Method for Automatic Processing of Audit Content Based on Bidirectional Neural Network Mapping

Abstract

Currently, the analytical procedures used during the audit are based on data mining techniques. The object of the research is the process of the content auditing of the receipt of raw materials for production and the manufactured products. The aim of the work is to increase the effectiveness and efficiency of audit due to mapping by full (bidirectional) counterpropagating neural network of content of the receipt of raw materials for production and the manufactured products while automating procedures for checking their compliance. The vectors of feature for the objects of the sequences of the receipt of raw materials for production and the manufactured products are generated, which are then used in the proposed method. The created method, in contrast to the traditional one, provides for a batch mode, which allows the method to increase the learning rate by an amount equal to the product of the number of neurons in the hidden layer and the power of the training set, which is critically important in the audit system for the implementation of multivariate intelligent analysis, which involves enumerating various methods of forming subsets analysis. The urgent task of increasing the audit efficiency was solved by automating the mapping of audit indicators by full (bidirectional) counterpropagating neural network. A learning algorithm based on -means has been created, intended for implementation on a GPU using CUDA technology, which increases the speed of identifying parameters of a neural network model. The neural network with the proposed training method based on the -means rule can be used to intellectualize the DSS audit. The prospects for further research are the application of the proposed method by neural network mapping for a wide class of artificial intelligence tasks, in particular, for creating a method for bidirectional mapping indicators of audit tasks.

Keywords

• 1 audit
• mapping by neural network
• full (bidirectional) counterpropagating neural network
• content of the receipt of raw materials for production and the manufactured products

1. Introduction

In the process of development of international and national economies and industry of IT in particular, it is possible to distinguish the following basic tendencies: realization of digital transformations, forming of digital economy, globalization of socio-economic processes and of IT accompanying them [1]. These processes result in the origin of global, multilevel hierarchical structures of heterogeneous, multivariable, multifunction connections, interactions and cooperation of managing subjects (objects of audit), the large volumes of information about them have been accumulated in the informative systems of account, management and audit.

Consequently, nowadays the scientific and technical issue of the modern information technologies in financial and economic sphere of Ukraine is forming of the methodology of planning and creation of the decision support systems (DSS) at the audit of enterprises in the conditions of application of IT and with the use of information technologies on the basis of the automated analysis of the large volumes of data about financial and economic activity and states of enterprises with the multi-level hierarchical structure of heterogeneous, multivariable, multifunction connections, intercommunications and cooperation of objects of audit with the purpose of expansion of functional possibilities, increase of efficiency and universality of IT-audit.

Currently, the analytical procedures used during the audit are based on data mining techniques [24]. Automated DSS audit means the automatic forming of recommendable decisions, based on the results of the automated analysis of data, that improves quality process of audit [5,6]. Unlike the traditional approach, computer technologies of analysis of data in the system of audit accelerate and promote the process accuracy of audit, that extremely critical in the conditions of plenty of associate tasks on lower and middle levels, and also amounts of indexes and supervisions in every task [7,8].

When developing a decision-making system in audit based on data mining technologies, three methods have been created: classifying variables, forming analysis sets, mapping analysis sets.

The peculiarity of the methodology for classifying indicators is that qualitatively different (by semantic content) variables are classified: numerological, linguistic, quantitative, logical. The essence of the second technique is determined by the qualitative meaning of the indicators. In accordance with this, sets are formed with the corresponding semantic content: document numbers, the name of indicators, quantitative estimates of the values of indicators, logical indicators.

The third technique is subordinated to the mappings of formed sets of the same type on each other in order to determine equivalence in the following senses: numerological, linguistic, quantitative, logical.

The most urgent problem is the mapping of quantitative indicators. The mapping of quantitative indicators of the audit can be implemented through an ANN with associative memory. The main ANNs with associative memory are presented in Table 1. The memory capacity was considered only for ANNs with a binary or bipolar data type that perform reconstruction or classification. HAM stands for hetero-associative memory, AAM stands for auto-associative memory.

