scholarly journals Learning in Feedforward Neural Networks Accelerated by Transfer Entropy

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 102 ◽  
Author(s):  
Adrian Moldovan ◽  
Angel Caţaron ◽  
Răzvan Andonie

Current neural networks architectures are many times harder to train because of the increasing size and complexity of the used datasets. Our objective is to design more efficient training algorithms utilizing causal relationships inferred from neural networks. The transfer entropy (TE) was initially introduced as an information transfer measure used to quantify the statistical coherence between events (time series). Later, it was related to causality, even if they are not the same. There are only few papers reporting applications of causality or TE in neural networks. Our contribution is an information-theoretical method for analyzing information transfer between the nodes of feedforward neural networks. The information transfer is measured by the TE of feedback neural connections. Intuitively, TE measures the relevance of a connection in the network and the feedback amplifies this connection. We introduce a backpropagation type training algorithm that uses TE feedback connections to improve its performance.

2021 ◽  
Vol 11 (4) ◽  
pp. 287-306
Author(s):  
Jarosław Bilski ◽  
Bartosz Kowalczyk ◽  
Andrzej Marjański ◽  
Michał Gandor ◽  
Jacek Zurada

Abstract In this paper1 a new neural networks training algorithm is presented. The algorithm originates from the Recursive Least Squares (RLS) method commonly used in adaptive filtering. It uses the QR decomposition in conjunction with the Givens rotations for solving a normal equation - resulting from minimization of the loss function. An important parameter in neural networks is training time. Many commonly used algorithms require a big number of iterations in order to achieve a satisfactory outcome while other algorithms are effective only for small neural networks. The proposed solution is characterized by a very short convergence time compared to the well-known backpropagation method and its variants. The paper contains a complete mathematical derivation of the proposed algorithm. There are presented extensive simulation results using various benchmarks including function approximation, classification, encoder, and parity problems. Obtained results show the advantages of the featured algorithm which outperforms commonly used recent state-of-the-art neural networks training algorithms, including the Adam optimizer and the Nesterov’s accelerated gradient.


2016 ◽  
Vol 25 (06) ◽  
pp. 1650033 ◽  
Author(s):  
Hossam Faris ◽  
Ibrahim Aljarah ◽  
Nailah Al-Madi ◽  
Seyedali Mirjalili

Evolutionary Neural Networks are proven to be beneficial in solving challenging datasets mainly due to the high local optima avoidance. Stochastic operators in such techniques reduce the probability of stagnation in local solutions and assist them to supersede conventional training algorithms such as Back Propagation (BP) and Levenberg-Marquardt (LM). According to the No-Free-Lunch (NFL), however, there is no optimization technique for solving all optimization problems. This means that a Neural Network trained by a new algorithm has the potential to solve a new set of problems or outperform the current techniques in solving existing problems. This motivates our attempts to investigate the efficiency of the recently proposed Evolutionary Algorithm called Lightning Search Algorithm (LSA) in training Neural Network for the first time in the literature. The LSA-based trainer is benchmarked on 16 popular medical diagnosis problems and compared to BP, LM, and 6 other evolutionary trainers. The quantitative and qualitative results show that the LSA algorithm is able to show not only better local solutions avoidance but also faster convergence speed compared to the other algorithms employed. In addition, the statistical test conducted proves that the LSA-based trainer is significantly superior in comparison with the current algorithms on the majority of datasets.


Electronics ◽  
2021 ◽  
Vol 10 (22) ◽  
pp. 2761
Author(s):  
Vaios Ampelakiotis ◽  
Isidoros Perikos ◽  
Ioannis Hatzilygeroudis ◽  
George Tsihrintzis

In this paper, we present a handwritten character recognition (HCR) system that aims to recognize first-order logic handwritten formulas and create editable text files of the recognized formulas. Dense feedforward neural networks (NNs) are utilized, and their performance is examined under various training conditions and methods. More specifically, after three training algorithms (backpropagation, resilient propagation and stochastic gradient descent) had been tested, we created and trained an NN with the stochastic gradient descent algorithm, optimized by the Adam update rule, which was proved to be the best, using a trainset of 16,750 handwritten image samples of 28 × 28 each and a testset of 7947 samples. The final accuracy achieved is 90.13%. The general methodology followed consists of two stages: the image processing and the NN design and training. Finally, an application has been created that implements the methodology and automatically recognizes handwritten logic formulas. An interesting feature of the application is that it allows for creating new, user-oriented training sets and parameter settings, and thus new NN models.


Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1218
Author(s):  
Adrian Moldovan ◽  
Angel Caţaron ◽  
Răzvan Andonie

Recently, there is a growing interest in applying Transfer Entropy (TE) in quantifying the effective connectivity between artificial neurons. In a feedforward network, the TE can be used to quantify the relationships between neuron output pairs located in different layers. Our focus is on how to include the TE in the learning mechanisms of a Convolutional Neural Network (CNN) architecture. We introduce a novel training mechanism for CNN architectures which integrates the TE feedback connections. Adding the TE feedback parameter accelerates the training process, as fewer epochs are needed. On the flip side, it adds computational overhead to each epoch. According to our experiments on CNN classifiers, to achieve a reasonable computational overhead–accuracy trade-off, it is efficient to consider only the inter-neural information transfer of the neuron pairs between the last two fully connected layers. The TE acts as a smoothing factor, generating stability and becoming active only periodically, not after processing each input sample. Therefore, we can consider the TE is in our model a slowly changing meta-parameter.


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