechanisms in the synthesis of spiking
neural networks
Serhii Leoshchenkoa, Andrii Oliinyka, Sergey Subbotina, Matviy Ilyashenkoa and Artem
Borovikova
a
National university “Zaporizhzhia polytechnic”, Zhukovskogo street 64, Zaporizhzhia, 69063, Ukraine
Abstract
Since the advent and start of active research on the results of IBM True North, attention to
spiking neural networks (SNN) has increased significantly. Such neural networks have even
greater potential in the field of artificial intelligence than deep, recurrent and other modern
artificial neural network (ANN) architectures. This is easily explained by the ease of their
arrangement into neuromorphic systems. However, in most cases, it is difficult to synthesize
and train such neuromodels, because classical methods cannot be applied to such complex
models. A number of works suggest the use of Composite Pattern Producing Networks. This
approach is more similar to another method of ANN synthesis, namely a group of
neuroevolution methods that, together with the meta-parameters of the network,
evolutionarily modify its structure: Topology and weight Evolving Artificial Neural Network
(TWEANN). Therefore, the aim of this work is to investigate the possibility of using
neuroevolution methods and its individual mechanisms during SNN synthesis.
Keywords 1
machine learning, artificial intelligence, artificial neural networks, neuroevolution, synthesis,
topology, spiking neural network, recurrent neural network, deep neural network, deep
learning
1. Introduction
Quite often, the operation of ANN is compared to the work of the brain. However, such networks
have taken only the most superficial form and essence from real, living organisms. Due to the too
large difference between real neural networks and ANNs, it is necessary to invent different surrogate
methods of network training. Naturally, nowhere in nature does not exist something like
backpropagation network training, just as there is no unsupervised learning in its pure form [1-4].
SNNs were created with a greater reference to the real work of the brain, and use a method of
transmitting information in the likeness of biological neurons (Fig. 1). So, for example, in brain
neurons, an impulse is generated at the moment when the current sum of changes in the membrane
potential crosses the threshold [5-7]. The pulse occurrence rate and time model of pulse bundle carry
information about the external stimulus and ongoing calculations. SNN is based on a similar method
of pulse generation and information transmission: neurons use differentiated, nonlinear activation
functions, the use of which allows you to create structures with a thickness of more than one layer.
The first SNN model was proposed back in 1952 by Alan Hodgkin and Andrew Huxley [8]. The
main feature of such a model is the generation and propagation of action potentials in neurons [8].
After that, with biological refinements and high computational costs, various models of neurons were
proposed: Jolivet, Timothy and Gerstner [9]; Izhikevich [10]; Delorme [11]. The latter is very
CMIS-2022: The Fifth International Workshop on Computer Modeling and Intelligent Systems, May 12, 2022, Zaporizhzhia, Ukraine
EMAIL: sergleo.zntu@gmail.com (S. Leoshchenko); olejnikaa@gmail.com (A. Oliinyk); subbotin@zntu.edu.ua (S. Subbotin);
matviy.ilyashenko@gmail.com (M. Ilyashenko); atemiks@gmail.com (A. Borovikov)
ORCID: 0000-0001-5099-5518 (S. Leoshchenko); 0000-0002-6740-6078 (A. Oliinyk); 0000-0001-5814-8268 (S. Subbotin); 0000-0003-
4624-4687 (M. Ilyashenko); 0000-0003-1429-5930 (A. Borovikov)
© 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
popular, as it takes into account the properties of an external stimulus, accumulating the flow of
charge through the cell membrane, when crossing a certain threshold.
Figure 1: The simple example of SNN architecture
Later, thanks to the research of Kohonen, Grossberg and Anderson, a powerful theoretical
foundation was formed, with the help of which it became possible to further develop ANN, namely
the design and implementation of multilayer structures [5-7]. But learning is still a huge challenge.
