=Paper=
{{Paper
|id=Vol-2864/paper6
|storemode=property
|title=Implementation of Probabilistic Data Structures in the Processes of Neuroevolutionary Synthesis
|pdfUrl=https://ceur-ws.org/Vol-2864/paper6.pdf
|volume=Vol-2864
|authors=Serhii Leoshchenko,Andrii Oliinyk,Sergey Subbotin,Viktor Lytvyn,Oleksandr Korniienko
|dblpUrl=https://dblp.org/rec/conf/cmis/LeoshchenkoOSLK21
}}
==Implementation of Probabilistic Data Structures in the Processes of Neuroevolutionary Synthesis==
https://ceur-ws.org/Vol-2864/paper6.pdf
Implementation of probabilistic data structures in the
processes of neuroevolutionary synthesis
Serhii Leoshchenkoa, Andrii Oliinyka, Sergey Subbotina, Viktor Lytvyna and Oleksandr
Korniienkoa
a
National university “Zaporizhzhia polytechnic”, Zhukovskogo street 64, Zaporizhzhia, 69063, Ukraine
Abstract
Neuroevolutionary synthesis is an alternative to training a pre-designed neural network. The
use of neuroevolution methods is explained by fewer free parameters, less dependence on the
expert, and usually better adaptive characteristics. However, neuroevolution methods are
more resource-intensive, because the synthesis uses populations consisting of a large number
of networks. Various mechanisms, such as parallelization, can be used to solve problems
related to synthesis time. However, they usually lead to even more memory usage in the
process. Mechanisms such as selective pressure only partially solve this problem.
Probabilistic data structures have proven to be a fairly compact storage mechanism.
Therefore, the paper provides an example and analysis of ways to use probabilistic data
structures during the neuroevolutionary synthesis of artificial neural networks.
Keywords 1
Neuroevolutionary, synthesis, artificial neural networks, probabilistic data structures,
encoding, sequencing, genetic operators
1. Introduction
Artificial neural networks (ANN) are one of the areas of scientific research in the field of creating
artificial intelligence [1-3], which is based on the desire to imitate the human nervous system [3-5].
Including its (nervous system's) ability to correct mistakes and self-learn [5-7]. The scope of
application of ANNs is constantly expanding, today they are used in such areas as:
machine learning, which is a type of artificial intelligence [1-7]. It is based on training the
ANN on the example of millions [8-11] of tasks of the same type. Nowadays, machine learning is
actively implemented by Google [12-15], Bing [16], [17], and Baidu [18], [19] search engines. So
based on the millions of search queries that we all enter into search systems every day, their
algorithms learn to show us the most relevant results so that we can find exactly what we are
looking for [14], [15];
in robotics [20], [21], neural networks are used to develop numerous algorithms for the Iron
"brains" of robots. Here, training usually uses methods that implement a reinforcement learning
strategy, such as swarm intelligence or the actor-critical method (A2C and A3C) [22-25];
computer system architects use neural networks to solve the problem of parallel computing
[4], [7];
with the help of neural networks, scientists can solve various complex mathematical problems
[6].
As already mentioned in one of the theses, before direct training of the ANN, it is necessary to
train. This can be done using certain examples (supervised learning), using information about the
environment and the state of the "agent" in that environment (reinforcement learning), or without any
CMIS-2021: The Fourth International Workshop on Computer Modeling and Intelligent Systems, April 27, 2021, Zaporizhzhia, Ukraine
EMAIL: sergleo.zntu@gmail.com (S. Leoshchenko); olejnikaa@gmail.com (A. Oliinyk); subbotin@zntu.edu.ua (S. Subbotin);
lytvynviktor.a@gmail.com (V. Lytvyn); al.korn95@gmail.com (O. Korniienko)
ORCID: 0000-0001-5099-5518 (S. Leoshchenko); 0000-0002-6740-6078 (A. Oliinyk); 0000-0001-5814-8268 (S. Subbotin); 0000-0003-
4061-4755 (V. Lytvyn); 0000-0003-4812-5382 (O. Korniienko)
© 2021 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)
clear input information at all (unsupervised learning) [26-33]. Neuroevolution methods can be used
for all approaches, because usually, in addition to conventional training (parametric synthesis),
neuroevolution methods adjust the structure (topology) of the ANN (structural synthesis) [37], [38].
