scholarly journals Hardware implementation of radial-basis neural networks with Gaussian activation functions on FPGA

2021 ◽  
Author(s):  
Volodymyr Shymkovych ◽  
Sergii Telenyk ◽  
Petro Kravets
Keyword(s):  
Neural Networks ◽  
Hardware Implementation ◽  
Gaussian Function ◽  
Activation Function ◽  
Rbf Neural Networks ◽  
Activation Functions ◽  
Rbf Network ◽  
Combination Scheme ◽  
Radial Basis ◽  
Hidden Layer

AbstractThis article introduces a method for realizing the Gaussian activation function of radial-basis (RBF) neural networks with their hardware implementation on field-programmable gaits area (FPGAs). The results of modeling of the Gaussian function on FPGA chips of different families have been presented. RBF neural networks of various topologies have been synthesized and investigated. The hardware component implemented by this algorithm is an RBF neural network with four neurons of the latent layer and one neuron with a sigmoid activation function on an FPGA using 16-bit numbers with a fixed point, which took 1193 logic matrix gate (LUTs—LookUpTable). Each hidden layer neuron of the RBF network is designed on an FPGA as a separate computing unit. The speed as a total delay of the combination scheme of the block RBF network was 101.579 ns. The implementation of the Gaussian activation functions of the hidden layer of the RBF network occupies 106 LUTs, and the speed of the Gaussian activation functions is 29.33 ns. The absolute error is ± 0.005. The Spartan 3 family of chips for modeling has been used to get these results. Modeling on chips of other series has been also introduced in the article. RBF neural networks of various topologies have been synthesized and investigated. Hardware implementation of RBF neural networks with such speed allows them to be used in real-time control systems for high-speed objects.

Analysis of Non-Linear Activation Functions for Classification Tasks Using Convolutional Neural Networks

2019 ◽  
Vol 12 (3) ◽  
pp. 156-161 ◽  
Author(s):  
Aman Dureja ◽  
Payal Pahwa
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
Activation Function ◽  
Primary Objective ◽  
Experimental Comparison ◽  
Activation Functions ◽  
Practical Applications ◽  
Network Activation ◽  
Non Linear ◽  
Hidden Layer

Background: In making the deep neural network, activation functions play an important role. But the choice of activation functions also affects the network in term of optimization and to retrieve the better results. Several activation functions have been introduced in machine learning for many practical applications. But which activation function should use at hidden layer of deep neural networks was not identified. Objective: The primary objective of this analysis was to describe which activation function must be used at hidden layers for deep neural networks to solve complex non-linear problems. Methods: The configuration for this comparative model was used by using the datasets of 2 classes (Cat/Dog). The number of Convolutional layer used in this network was 3 and the pooling layer was also introduced after each layer of CNN layer. The total of the dataset was divided into the two parts. The first 8000 images were mainly used for training the network and the next 2000 images were used for testing the network. Results: The experimental comparison was done by analyzing the network by taking different activation functions on each layer of CNN network. The validation error and accuracy on Cat/Dog dataset were analyzed using activation functions (ReLU, Tanh, Selu, PRelu, Elu) at number of hidden layers. Overall the Relu gave best performance with the validation loss at 25th Epoch 0.3912 and validation accuracy at 25th Epoch 0.8320. Conclusion: It is found that a CNN model with ReLU hidden layers (3 hidden layers here) gives best results and improve overall performance better in term of accuracy and speed. These advantages of ReLU in CNN at number of hidden layers are helpful to effectively and fast retrieval of images from the databases.

scholarly journals Effects of Nonlinearity and Network Architecture on the Performance of Supervised Neural Networks

Algorithms ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 51
Author(s):  
Nalinda Kulathunga ◽  
Nishath Rajiv Ranasinghe ◽  
Daniel Vrinceanu ◽  
Zackary Kinsman ◽  
Lei Huang ◽  
...  
Keyword(s):  
Neural Networks ◽  
Network Architecture ◽  
Network Models ◽  
Activation Function ◽  
Activation Functions ◽  
Nonlinear Functions ◽  
Neural Network Models ◽  
Hidden Layer ◽  
Fully Connected ◽  
Insight Into

The nonlinearity of activation functions used in deep learning models is crucial for the success of predictive models. Several simple nonlinear functions, including Rectified Linear Unit (ReLU) and Leaky-ReLU (L-ReLU) are commonly used in neural networks to impose the nonlinearity. In practice, these functions remarkably enhance the model accuracy. However, there is limited insight into the effects of nonlinearity in neural networks on their performance. Here, we investigate the performance of neural network models as a function of nonlinearity using ReLU and L-ReLU activation functions in the context of different model architectures and data domains. We use entropy as a measurement of the randomness, to quantify the effects of nonlinearity in different architecture shapes on the performance of neural networks. We show that the ReLU nonliearity is a better choice for activation function mostly when the network has sufficient number of parameters. However, we found that the image classification models with transfer learning seem to perform well with L-ReLU in fully connected layers. We show that the entropy of hidden layer outputs in neural networks can fairly represent the fluctuations in information loss as a function of nonlinearity. Furthermore, we investigate the entropy profile of shallow neural networks as a way of representing their hidden layer dynamics.

scholarly journals Trigonometric Inference Providing Learning in Deep Neural Networks

2021 ◽  
Vol 11 (15) ◽  
pp. 6704
Author(s):  
Jingyong Cai ◽  
Masashi Takemoto ◽  
Yuming Qiu ◽  
Hironori Nakajo
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Deep Neural Networks ◽  
Activation Function ◽  
Trigonometric Approximation ◽  
Model Parameters ◽  
Training Algorithms ◽  
Activation Functions ◽  
Classical Training ◽  
Sum Formula