Since activation functions are derived, there is room for using gradient optimization methods to train
neural networks. With the proliferation of available large labeled data sets for training neural
networks, with the increasing computing power of GPUs, and advanced regularization techniques,
neural networks are becoming incredibly multi-layered, allowing you to generalize large amounts of
invisible data. Layering is a huge advantage in the performance of neural networks [1-3].
It is well known that the brain's ability to recognize complex visual patterns or identify a speaker
in a noisy environment is the result of several consecutive processing steps and a variety of learning
mechanisms that are also built into SNN with deep learning [8-11]. Compared to ANN and deep
learning, SNN learning is at the earliest stages of development. An important feature of this type of
system is the neural architecture. It is much better suited for processing space-time data, especially in
online mode. The representation of data in time and space that SNNs possess allows such neural
networks to perform calculations at the level of the human brain, as well as to understand brain
activity in the spatiotemporal structure. It is very important to understand in the coming years how to
train such neural networks to perform various tasks [1-7].
In case of looking SNN from an engineering point of view, it can also be found interesting tasks
here. This type of neural network has a number of advantages in hardware implementation over
conventional ANNs. The pulse bundle in the SNNs is scattered over time, each of them contains a
huge amount of information, which can significantly reduce power consumption. Thus, you can create
a hardware platform with moderate resource intensity indicators that adapts its work to pulse activity.
It is worth noting that SNNs inspired by the biological example, in principle, recognize images
much better and faster than conventional ANNs [12]. Moreover, SNNs allow the use of training
methods that depend on the time of occurrence of impulses between pairs of directly connected
neurons, in which information for changing the weight of edges is available locally. This training
method is very similar to what happens in many parts of the brain.
The resulting pulse bundle is represented as undifferentiated sums of Delta functions. Accordingly,
it is difficult to apply derivative-based optimization methods to SNN training, although various types
of approximate derivatives have recently been actively studied. Despite the fact that in theory pulse
neural networks have equivalent computing power in turing [13], it is still problematic to train SNNs,
especially those with a multi-layered architecture. In many existing pulse neural networks, only one
layer can be trained. If it is possible to provide pulse systems with multi-layer training, then
productivity in various tasks will increase tenfold.
The architecture of pulsed neural networks consists of pulsed neurons and interconnected
synapses. Pulse bundle in neural networks of impulse neurons propagate through synaptic
connections. A synapse can be either excitatory, when the membrane potential of a neuron increases
after receiving a signal, or slowing down. The amount of rib weight can change as a result of training.
Deep learning of multilayer SNNs is a real mystery, since the undifferentiation of pulse bundle does
not allow the use of popular methods, such as the backpropagation method (Fig. 2) [14-19].
Figure 2: Using the backpropagation method for correcting weights coefficients
2. Related Works
As mentioned earlier, the training of all kinds of artificial neural networks occurs by adjusting
scalar synaptic weights. In SNNs, can be used training methods that are close to those used by the
brain. Scientists have identified many variants of this training method, but all of them fall under the
general term dendritic plasticity (STDP) [20]. A key feature of dendritic plasticity is that the weight of
the rib connecting pre- and postsynaptic neurons is regulated with their pulse time in the range of
approximately tens of milliseconds in duration.
2.1. Method SpikeProp
This is the first method of training SNNs by error propagation [21], [22]. The cost function takes
into account the fluctuation period, and thus this method can classify nonlinearly separated data for a
time-encoded XOR problem using a 3-level architecture. The main decision at the stage of
development of the method was the choice of the Gerstner neuron model (so-called, SRM) [23].
Using this model, the question of taking derivatives at the oscillation output was circumvented, since
the required result was directly modeled as a continuous value. One of the limitations of this method
is that each original unit was forced to generate exactly one oscillation. In addition, the values of
continuous variables, such as in XOR problems, had to be encoded as delays between fluctuations,
which can be quite long.