As follows from Table 1, most neural networks have one or more disadvantages:

1. not used to reconstruct either the original or another sample;

2. do not work with real data.

3. do not have a high capacity of associative memory.

The aim of the work is to increase the efficiency of automatic data analysis in the audit DSS by means of a bidirectional (forward and reverse) neural network mapping of sets of audit indicators in order to identify systematic misstatements that lead to misstatement of reporting. In the audit system, the topical task of the middle level is the automation of the analysis of the conformity of the content of the supply of raw materials for production and the manufactured products (by the periods of quantization of the verification period).

It is assumed that the audit indicators are noisy with Gaussian noise, which in turn simulates random accounting errors (as opposed to systematic ones). It is also assumed that the residuals for the quantization periods are distributed according to the normal law, the parameters of which can be estimated from the accounting data. For the achievement of the aim it is necessary to solve the following tasks: • formalize the content of the audit process of the receipt of raw materials for production and the manufactured products; • choose a neural network model for mapping audit indicators (which are noisy with Gaussian noise, which in turn simulates random accounting errors (as opposed to systematic ones, which lead to distortion of reporting)); • choose a criterion for evaluating the effectiveness of a neural network model; • propose a method for training a neural network model in batch mode; • propose an algorithm for training a neural network model in batch mode for implementation on a GPU; • perform numerical studies.

2. MATERIALS AND METHODS 2.1. Formalize the content of the audit process of the receipt of raw materials for production and the manufactured products

Formalize the content of the supply of raw materials for production and the manufactured products are formed on the basis of audit variables (Table 2). Elements of mapping sets – data of the receipt of raw materials for production and the manufactured products by the periods of quantization of the verification period. The vector of the receipt of raw materials features = ( 1, . . . , ) formed by indicators of quantity of raw materials by type , ∈ . The vector of manufactured products features = ( 1, . . . , ) is formed by indicators of the quantity of manufactured products by type Feature vectors for mapping raw material received - product produced

Input vector elements

Output vector elements D sense type of operation (receipt of raw materials for

production) type of raw materials set of types of raw

materials quantity of raw materials

cost of raw material total cost of raw material designation ( ) , ( )

sense type of operation (production of finished products (semi-finished

products)) type of product set of types of product

quantity of product direct material costs for a product

type of a raw material type direct material costs for a product type , ∈ . 1.

associative memory.

computational complexity.

( 2 ) ( 2 ) =( ∗1 , . . . , ∗ ), is represented as

To assess the dimension of the features vector, an analysis was made of the nomenclature of purchases of raw materials (components) of large machine-building enterprises. So, based on this analysis, we can conclude that the sections of the nomenclature are on average from 8 to 12, the number of groups in each section is from 2 to 10.

We represent the implementation of the "generalized audit" in the form of a mapping (comparison) of generalized quantitative features of the audited sets. The formation of generalized quantitative features can be performed using ANN. 2.2.

Choosing a neural network model for mapping audit sets

In the work, the Full (bidirectional) Counterpropagating Neural Network (FCPNN), which is a non-recurrent static two-layer ANN, was chosen as a neural network. FCPNN output is linear. unlike most ANNs are used to reconstruct another sample using auto-associative and heterounlike bidirectional associative memory and the Boltzmann machine, it works with real data. unlike bidirectional associative memory and the

Boltzmann machine, it has less

FCPNN model performing mapping of each input sample = ( 1, . . . , ) to output sample ∗ =

( 1 ) – connection weight from the -th element of the input sample to the -th neuron, (∗2) – connection weight from the neuron-winner ∗ to -th element of output sample, ( 1 ) – the number of neurons in the hidden layer.