Such methods are separated into a separate group of methods for the evolution of interneuronal
connections and network topologies (TWEANNs) [37] ,[38], which are individuals in the population.
However, one of the main disadvantages of neuroevolution methods is their resource intensity.
Large amounts of synthesis time are usually explained by the search for the most optimal ANN
structure, which is achieved by using evolutionary mechanisms in individual populations. On the
other hand, taking into account the fact that in usual network training, using gradient methods, it is
necessary to design topologies first and only then train it, it should be noted that neuroevolutionary
synthesis automates this subprocess [39-42]. Moreover, the use of parallelization can significantly
speed up the synthesis process [39-42]. And given the fact that almost all neuroevolution methods can
be parallelized, this removes the speed problem. However, parallelization imposes additional memory
requirements on the computing system. The use of selective pressure mechanisms [43] can increase
the level of adaptability of final decisions and reduce memory usage, but in sequential systems it can
lead to a low level of genetic diversity.
Therefore, the question arises about using certain special structures to preserve information about
the population. Moreover, the use of these structures is possible at the stage of encoding genetic
information about an individual, even at the beginning of synthesis.
Probabilistic data structures (PDS) are a group of data structures that are extremely useful for big
data and streaming applications [44-46]. Generally speaking, these data structures use hash functions
to randomize and compactly represent a set of elements. Data collisions are ignored (usually using a
number of mechanisms that prevent such situations), and errors are controlled at a certain threshold.
Compared to error-free approaches, these algorithms use much less memory and have a constant
query time. Moreover, support for union and intersection operations provides a low level of
parallelization complexity.
Therefore, let's look at what stages of synthesis the use of PDS is justified and appropriate. The
main stages are shown in Figure 1.
Figure 1: Synthesis stages where PDS can be implemented
Analyzing Figure1 note that the implementation of PDS during synthesis is advisable at the
following stages:
encoding of genetic information about ANN, as individuals of the population;
crossover of individuals (since PDS supports unification and intersection).
Special cases can be considered situations when information about the ANN is transmitted, for
example, between the cores of parallel computing systems or computing nodes, as shown in Figure 2.
Population initialization
Evaluating individuals Evaluating individuals Evaluating individuals
Selection and formation of Selection and formation of Selection and formation of Coding
the parent pool the parent pool the parent pool (PDS)
Recombination (crossover) Recombination (crossover) Recombination (crossover)
Thread1
Thread2
Variations (mutation) Variations (mutation) Threadn Variations (mutation)
Evaluating individuals
Solution
Figure 2: ANNs forwarding in parallel systems
2. Literature Review
Statistical analysis and analysis of data that related to big data is a common and quite relevant task,
especially in such areas as smart systems, Internet of things (IoT), Cognitive Internet of Things
(CIoT), web analytics [44-47]. One of the options for organizing data storage when analyzing big data
is powerful distributed databases and data warehouses: Hydra [48], [49], Hadoop [50] and NetApp
[51], [52]. For processing, the same methods can be used, as in MapReduce, to search for a HashSet
[49], [52]. However, such approaches are fraught with low problems in real-time data processing, due
to the excessive importance of high-latency analytical processes and poor applicability. Therefore, if
simple additive metrics (such as total transactions, total page views, or average conversion price) are
most valuable during analytics, it is obvious that the raw data can be effectively summed up, for
example, on a daily basis or using simple counters in the flow. Calculating more complex metrics
(such as average humidity, the number of unique users, or the most frequently encountered elements)
is more complex and requires more resources if implemented consistently. PDS allows to evaluate
these and many other metrics and manipulate [44-46] the accuracy of estimates for memory
consumption. These data structures can be used as temporary data accumulators in query processing
procedures, or perhaps more importantly, as a compact, sometimes surprisingly compact, replacement
for raw data in streaming computing.