2.2. Method Remote supervised learning (ReSuMe)
This training method consists of a single oscillating neuron, which receives vibrations from many
other oscillating presynaptic neurons [24]. The goal is to train the synapse to trigger a postsynaptic
neuron to generate oscillation waves with the desired oscillation period. ReSuMe adapted the delta
rule used for non-pulse linearized units to SNN. In the delta rule, the weights change proportionally:
y d y real x y d x y real x , (1)
where x is presynaptic input;
y d is desired output value;
y real is real value at the output.
By reformulating the equation above, you can get the sum of STDP s anti- STDP:
STDP S in , S d STDP S in , S real . (2)
STDP
The above is a function of correlation between presynaptic and desired oscillation
STDP
periods, where is depends on presynaptic and real oscillation periods. Since this method
uses a correlation between a set of presynaptic neurons and a wavering neuron, there is no physical
connection between them. This is why this method is called remote.
2.3. Method Chronotron
This method was developed based on the Temporal method [25], which could train individual
neurons to recognize the encoding at the exact time of arrival of the oscillation. A limitation of the
Temporal method was the ability to output 0 or 1 at the output during the selected time interval.
Because of this, it was impossible to encode information about the time of arrival of the oscillation in
the output data. The creation of Chronotron was influenced by the success of SpikeProp and its
successors. The idea of Chronotron was to use more complex units of distance measurement: VP [26]
between two vibrations for the training. They adapted the VP distance so that it was piecewise
differentiated and suitable as a function of cost to perform gradient descent with respect to weights.
2.4. Problems of existing methods
Among the existing methods, there are several main disadvantages. First, each channel needs a
separate quick convergence scheme. That is, there is a risk of multiplying derivatives on each channel,
which in the future can impose large computational needs [21-26].
Secondly, it becomes quite difficult to get a large number of channels due to pulse distortions that
occur when connecting matching circuits to coaxial cables [21-26].
But the key problem is always the question of topology (the structure of such a network). There
are many approaches that apply reverse propagation to SNNs. But such methods cannot use
traditional reverse propagation and change gradient updates or SNNs themselves to overcome this
complexity. These types of methods often impose architectural constraints on the resulting SNNs, for
example, requiring a feedforward connections SNN architecture. Therefore, there are many SNN
topologies with desired properties, such as repeatability, that cannot be optimized using these methods
[21-26].
That is why it is an urgent task to develop evolutionary methods for the full synthesis of the SNN
model. When implementing the methods of the evolutionary approach, SNN population assessment
will allow us to further use the processes of stochastic variation and selection to create the next
population or control these processes. During successive iterations of mutations and selection of
individual networks with increasing fitness, which can be broadly defined as accuracy in the
classification problem or maximum reward from the environment, the new solutions will be
qualitatively different from the previous ones. One of the significant advantages of evolutionary
approaches is their flexibility. As for SNNs, evolutionary optimization can potentially affect any
network topology, as well as optimize any network parameter.
3. Proposed method
In general, the method proposed in this paper is similar to a modified genetic algorithm (MGA) for
synthesizing ordinary ANNs [27]. So, at the beginning, it should be noted that direct encoding of the
structure of individuals is used to perform synthesis, each of which is a separate neural network, but
the basis of such encoding is inter-neural connections. This makes it possible to track the origin of
each parameter (node or connection) in the genome in more detail. In the subsequent stages of the
method, this greatly simplifies the processes of crossing and mutation, allowing you to build and
change genetic information about individuals [27].
The main innovation is the use of certain template mechanisms, namely neural patterns (NP) based
on Composite Pattern Producing Networks (CPPN) technology [28]. This mechanism provides
abstraction of the processes of natural evolution [28]. NPs will consist of neurons with various
activation functions, including periodic functions such as sinusoidal and symmetric functions such as
absolute value. The basic idea is based on the fact that a CPPN-based NP with multiple entry points
can determine the relationship between a pair of points. A fixed set of neurons is introduced as a
specific substrate to the NP, which further simplifies neurosynthesis using MGA.