( 2 ) ( 2 ) ( 2 ) ∗ = ( ∗1 , . . . , ∗ ), is represented as

FCPNN model performing mapping of each output sample = ( 1, . . . , ) to input sample ( 1 ) – connection weight from the -th element of the input sample to the -th neuron of ∗

( 2 ) – connection weight from the neuron-winner ∗ of hidden layer to -th element of output ( 1 ) – the number of neurons in the hidden layer. 2.3.

Criterion choice for assessing the effectiveness of a neural network model for mapping audit sets

In this work for training model FCPNN was chosen target function, that indicates selection of the vector ( 1( 11 ), . . . , of ( 1 ) between the model sample and the test sample) parameter values = ( 1( 11 ), . . . , ( 1 ), 1(12), . . . , ( 1 ) ),

( 1 ) ( 2 ) ( 2 ) ( 1 ), 11 , . . . , ( 2 ) ( 1 ) ) which deliver the minimum

mean square error (difference =

1 1 2 ∑ =1 ( 2) ∗ − 2 + 1

∑ =1 ( 2 ) ∗ − 2 → , = ( 2 ) ( 2 )∗ – -th, output sample according to the model, where – -th test output sample, – -th test input sample, – training set power,

– is length of the sample , – is length of the sample .

( 2 )∗ – -th, input sample according to the model, 2.4.

Training method for neural network model in batch mode

hidden layer.

The disadvantage of FCPNN is that it does not have a batch learning mode, which leads to reducing of the learning speed. For FCPNN was used concurrent training (combination of training with and without a teacher). This work proposes training FCPNN in batch mode. following blocks (Fig. 1).

First phase (training of the hidden layer) (steps 1-6).

The first phase allows you to calculate the weights of the hidden layer

( 1 ) and consists of the 1.

Learning iteration number = 0, initialization by uniform distribution on the interval ( 0,1 ) or [-0.5, 0.5] of weights

( 1 )( ), ∈ 1, , ∈ 1, ( 1 ), ∈ 1, where – is length of the sample , – is length of the sample and ( 1 ) – the number and the neurons in the , ∈ }, ∈ 1, , where – -th training input vector, – -th training output vector, – training set power.

Initial shortest distance ̄(0) =0.

2. Calculating the distance to all hidden neurons.

i- th neuron of the hidden basis is determined by the formula:

Distance from µ-th input sample to each i-th neuron and from each µ-th output sample to each ( 1 )( ) – connection weight from k-th input sample to i-th neuron at time , ( 3 ) hidden layer at time .

( ) – pretrained connection weight from s-th element of output sample to i-th neuron of 1. Initializing the weights of the neurons of the hidden layer 2. Calculating the distance to all hidden neurons 3. Calculating the shortest distance and choosing the neuron 4. Setting the weights of the hidden layer neurons associated 5. Calculating the average sum of the least distances yes ( 4 ) ( 5 ) ( 6 ) (6’) ( 7 )

3. Calculating the shortest distance and choosing the neuron with the shortest distance Calculating the shortest distance

and choosing the neuron-winner ∗ , for which the distance

is shortest neighbors based on k-means rule 4. Setting the weights of the hidden layer neurons associated with the neuron-winner ∗ and its ( + 1) = ( + 1) =

∑ =1 ℎ( ,

∑ =1 ℎ( , ) ∗ ) , ∈ 1, , ∈ 1, ( 1 ),

∗ where ℎ( , ∗) – rectangular topological neighborhood function, 5. Calculating the average sum of the shortest distances

6. Checking the termination condition

If | ̄( + 1) − ̄( )| ≤ , the finish, else

= + 1, go to step 2.

Second phase (training the output layer) (steps 7-12). The second phase allows you to calculate the weights of the output layer ( 2 ) and

( 2 ) and consists of the following blocks (Fig. 2).