A number of PDS’s will be analyzed in abstracts, while others are described in detail using a
detailed mathematical analysis of these structures can be found in the original articles. Preliminary
comments are as follows [47]:
for some structures, such as Loglog Counter or Bloom filter, there are simple and practical
formulas that allow you to determine the structure parameters based on the expected amount of
data and the required error probability. Other structures, such as Count-Min Sketch or Stream-
Summary, have a complex dependence on the statistical properties of data, and experiments are the
only reasonable way to understand their applicability to real-world use cases;
the applicability of the PDSs is not strictly limited to the above queries or a single set of data.
Experiments and other works prove that structures filled with different data sets can often be
combined to handle complex queries, and other types of queries can be supported using custom
versions of the described algorithms.
2.1. Bloom filter
Bloom filter is probably the most well-known and widely used PDS [53-56]. Bloom filter is
similar to Linear Counting, but it is designed to maintain the identity of each element, not statistics. A
Bloom filter is a bit array of M bits initialized at 0. To add an element, it is processed by k hash
functions to get k array positions, and set the bits in these positions to 1. To request an element, it is
passed to k hash functions to get k array position. If any of the bits in these positions are 0, then the
element is definitely not included in the set. If all bits are equal to 1, then the element can be in the
set. That is, If the filter has a relatively large size compared to the number of individual elements,
each element has a relatively unique signature and you can check a specific value – whether it is
already registered in the bit set or not. If all the bits of the corresponding signature are units, then the
answer is yes (with a certain probability, of course). Bloom filter with a false positive rate of 1%
requires only 9.6 bits per element, regardless of the size of the elements [54-56].
Similar to Linear Counting, Bloom filter supports bit typing. However, as the from description
makes clear, each value is mapped not to one, but to a certain fixed number of bits using several
independent k hash functions.
Let's consider formulas that allow us to calculate the parameters of the Bloom filter as a function
of error probability and capacitance. Given false positive probability p and the estimated number of
insertions n , the length of the bit array can be calculated as [54-56]:
n ln p
m , (1)
ln 2 2
where m is filter (sketch) size (bits);
p is an error probability (false positive);
n is maximum cardinality (capacity).
The hash functions used for bloom filter should generally be faster than cryptographic hash
algorithms with good distribution and collision resistance.
m
k ln 2 , (2)
n
where k is number of hash functions.
In Figure 3 shows an example of placing elements in Bloom filter.
Consider an example: we enter x , y and z in the filter with k 3 hash functions, as shown in the
figure above. Each of these three elements has three bits, each with a value of 1 in the bit array. When
we search for w in the set because one of the bits is not set to 1, Bloom filter will tell us that it is not
in the set [53-56].
Figure 3: Placing elements in Bloom filter
2.2. MinHash
To begin with, MinHash is not just a PDS. In computer science and data mining, MinHash is a
method for quickly estimating how similar two sets are. This scheme was invented by Andrei Broder
(1997) [57] and was originally used in the AltaVista search engine to detect duplicate web pages and
exclude them from search results [58]. It has also been used in large-scale clustering tasks, such as
clustering documents based on the similarity of their word sets.
Let's introduce the concept of Jacquard similarity coefficient (Jaccard similarity coefficient) [57],
[58]:
A B
J A, B . (3)
A B
In other words, the number of elements in the cross-section is divided by the number of elements
in the union. This estimate is called the Jacquard coefficient, the coefficient is zero when the sets have
no common elements, and one when the sets are equal, in other cases the value is somewhere in the
middle. In general, the calculation of such a coefficient boils down to the fact that at the beginning we
need to divide the sets into separate parts, these will be the elements of our sets, then we need to
somehow calculate the dimensions of the intersection and union. Usually, to efficiently perform the
last two operations, sets are represented as hash tables without key-associated values.this structure
works very quickly. Building a table: On , you need two of them, calculating the cross section: On
and calculating the union is also On , where n is the number of elements in the set [57], [58].
Here are two sets A , B and h a hash function that can count hashes for elements of these sets.
Next, we define the function hmin S , which calculates the function h for all members of any set S
and returns its lowest value. Now, let's start calculating hmin A and hmin B for different pairs of sets,
the question is: what is the probability that hmin A hmin B .
This probability must be proportional to the size of the intersection of sets: in the absence of
common terms, it tends to zero, and to one, when the sets are equal, in intermediate cases it is
somewhere in the middle. This is the J A, B so Jacquard coefficient.