In general, at the beginning of evolution, we obtain a population with NPs:
P Ind1 , Ind 2 , Ind3 ,..., Ind n NP1 , NP2 , NP3 ,..., NPn , that determine the connection patterns of
the resulting SNNs P NP1 , NP2 , NP3 ,..., NPn SNN1 , SNN 2 , SNN 3 ,..., SNN n . Each NP is defined
by encoded genetic information with the definition of its internal weights and activation functions.
However, it is important to note that each individual neuron in an NP can have any activation function
from a specific set (sin, tanh, gauss, relu, identity):
NP SNN struct , param Node, Connections, weights, Function [29-31]. To decipher SNN
from NP, the coordinates for a pair of neurons are passed to the network that creates the NP. The
network output determines the weight and delay of the connection between two neurons in the dive
neural network. This process is repeated for each pair of neurons to build a complete network.
After preparing the population, it is possible to perform further synthesis. The main steps for
synthesizing and decoding SNN from NP are shown in Fig. 3.
However, several nuances of this synthesis should be noted:
the positions of SNN neurons, in the form of NP, are pre-recorded during the evolutionary
search for each individual. That is, any mutation and modification is possible only in the form of a
new individual;
each solution is decoded and evaluated to complete a given task (classification or
management). Therefore, the suitability of the solution is determined by the performance of the
generated SNN for the specified task;
speciation is used to protect innovations in new solutions and can stop if they are not
available.
Figure 3: The general scheme of the method
4. Experimental research
To study the results of the method, the task of medical diagnostics was chosen. A data set was
selected as input about characteristics of patients with pneumonia, which was recently presented by
authors M.-A. Kim, J. Seok Park,C. W. Lee, and W.-I. Choi [32]. Total sample size: 77490 values.
Table 1 shows the characteristics of the data set.
For this task, the development of neuromodels will make it much easier to determine the further
diagnosis of a person after collecting data on their well-being. Given that pneumonia is one of the
most important signs and complications of COVID-19 [33], [34], after additional training on
advanced data, this model can be used to diagnose patients or predict the further development of
disease dynamics.
The effectiveness of SNN models will be compared with neuromodels based on recurrent neural
networks (RNNs) (Fig. 2.a)) and deep neural networks (DNNs) (Fig. 2.b)) [35].
RNN is a type of ANN and is used in natural language processing and speech recognition
applications. The RNN model is designed to recognize consistent data characteristics and then use
templates to predict the future scenario [35]. A DNN is a neural network with a certain level of
complexity, a neural network with more than two layers. DNNs use sophisticated mathematical
modeling to process data in complex ways [35].
For the experiments, a workstation with the following characteristics was used: Intel Core i5-
12600 central processor (3.30-4.80 GHz (Intel Turbo Boost 2.0), 6 cores and 12 threads), 16 Gb RAM
(dual-channel mode), SK hynix SC308 128 GB SSD (M.2), the Python programming language.
Table 2 shows the results of synthesis methods with different typologies of neural networks.
Table 1
General characteristics of the data set
Total number of values 77490 Number of attributes 54
The type of the data Numeric (after Number of instances' 1435
consideration of)
Table 2
General results on the data set
Methodof synthesis Synthesis Time, s Error at the training Error at the test
sample sample
MGA SNN 9352 0.01 0.137
MGA RNN 6793 0.018 0.148
MGA DNN 7625 0.014 0.138
5. Discussions of results
From the analysis of the obtained experimental results, we can conclude that the proposal to use
neuroevolution methods for SNNs synthesis shows good results for its further deployment and use.
After all, for networks of this class, the issue of a complex and sometimes not fully clear structure is
always relevant. The use of neuroevolutionary approaches with NP encoding and decoding greatly
facilitates this task, because in this case structural synthesis is reduced to well-known approaches to
neuroevolutionary synthesis using TWEANNs. Parametric synthesis, on the other hand, is fine-tuning
at exclusively defined stages without having to iteratively calculate fitness functions or its derivatives
over and over again.