7. Learning iteration number = 0, initialization by uniform distribution on the interval ( 0,1 ) or [0.5, 0.5] of weights ( 2 ) ( ), ( 2 )

( ), ∈ 1, ( 1 ), ∈ 1, , ∈ 1, , where – length of the

Initial shortest distance ̄(0) =0. – -th training output vector,

– training set power. layer. input sample , – length of the output sample , ( 1 ) – the number and the neurons in the hidden , ∈ }, ∈ 1, , where – -th training input vector, 7. Initialization of the neuron weights of the output layer 8. Calculating the distance to all hidden neurons 9. Calculating the shortest distance and choosing the neuron with the shortest distance 10. Calculating the distance to all output neurons 11. Setting the weights of the hidden layer neurons associated with the neuron-winner and its neighbors 12. Calculating the average sum of the least distances z (n + 1) 13. z (n + 1) − z (n) > ε

no 14. Output the weights yes time ,

layer at time .

8. Calculating the distance to all hidden neurons

Sum of distances from µ-th input sample in input layer from each i-th neuron of the hidden layer and from each µ-th output sample in the input layer to each i-th neuron of the hidden layer is determined by the formula: ( 1 ) – pretrained connection weight from k-th element of input sample to i-th neuron at ( 1 ) – pretrained connection weight from s- th element of input sample to i- th neuron of hidden

9. Calculating the shortest distance and choosing the neuron with the shortest distance. Calculating the shortest distance

and choosing the neuron-winner ∗, for which the distance is shortest.

∗ = , ∈ 1, , ∈ 1, ( 1 ).

( 9 ) ( 10 ) 10. Calculating the distance to all output neurons. from the neuron-winner

∗ to µ-th input and output sample in output layer is = ∑ =1( − (∗2)( ))2 + the input sample in output layer at time , neighbors based on k-means rule where (∗2 )( ) – weight of connection from the winner neuron ∗ of hidden layer to j-th element of 11. Setting the weights of the output layer neurons associated with the neuron-winner ∗ and its where ℎ( , ∗) – rectangular topological neighborhood function, 12. Calculating the average sum of the shortest distances 13. Checking the termination condition

If | ̄( + 1) − ̄( )| ≤ , the finish, else = + 1, go to step 8. 2.5.

Algorithm for training neuron network model in batch mode for implementation on GPU

For the proposed method of training FCPNN on audit data example, examines the algorithm for implementation on a GPU with usage of CUDA parallel processing technology.

The first phase (training the hidden layer). The first phase based on formulas ( 1 )-( 7 ) is shown in

Step 1 – Operator enters lengths of the sample , the lengths of the sample , the number and the neurons in the hidden layer ( 1 ), power of the training set , training set

Step 2 – Initialization by uniform distribution over the interval ( 0,1 ) or [-0.5, 0.5] of weights {( , )| ∈ ,

∈ }, ∈ 1, .

GPU, which are grouped into P blocks. Each thread calculates the distance from µ-th input sample to

Step 3 – Calculation of distances to all hidden neurons of the ANN, using ⋅ ( 1 ) threads on each i-th neuron .

Step 4 – Computation based on shortest distance reduction and determining the neurons with the work of each block is a neuron-winner ∗ with the smallest distance .

shortest distance using ⋅ ( 1 ) threads on GPU, which are grouped into P blocks. The result of the

Step 5 – Setting the weights of the output layer neurons associated with the neuron- winner its neighbors based on reduction using ⋅ ( 1 ) ⋅ threads on GPU, which are grouped into ⋅ ( 1 ) blocks. The result of the work of each block is the weight

Step 6 – Setting the weights of the output layer neurons associated with the neuron- winner its neighbors based on reduction using ⋅ ( 1 ) ⋅ threads on GPU, which are grouped into ⋅ ( 1 ) blocks. The result of the work of each block is the weight

Step 7 – Calculation based on reduction of the average sum of the shortest distances using threads on GPU, which are grouped into 1 block. The result of the block is the average sum of the ( 1 )

( + 1). (1)( + 1). smallest distances ̄( + 1). ̄( )| ≤ , then finish, else – increasing number of iteration = + 1, go to step 3.