However, if we just count hmin A and hmin B for our two sets and then compare the values, it
won't give us anything, because there are only two options: equal or not equal. We need to somehow
get enough statistics for our sets to calculate J A, B close to the truth. This is done simply, instead of
one function h , we introduce several independent hash functions, or rather k functions [57]:
1
k 2, (3)
where is the highest error value is desired. So, to calculate J A, B with an error of no more than
0.1, you need 100 hash functions. On the one hand, this is a lot. So let discuss in what will be the
optimization.
First, we can calculate the so-called H min S signature, i.e. the minima of all hash functions for the
set S . The complexity of calculating it is greater than when building a hash table, but, nevertheless, it
is linear, and you only need to do this for each document once, for example, when adding it to the
database, then it is enough to operate only with signatures [58].
Secondly, the signature has a fixed size for a given maximum error value. In order to compare any
two sets of any size, you need to perform a fixed number of operations. In addition, in theory,
signatures are much more convenient to index. In theory, because their indexing does not fit very well
on relational databases, it is also not particularly suitable for full-text engines.
2.3. Count‐Min Sketch
Count-min sketch is a PDS that is a table of event frequencies in a data stream. It uses hash
functions to map events to frequencies, but unlike a hash table, it uses only sublinear space, by
recalculating some events due to collisions [47], [59].
The Count-min sketch structure can be represented as a sketch with depth d and width w as at
Figure 4.
Depth d
Width w
Figure 4: Count‐min sketch with depth d and width w
Then we represent the distribution of values in the Count–min sketch array, based on the principle
shown in Figure 5 this distribution can be considered a sketch.
Figure 5: Distribution of values in the structure
In general, we will have a representation with a distribution according to the following rules (4)
and (5).
estimation 2 max cardinalityhashfunction / widthsketch , (4)
1 0.5depthsketch , (5)
estimation is an evaluation error;
is a probability for a value with Count-min sketch;
cardinalit y hashfuncti on is a power of the hash function;
depthsketch is a sketch depth (height) ;
widthsketch is a sketch width.
It is worth noting that the width of the sketch limits the error value (4), and the height (depth)
controls the probability that the score will break this limit (5) [47], [59].
2.4. Comparison of PDS for further work
Let's compare the analyzed PDS. The comparison is shown in tabular form in Table. 1.
Table 1
PDS comparison
Comparison criteria Bloom Filter MinHash Count‐Min Sketch
Required number of Low High Low
hash functions
Complexity of hash Low Low Low
functions
Sketch size Medium Big Small
Frequency of false Very low Low Low
positives
Ability to add / / delete Requires modifications Missing Maybe
items
As can be seen from the tabular comparison, all the analyzed PDS have certain disadvantages,
which may become certain limitations for their further practical use during neurosynthesis [47], [60].
So for Bloom Filter, there are restrictions on adding or removing elements. This problem is solved in
the latest modifications, but such mechanisms significantly complicate the work. MinHash requires a
large number of hash functions while running, and while they may be quite simple, calculating them
still takes up some time resources. Moreover, when using a large number of such hash functions, the
sketch of the resulting view also becomes more complicated. Count-Min Sketch looks like the best
option in this comparison, precisely because of the low complexity of the sketch and low
requirements for the number and complexity of hash functions. However, it should still be noted that
there is a higher probability of false triggering (although it is also noted in other PDS cases) [47],
[60].
Therefore, we will plan the further use scheme based on these shortcomings.
3. Materials and methods
Based on the above-mentioned features, subprocesses of neurosynthesis and analysis of the most
popular PDS, we will determine the scheme of implementation of PDS in the process of
neuroevolutionary synthesis of ANN:
Bloom Filter will be used when sending information about the ANN between the cores of a
parallel system;
MinHash is used in the sequential execution of neuroevolutionary synthesis to encode genetic
information about individuals, to assess acceleration at the breeding stage;
Count-Min Sketch will also be used to encode genetic information about individuals during
neuroevolution synthesis.