On the other hand, we can conclude that the practical use of SNN-class neural networks is still
extremely promising, because the results obtained for the accuracy of work cannot fully demonstrate
the feasibility of significant time costs. Thus, the values of errors in both cases (training and testing)
do not differ in significance, which could cover the time spent on the synthesis of such networks and
their subsequent calculations. After all, it is worth noting that in the absence of specialized equipment
for emulating the operation of SNN, the execution of this process on a regular workstation is also
accompanied by time overlays.
Figure 4: The comparing of RNN and DNN topologies
It is also worth analyzing the work with complex topologies of classical ANNs separately. Thus,
the differences in synthesis time are explained by a simpler calculation and correction of recurrent
connections in contrast to the calculation of nodes and weights of interneuronal connections in a set of
hidden layers. And the analysis of the accuracy of the synthesized solutions based on training and test
data shows that the difference in accuracy is not critical and is acceptable within the task. That is why
we can talk about a specific indication, about the use of a particular ANN topology, depending on
which of the resources is more important: the time of synthesis and operation of the neuromodel or its
accuracy.
6. Conclusion
This paper presents an approach to neuroevolution synthesis of complex ANN topologies, namely
SNN. The aim of the work was to demonstrate the feasibility and effectiveness of the method. The
experiments shown demonstrate the strengths and weaknesses of the approach, as well as identify
ways for future research.
One of the main problems that is tracked from the very beginning is the sensitivity to mutations of
rigidly defined neuromodel structures. Because mutation of even one structural unit (for example,
between neural connections) leads to the creation of a completely new individual, which can
sometimes be perceived as undesirable computational difficulties.
However, the main theoretical advantage of this approach to SNN synthesis is the possibility of
controlled network development to a large size. In this work, only networks with fewer than a
hundred neurons were tested. Therefore, network scaling properties are a further area of research.
Another important research perspective is the introduction and use of methods for indirect
encoding of NP and ANN individuals in general during synthesis. Such approaches can help to study
in more detail the many variants of relationships between unique SNN characteristics. For example,
different input encoding strategies can lead to variability in the configuration of neurons for NP.
Future work may use more of the relationships between neuroevolution and SNNs and extend this
method to more complex tasks.
7. Acknowledgements
The work was carried out with the support of the state budget research projects of the state budget
of the National University "Zaporozhzhia Polytechnic" “Development of methods and tools for
analysis and prediction of dynamic behavior of nonlinear objects” (state registration number
0121U107499) and “Intelligent methods and tools for diagnosing and predicting the state of complex
objects” (state registration number 0122U000972).
8. References
[1] D. Ping, The Machine Learning Solutions Architect Handbook: Create machine learning
platforms to run solutions in an enterprise setting, Packt Publishing, Birmingham, 2022.
[2] A. Burkov, Machine Learning Engineering, True Positive Inc., Quebec City, 2020.
[3] A. Park, Machine Learning: 2 Books in 1 – The Complete Guide for Beginners to Master Neural
Networks, Artificial Intelligence, and Data Science with Python, 2nd. ed., Independently
published, 2022.
[4] S. Alkhalifa, Machine Learning in Biotechnology and Life Sciences: Build machine learning
models using Python and deploy them on the cloud, Packt Publishing, Birmingham, 2022.
[5] C.C. Aggarwal, Neural Networks and Deep Learning: A Textbook, Springer, Berlin, 2018.
[6] P.R. Hiesinger, The Self-Assembling Brain: How Neural Networks Grow Smarter, Princeton
University Press, Princeton, 2021.
[7] D. Graupe, Principles of Artificial Neural Networks: Basic Designs to Deep Learning (4th
Edition) (Advanced Circuits and Systems), 4th ed., WSPC, Singapore, 2019.