Step 8 – If average sum of smallest distances of neighboring iterations are close, | ̄( + 1) − (12) (12’) (13)

Step 9 – Recording of weight

( 1 )( + 1) and

( 1 )( + 1) in the database.

Second phase (training of output layer). The second phase based on formulas ( 8 )-(13) is showed in

Step 1 – Operator enters lengths of the sample , the lengths of the sample the number and the neurons in the hidden layer ( 1 ), power of the training set , training set , ∈ , ∈

, ∈ 1, .

Step 2 – Initialization by uniform distribution over the interval ( 0,1 ) or [-0.5, 0.5] of weights

Step 3 – Calculation of distances to all hidden neurons of the ANN, using ⋅ ( 1 ) threads on GPU, which are grouped into P blocks. Each thread calculates the distance from µ-th input sample to each -th neuron . neuron-winner ∗ to µ-th output sample .

Step 4 – Computation based on shortest distance reduction and determining the neurons with the work of each block is a neuron-winner ∗ with the smallest distance .

shortest distance using ⋅ ( 1 ) threads on GPU, which are grouped into blocks. The result of the Step 5 – Calculating distances from the neuron-winner ∗ to µ-th output sample using ⋅ ( ) threads on GPU, which are grouped into blocks. Each thread calculates the distance from the

Step 6 – Setting the weights of the output layer neurons associated with the neuron-winner its neighbors based on reduction using ( 1 ) ⋅ ⋅ threads on GPU, which are grouped into ( 1 ) ⋅ blocks. The result of the work of each block is the weight ( 2 )( + 1).

Step 7 – Setting the weights of the output layer neurons associated with the neuron-winner its neighbors based on reduction using ( 1 ) ⋅ ⋅ threads on GPU, which are grouped into ( 1 ) ⋅ block. The result of the block is the average sum of the smallest distances

Step 8 – Calculation based on reduction of the average sum of the shortest distances using threads on GPU, which are grouped into 1 block. The result of the block is the average sum of the ( 2 )( + 1). ̄( )| ≤ , then finish, else – increasing number of iteration = + 1, go to step 3.

Step 10 – Recording of weight (2)( + 1) and ( 2)( + 1), in the database.

Step 9 – If average sum of smallest distances of neighboring iterations are close, | ̄( + 1) −

Evaluation of computational complexity of the proposed method using the GPU, and the traditional method of teaching FOCPNN were based on the number of calculation distances, computing of which is the most consuming part of method. Moreover, 1 – the maximum number of iterations of the first training phase, 2 – the maximum number of iterations of the second training phase, ( 1 ) – the number of neurons in the hidden layer, – the power of the training set. 2.7.

Discussion 2.8.

Conclusion

The traditional FCPNN learning method does not provide support for batch mode, which increases computational complexity (Table 3). Proposed method eliminates this flaw and allows for approximate increase of learning rate in ( 1 ). By reducing the computational complexity, it is possible to increase the accuracy of the method by decreasing the parameter ε and increasing the number of neurons in the hidden and output layers.

1. The urgent task of increasing the effectiveness of audit in the context of large volumes of analyzed data and limited verification time was solved by automating the formation of generalized features of audit sets and their mapping by means of a full bidirectional counterpropagating neural network.

2. For increased learning rate of full bidirectional counterpropagating neural network, was developed a method based on the -means rule for training in batch mode. The proposed method provides: approximately increase learning rate in ( 1 ), where ( 1 ) is the number of neurons in the hidden layer and is the power of the learning set.

3. Created a learning algorithm based on -means, intended for implementation on a GPU using

CUDA technology.

4. The proposed method of training based on the -means rule can be used to intellectualize the

DSS audit. Prospects for further research is the study of the proposed method for a wide class of artificial intelligence tasks, as well as the creation of a method for bidirectional mapping audit features to solve audit problems.

3. References

References

[1] The World Bank: World Development Report 2016: Digital Dividends , 2016 . URL: https://www.worldbank.org/en/publication/wdr2016.