Previously, it has been noted that all genetic information about neural networks is encoded using
direct coding sequencing [61-64]. In general, this approach is based on coding connections: the
genotype of an individual presents information about the weights ( WW ) of interneuronal connections
of the neuromodel, but each gene will contain information about the indices of the initial ( N i ) and
final ( N o ) communication neuron, as well as its weight. In the case when the method works with
recurrent neural networks, an additional cell with the feedback weight is added, its index is
determined by the index of the original neuron.
When using Bloom filter, four hash functions will be used, which will be used to sequentially
encode values from an array of interneuronal relationships [65]:
H 1 N i H 2 N o H 3WW f WW , (6)
So, to find the value of f WW , hash WW four times, perform three table searches, and exclude-or
combine-four values. In practice, four v hashes can be reduced to a single 64-bit or 128-bit hash,
which is divided into four 16-bit or 32-bit values, respectively.
Such an operation will be performed with the best individuals before sending them from parallel
cores to the main thread of the parallel system to investigate the reduction of overhead costs.
MinHash will be used for coding and subsequent comparison in sequential neuroevolution
synthesis. However, since adding or removing data from such a structure is not possible (or not
rational due to computational costs), the population size will increase and the number of epochs will
decrease [57].
When using Count-min Sketch, an array of data about the ANN is represented as a specific sketch
and decoded afterwards as at Figure 6.
Figure 6: Encoding and decoding information about the ANN using Count‐min sketch
Thus, the proposed encoding method begins with an initial representation of a matrix constructed
from so called polymer cells containing information about the input-output connections between
neurons and the weights of such connections.
Next, hash functions are defined (by default, we recommend taking 4 hash functions) and a matrix
is created for their output, as shown in Figure6.
After that, hash outputs are calculated for each element of the ANN data stream and the
corresponding counter in the matrix is increased.
Thus, increasing the corresponding counts in the matrix, we get an updated matrix.
In some cases, due to a hash collision, it is possible that the received frequency of the element is
slightly higher than expected. The encoding accuracy will depend on how unique the hash functions
that return the element value are. Also, the larger the hash function, the more accurate the frequency
will be.
In this case, the probabilistic data structure Count–min sketch allows you to calculate the
frequency of big data flows in sublinear space with an estimated time complexity, that is O1 , with a
constant time component that does not depend on the parameters of the neural network model.
4. Experimental research
For an experimental study of the work, it was decided to choose a moderate sample of data as a
sample, which would not initially require additional complications of neural networks, since this can
become a problem in the case of using MinHash. test it on two tasks that would differ in scale. This is
how the Tic-Tac-Toe Endgame Data Set was selected [66-69]. The main characteristics of the sample
are shown in Table 2.
As a parallel computing system, the equipment of Department of the software tools the National
university "Zaporizhzhia polytechnic" was used: Xeon processor E5-2660 v4 (14 cores), RAM 4x16
GB DDR4, the programming model of Java threads.
Table 2
Characteristics of the tic‐Tac‐Toe endgame data set sample
Tic‐Tac‐Toe Endgame Data Set
Data Set Characteristics: Multivariate Number of Instances: 958
Attribute Characteristics: Categorical Number of Attributes: 9
To test the MinHash case, the metaparameters specified in Table 3 will be set.
Table 3
Metaparameters for the MinHash use case
Comparison criteria Bloom Filter
Population size 100
Number of training epochs 1
Elite size 5%
Activation function (fitness functions) hyperbolic tangent
Probability of mutation 25%
Crossover type two‐point
Types of mutation deleting an interneuronal connection
removing a neuron
adding interneuronal connection
adding a neuron
changing the activation function
For testing the Count–min sketch case, the main parameters remain unchanged, but the number of
epochs increases to 5.
When testing the Bloom Filter use case, not only the meta parameters of the method were met, but
also the hardware usage parameters specified in Table 4.
Table 4
Metaparameters for the Bloom Filter use case
Comparison criteria Bloom Filter
Population size 100
Number of training epochs 5
Elite size 5%
Activation function (fitness functions) hyperbolic tangent
Probability of mutation 25%
Type of crossover on parallel threads two‐point
Type of crossover on the main thread uniform (two‐point)
Types of mutation deleting an interneuronal connection
removing a neuron
adding interneuronal connection
adding a neuron
changing the activation function
Number of cores (threads) 14
The test results for the tic-tac-Toe Endgame data set sample presented using MinHash are shown
in Table 5.