[8] A.Hodgkin, A. Huxley, A quantitative description of membrane current and its application to
conduction and excitation in nerve, J. Physiol, vol. 117(4), (1952) 500-544. doi:
10.1113/jphysiol.1952.sp004764
[9] R. Jolivet, J. Timothy, W. Gerstner, The Spike Response Model: A Framework to Predict
Neuronal Spike Trains, in: Proceedings of the 2003 joint international conference on Artificial
neural networks and neural information processing, ICANN/ICONIP'03, ACM Digital Library,
2003, pp. 846-853. doi: 10.1007/3-540-44989-2_101
[10] E. Izhikevich, Simple model of spiking neurons, Transactions of neural networks, vol. 14, (2003)
1569-1572. doi: 10.1109/TNN.2003.820440
[11] A. Delorme et al., SpikeNET: A simulator for modeling large networks of integrate and fire
neurons, Neurocomputing, vol. 26(7), (1999) 989-996. doi: 10.1016/S0925-2312(99)00095-8
[12] 14 . M. Pfeiffer, T. Pfeil, Deep learning with spiking neurons: Opportunities and challenges,
Frontiers in Neuroscience, vol. 12: 774 (2018). doi: 10.3389/fnins.2018.00774
[13] 13 W. Maass, Lower bounds for the computational power of networks of spiking neurons, Neural
Computation, vol. 8, (1996) 1-40.
[14] J.A.J. Alsayaydeh, A. Aziz, A.I.A. Rahman, S.N.S. Salim, M. Zainon, Z.A. Baharudin, M.I.
Abbasi, A.W.Y. Khang, Development of programmable home security using GSM system for
early prevention, vol. 16(1) (2021) 88-97.
[15] J.A.J. Alsayaydeh, W.A.Y. Khang, W.A. Indra, V. Shkarupylo, J. Jayasundar, Development of
smart dustbin by using apps, ARPN Journal of Engineering and Applied Sciences, vol. 14(21)
(2019) 3703-3711.
[16] J.A.J. Alsayaydeh, W.A.Y. Khang, W.A. Indra, J.B. Pusppanathan, V. Shkarupylo, A.K.M. Zakir
Hossain, S. Saravanan, Development of vehicle door security using smart tag and fingerprint
system, ARPN Journal of Engineering and Applied Sciences, vol. 9(1) (2019) 3108-3114.
[17] J.A.J. Alsayaydeh, W.A.Y. Khang, A.K.M.Z Hossain, V. Shkarupylo, J. Pusppanathan, The
experimental studies of the automatic control methods of magnetic separators performance by
magnetic product, ARPN Journal of Engineering and Applied Sciences, vol. 15(7) (2020) 922-
927.
[18] J.A.J. Alsayaydeh, W.A. Indra, W.A.Y. Khang, V. Shkarupylo, D.A.P.P. Jkatisan, Development
of vehicle ignition using fingerprint, ARPN Journal of Engineering and Applied Sciences, vol.
14(23) (2019) 4045-4053.
[19] J.A. Alsayaydeh, M. Nj, S.N. Syed, A.W. Yoon, W.A. Indra, V. Shkarupylo, C. Pellipus, Homes
appliances control using bluetooth, ARPN Journal of Engineering and Applied Sciences, vol.
14(19) (2019) 3344-3357.
[20] S. Tazerart, D. E. Mitchell, S. Miranda-Rottmann, R. Araya, A spike-timing-dependent plasticity
rule for dendritic spines, Nature Communications, vol. 11 (2020). doi: 10.1038/s41467-020-
17861-7
[21] R.V. Florian, Supervised Learning in Spiking Neural Networks. In: Seel N.M. (eds)
Encyclopedia of the Sciences of Learning. Springer, Boston, MA, 2012. doi: 10.1007/978-1-
4419-1428-6_1714
[22] S. M. Bohte, Error-backpropagation in temporally encoded networks of spiking neurons, in:
Proceedings of the Artificial Neural Network and Machine Learning, ICANN 2011, ACM
Digital Library, 2011, pp. 60-68.