[2] M. Schultz , and M. Tropmann-Frick . Autoencoder Neural Networks versus External Auditors: Detecting Unusual Journal Entries in Financial Statement Audits . Proceedings of the 53rd Hawaii International Conference on System Sciences (HICSS-2020) , Maui, Hawaii, USA. 2021 , pp. 5421 - 5430 . doi: 10 .24251/hicss. 2020 . 666 .

[3] J. Nonnenmacher , F. Kruse , G. Schumann, G. Marx . Using Autoencoders for Data-Driven Analysis in Internal Auditing . In Proceedings of the 54th Hawaii International Conference on System Sciences, Maui , Hawaii, USA, 2021 , pp. 5748 - 5757 . doi: 10 .24251/hicss. 2021 . 697 .

[4] Y. Bodyanskiy , O. Boiko , Y. Zaychenko , G. Hamidov and A. Zelikman . The Hybrid GMDHNeo-fuzzy Neural Network in Forecasting Problems in Financial Sphere . Proceedings of 2nd International Conference on System Analysis & Intelligent Computing (SAIC) , Kyiv, Ukraine, IEEE, 2020 , pp. 1 - 6 , doi: 10.1109/SAIC51296. 2020 . 9239152 .

[5] T. Neskorodіeva , E. Fedorov , I. Izonin. Forecast Method for Audit Data Analysis by Modified Liquid State Machine . Proceedings of the 1st International Workshop on Intelligent Information Technologies & Systems of Information Security (IntelITSIS 2020 ), Khmelnytskyi, Ukraine, 10 - 12 June, 2020 : proceedings. - CEUR-WS vol. 2623 , 2020 , pp. 25 - 35 .

[6] T. Neskorodіeva , E. Fedorov . Method for Automatic Analysis of Compliance of Expenses Data and the Enterprise Income by Neural Network Model of Forecast . Proceedings of the 2nd International Workshop on Modern Machine Learning Technologies and Data Science (MoMLeT&DS-2020) , Lviv-Shatsk, Ukraine , 2 -3 June, 2020 : proceedings. - CEUR-WS, Volume I: Main Conference . vol. 2631 , 2020 , pp. 145 - 158 .

[7] A.V. Barmak , Y.V. Krak , E.A. Manziuk , V.S. Kasianiuk . Information technology separating hyperplanes synthesis for linear classifiers . Journal of Automation and Information Sciences , vol. 51 ( 5 ) ( 2019 ) 54 - 64 . doi: 10 .1615/JAutomatInfScien.v51. i5 . 50

[8] T.V. Prokopenko , O. Grigor . Development of the comprehensive method to manage risks in projects related to information technologies . Eastern-European Journal of Enterprise Technologies vol. 2 , 2018 , pp. 37 - 43 . doi: 10 .15587/ 1729 - 4061 . 2018 . 128140 .

[9] U.P. Singh , S. Jain , A. Tiwari , R.K. Singh . Gradient evolution-based counter propagation network for approximation of noncanonical system . Soft Computing , 23 13 , ( 2019 ) 4955 - 4967 . doi: 10 .1007/s00500-018-3160-7.

[10] A. Asokan , K. Gunavathi , R. Anitha . Classification of Melakartha ragas using neural networks . Proceedings of the International Conference on Innovations in Information, Embedded and Communication Systems (ICIIECS-2017) , 17 - 18 March 2017, Coimbatore, India. IEEE. 2017 , pp. 1 - 6 . doi: 10 .1109/ICIIECS. 2017 . 8276040 .

[11] Sonika ; A. Pratap; M. Chauhan ; A. Dixit . New technique for detecting fraudulent transactions using hybrid network consisting of full-counter propagation network and probabilistic network . 2016 International Conference on Computing, Communication and Automation (ICCCA) , 29 - 30 April 2016, Greater Noida , India, IEEE. 2016 , pp. 29 - 30 . doi: 10 .1109/CCAA. 2016 . 7813713 .