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1

Fast computational approach to the Levenberg-Marquardt algorithm for training feedforward neural networks

Bilski Jarosław, Smoląg Jacek, Kowalczyk Bartosz, Grzanek Konrad, Izonin Ivan

Journal of Artificial Intelligence and Soft Computing Research

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2023

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Vol. 13, No. 2

45--61

EN

This paper presents a parallel approach to the Levenberg-Marquardt algorithm (LM). The use of the Levenberg-Marquardt algorithm to train neural networks is associated with significant computational complexity, and thus computation time. As a result, when the neural network has a big number of weights, the algorithm becomes practically ineffective. This article presents a new parallel approach to the computations in Levenberg-Marquardt neural network learning algorithm. The proposed solution is based on vector instructions to effectively reduce the high computational time of this algorithm. The new approach was tested on several examples involving the problems of classification and function approximation, and next it was compared with a classical computational method. The article presents in detail the idea of parallel neural network computations and shows the obtained acceleration for different problems.

2

An Overview of the Methods of Synthesis, Realization and Implementation of Orthogonal 3-D Rotation Filters and Possibilities of Further Research and Development

Poczekajło Paweł

International Journal of Electronics and Telecommunications

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2021

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Vol. 67, No. 2

295--300

EN

In the paper, an overview of the methods and algorithms of synthesis, realization and implementation used by the author to obtain orthogonal 3-D filters with a structure made of Givens rotations has been presented. The main advantage of orthogonal filters, which may have a lower sensitivity to quantization of the coefficients, was indicated. The author proposed a number of possible changes and modifications of individual stages, which may result in obtaining filters with even better parameters. The work will be the basis for the direction of further research.

3

Local Levenberg-Marquardt algorithm for learning feedforwad neural networks

Bilski Jarosław, Kowalczyk Bartosz, Marchlewska Alina, Zurada Jacek M.

Journal of Artificial Intelligence and Soft Computing Research

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2020

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Vol. 10, No. 4

299--316

EN

This paper presents a local modification of the Levenberg-Marquardt algorithm (LM). First, the mathematical basics of the classic LM method are shown. The classic LM algorithm is very efficient for learning small neural networks. For bigger neural networks, whose computational complexity grows significantly, it makes this method practically inefficient. In order to overcome this limitation, local modification of the LM is introduced in this paper. The main goal of this paper is to develop a more complexity efficient modification of the LM method by using a local computation. The introduced modification has been tested on the following benchmarks: the function approximation and classification problems. The obtained results have been compared to the classic LM method performance. The paper shows that the local modification of the LM method significantly improves the algorithm’s performance for bigger networks. Several possible proposals for future works are suggested.

4

Wpływ kwantowania współczynników na działanie filtru Gaussa dla realizacji bezpośredniej i ortogonalnej (rotatory Givensa)

Poczekajło Paweł

Przegląd Elektrotechniczny

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2019

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R. 95, nr 5

175--178

PL

W artykule przedstawiono dwie realizacje filtru Gaussa 1D. Pierwsza oparta jest na bezpośredniej implementacji splotu, druga bazuje na filtrze ortogonalnym realizowanym za pomocą rotatorów Givensa. Obie realizacje został przeanalizowane pod kątem wrażliwości na kwantowanie współczynników dla 8-, 16- i 24-bitowych rejestrów. Wyznaczono i porównano błędy średniokwadratowe charakterystyki amplitudowej oraz błędy dla odpowiedzi systemu na pobudzenie losowym szumem i deltą Kroneckera.

EN

In the paper, two realizations of 1D Gauss filter are presented. The first realization is based on direct structure with convolution, in the second orthogonal filter with use Givens rotations is realized. Both systems are analyzed of sensitivity on coefficient quantization for 8-, 16- and 24- bits length of register. Also determined mean squared errors for amplitude characteristics, impulse responses and responses on noise excitation.

5

Analiza wybranych metod realizacji sprzętowej rotatorów Givensa w układzie FPGA

Poczekajło P.

Przegląd Elektrotechniczny

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2018

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R. 94, nr 9

26--28

PL

W artykule przedstawiono analizę wybranych metod sprzętowej realizacji rotatorów Givensa. Jako bazę sprzętową wybrano układ FPGA Altera Cyclone 5 SX SoC. Dokonano również pomiaru szeregu parametrów sprzętowych oraz sprawdzono dokładność działania, następnie porównano wyniki w celu wybrania najlepszej realizacji. Badania zostały zrealizowane w ramach prac nad ortogonalnymi filtrami potokowymi realizowanymi za pomocą rotatorów Givensa.

EN

In the paper, analysis of selected methods of hardware implementation of Givens rotators is presented . The author use the FPGA chip Altera Cyclone 5 SX SoC. Hardware parameters of structures are measure. Also accuracy of operations are analysed. Results are compared and selected the best implementation. The research are realisation as part of the work on orthogonal filters implemented with Givens rotators.