[23] W. Gerstner, W. M. Kistler, Spiking neuron models: Single neurons, populations, plasticity,
Cambridge University Press, Cambridge, 2002.
[24] F. Ponulak, A. Kasinski, Supervised learning in spiking neural networks with ReSuMe: Sequence
learning, classification, and spike shifting, Neural Computation, vol. 22, (2009) pp. 467-510. doi:
10.1162/neco.2009.11-08-901
[25] R. Gütig, H. Sompolinsky, The tempotron: A neuron that learns spike timing-based decisions,
Nature Neuroscience, vol. 9, (2006) 420-428. doi: 10.1038/nn1643
[26] T. Serre, Hierarchical models of the visual system, Encyclopedia of Computation Neuroscience,
Springer, New York, NY, 2014. doi: 10.1007/978-1-4614-7320-6_345-1
[27] S. Leoshchenko, A. Oliinyk, S. Subbotin, N. Gorobii, T. Zaiko, Synthesis of artificial neural
networks using a modified genetic algorithm, in: Proceedings of the 1st International Workshop
on Informatics & Data-Driven Medicine, IDDM 2018, CEUR-WS, 2018, pp. 1-13
[28] D. Elbrecht, C. Schuman, Neuroevolution of Spiking Neural Networks Using Compositional
Pattern Producing Networks, in: Proceedings of the ICONS 2020: International Conference on
Neuromorphic Systems 2020, ICONS 2020, ACM Digital Library, 2020, pp. 1-5. doi:
10.1145/3407197.3407198
[29] A.Oliinyk, S. Skrupsky, S. Subbotin, Experimental research and analysis of complexity of
parallel method for production rules extraction. Automatic Control and Computer Sciences, 52
(2) (2018) 89-99. doi: 10.3103/S0146411618020062
[30] S. Leoshchenko, A. Oliinyk, S. Skrupsky, S. Subbotin, T. Zaiko, Parallel Method of Neural
Network Synthesis Based on a Modified Genetic Algorithm Application, in: Proceedings of the
8th International Conference on Mathematics. Information Technologies. Education,
MoMLeT&DS-2019, CEUR-WS, 2019, pp. 11–23.
[31] A.Oliinyk, S. Leoshchenko, V. Lovkin, S. Subbotin, T. Zaiko, Parallel data reduction method for
complex technical objects and processes, in: Proceedings of the 2018 IEEE 9th International
Conference on Dependable Systems, Services and Technologies, DESSERT-2018, IEEE, 2018,
pp. 496-501. doi: 10.1109/DESSERT.2018.8409184
[32] M.-A. Kim, J. Seok Park,C. W. Lee, W.-I. Choi, Pneumonia severity index in viral community
acquired pneumonia in adults, PLoS One, vol. 14(3) (2019). doi: 10.1371/journal.pone.0210102
[33] G. Raghu, K. C Wilson, COVID-19 interstitial pneumonia: monitoring the clinical course in
survivors, The Lancet Respiratory Medicine, vol. 8(9) (2020) 839-842. doi: 10.1016/S2213-
2600(20)30349-0
[34] A. Hani, N.H. Trieu, I. Saab, S. Dangeard, S. Bennani, G.Chassagnon, M.-P. Revel, COVID-19
pneumonia: A review of typical CT findings and differential diagnosis, Diagnostic and
Interventional Imaging, vol. 101(5) (2020), 263-268. doi: 10.1016/j.diii.2020.03.014
[35] S. Leoshchenko, A. Oliinyk, S. Subbotin, T. Zaiko, A Using modern architectures of recurrent
neural networks for technical diagnosis of complex systems. Proceedings of the 5th International
Scientific-Practical Conference Problems of Infocommunications. Science and Technology
(PICST2018), IEEE, Kharkiv, Ukraine, 2018, pp. 411–416. doi:
10.1109/INFOCOMMST.2018.8632015