The test results for the tic-tac-Toe Endgame data set sample presented using Count-Min Sketch are
shown in Table 6.
Table 5
Test results using MinHash
Memory usage
Time at the Error in the
Synthesis (at the Error in the
Method selection training
Time, s selection test sample
stage, s sample
stage)
MGA 2487 561 91% 0.11 0.24
MGA +
2189 287 61% 0.11 0.25
MinHash
Table 6
Test results using Count‐Min Sketch
Memory usage
Time at the Error in the
Synthesis (at the Error in the
Method selection training
Time, s selection test sample
stage, s sample
stage)
MGA 5364 1742 94% 0.024 0.13
MGA +
Count‐Min 4865 1025 56% 0.029 0.15
Sketch
The test results for the tic-tac-Toe Endgame data set sample presented using Bloom filter are
shown in Table 7.
Table 7
Test results using Bloom filter
Average time
Error in the
Synthesis Communication of Error in the
Method training
Time, s overhead communication test sample
sample
overhead
MGA 2494 0.4 199.5 0.022 0.1
MGA +
Bloom 1867 0.28 104.6 0.03 0.174
filter
5. Analysis of experimental results
Analyzing the presented results, we can come to the following conclusions. When using MinHash,
there were no significant improvements: it was at the selection stage that memory usage decreased
from 92% to 61%, but up to this point, memory usage has not changed. Also, the acceleration was
only at the selection stage, namely from 1742 s to 1025 s. However, the time for encoding and
decoding networks increased significantly, precisely because of the complexity of this process, so the
optimization was rather point-based and cannot be recommended for use in the future. In addition, we
should mention the low accuracy due to the reduction in the number of epochs and the inability to use
crossbreeding.
When using Count-min Sketch, the acceleration situation was similar, because during the
execution of the method, the acceleration was noticeable, but the process of encoding and decoding
individuals took too long, so the total synthesis time is almost the same. But memory usage has really
become justifiably optimized from 94% to 56%. This can be explained by the fact that, unlike
MinHash, almost during the entire process, in addition, such encoding made it possible to perform
mutation and crossing without significant problems. On the other hand, we should note a slight
decrease in the accuracy of operation (due to false positives of the decoded network).
Using Bloom filter made it possible to reduce the share of shipments and their time, because data
was sent from cores in a compact format. In addition, decoding networks on the main core did not
impose additional complex calculations on parallel cores. However, even this strategy did not
significantly improve the speed of work. Moreover, although uniform crossing was chosen on the
main core, during the development of information modules, the problem of organizing multi-parent
crossing arose. Therefore, unfortunately, it was necessary to use uniform crossover as a two-point
crossover.
In general, it can be seen that the most promising is the use of Count-min Sketch, because this
made it possible to perform the full synthesis process without additional complications.
6. Conclusions
The paper examines the variants and possibilities of using PDS in neuroevolutionary synthesis of
ANNs, which can significantly reduce memory usage during synthesis and speed up this process.
The scientific novelty lies in the fact that during neuroevolutionary synthesis at different stages
and with different execution schemes (sequential and parallel), it is proposed to use different PDS.
This made it possible to study options for reducing resource intensity pointwise and in general.
Studies have shown that despite the popularity of PDS for preserving big data in neuroevolutionary
synthesis, this approach meets a number of obstacles. Moreover, during the work, recommendations
were developed for the use of individual PDS for individual stages and approaches.
The practical significance lies in the fact that practical problems of coding the ANN are solved,
which can later be used for diagnostics, forecasting, evaluation and modeling. The results of the
experiments showed that the proposed coding methods make it possible to encode information about
the ANN more compactly for its subsequent transmission to workstations for use as a model for
diagnosis, prediction, evaluation and modeling.
Prospects for further research and development areas include a detailed analysis of the use of the
Count-Min sketch data structure. This is due to the most acceptable results when testing various PDS
and approaches to their use.
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” “Intelligent methods and software for
diagnostics and non-destructive quality control of military and civilian applications” (state registration
number 0119U100360) and “Development of methods and tools for analysis and prediction of
dynamic behavior of nonlinear objects” (state registration number 0121U107499).
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