Despite being heavily used in the training of deep neural networks (DNNs), multipliers are resource-intensive and insufficient in many different scenarios. Previous discoveries have revealed the superiority when activation functions, such as the sigmoid, are calculated by shift-and-add operations, although they fail to remove multiplications in training altogether. In this paper, we propose an innovative approach that can convert all multiplications in the forward and backward inferences of DNNs into shift-and-add operations. Because the model parameters and backpropagated errors of a large DNN model are typically clustered around zero, these values can be approximated by their sine values. Multiplications between the weights and error signals are transferred to multiplications of their sine values, which are replaceable with simpler operations with the help of the product to sum formula. In addition, a rectified sine activation function is utilized for further converting layer inputs into sine values. In this way, the original multiplication-intensive operations can be computed through simple add-and-shift operations. This trigonometric approximation method provides an efficient training and inference alternative for devices with insufficient hardware multipliers. Experimental results demonstrate that this method is able to obtain a performance close to that of classical training algorithms. The approach we propose sheds new light on future hardware customization research for machine learning.

Deep neural network based on generalized neo-fuzzy neurons and its learning based on backpropagation

2021 ◽  
Vol 26 (jai2021.26(1)) ◽  
pp. 32-41
Author(s):  
Bodyanskiy Y ◽  
◽  
Antonenko T ◽  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Learning Process ◽  
Activation Function ◽  
Point Of View ◽  
Basic Unit ◽  
Theoretical Point ◽  
Activation Functions ◽  
Approximation Properties ◽  
Network Training

Modern approaches in deep neural networks have a number of issues related to the learning process and computational costs. This article considers the architecture grounded on an alternative approach to the basic unit of the neural network. This approach achieves optimization in the calculations and gives rise to an alternative way to solve the problems of the vanishing and exploding gradient. The main issue of the article is the usage of the deep stacked neo-fuzzy system, which uses a generalized neo-fuzzy neuron to optimize the learning process. This approach is non-standard from a theoretical point of view, so the paper presents the necessary mathematical calculations and describes all the intricacies of using this architecture from a practical point of view. From a theoretical point, the network learning process is fully disclosed. Derived all necessary calculations for the use of the backpropagation algorithm for network training. A feature of the network is the rapid calculation of the derivative for the activation functions of neurons. This is achieved through the use of fuzzy membership functions. The paper shows that the derivative of such function is a constant, and this is a reason for the statement of increasing in the optimization rate in comparison with neural networks which use neurons with more common activation functions (ReLU, sigmoid). The paper highlights the main points that can be improved in further theoretical developments on this topic. In general, these issues are related to the calculation of the activation function. The proposed methods cope with these points and allow approximation using the network, but the authors already have theoretical justifications for improving the speed and approximation properties of the network. The results of the comparison of the proposed network with standard neural network architectures are shown

Evaluation of Parameter Settings for Training Neural Networks Using Backpropagation Algorithms

2022 ◽  
pp. 202-226
Author(s):  
Leema N. ◽  
Khanna H. Nehemiah ◽  
Elgin Christo V. R. ◽  
Kannan A.
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Activation Function ◽  
Neural Network Training ◽  
Network Parameter ◽  
Network Parameters ◽  
Network Training ◽  
Rate Minimum ◽  
Hidden Layer ◽  
Function Number

Artificial neural networks (ANN) are widely used for classification, and the training algorithm commonly used is the backpropagation (BP) algorithm. The major bottleneck faced in the backpropagation neural network training is in fixing the appropriate values for network parameters. The network parameters are initial weights, biases, activation function, number of hidden layers and the number of neurons per hidden layer, number of training epochs, learning rate, minimum error, and momentum term for the classification task. The objective of this work is to investigate the performance of 12 different BP algorithms with the impact of variations in network parameter values for the neural network training. The algorithms were evaluated with different training and testing samples taken from the three benchmark clinical datasets, namely, Pima Indian Diabetes (PID), Hepatitis, and Wisconsin Breast Cancer (WBC) dataset obtained from the University of California Irvine (UCI) machine learning repository.

Differential Evolution-Based Optimization of Kernel Parameters in Radial Basis Function Networks for Classification

2013 ◽  
Vol 4 (1) ◽  
pp. 56-80 ◽  
Author(s):  
Ch. Sanjeev Kumar Dash ◽  
Ajit Kumar Behera ◽  
Satchidananda Dehuri ◽  
Sung-Bae Cho
Keyword(s):  
Neural Networks ◽  
Differential Evolution ◽  
Radial Basis Function ◽  
Basis Function ◽  
Learning Algorithm ◽  
Basis Functions ◽  
Second Phase ◽  
Rbf Neural Networks ◽  
Radial Basis ◽  
Two Phases

In this paper a two phases learning algorithm with a modified kernel for radial basis function neural networks is proposed for classification. In phase one a new meta-heuristic approach differential evolution is used to reveal the parameters of the modified kernel. The second phase focuses on optimization of weights for learning the networks. Further, a predefined set of basis functions is taken for empirical analysis of which basis function is better for which kind of domain. The simulation result shows that the proposed learning mechanism is evidently producing better classification accuracy vis-à-vis radial basis function neural networks (RBFNs) and genetic algorithm-radial basis function (GA-RBF) neural networks.

Pulsar Detection for Wavelets SODA and Regularized Fuzzy Neural Networks Based on Andneuron and Robust Activation Function

2019 ◽  
Vol 28 (01) ◽  
pp. 1950003 ◽  
Author(s):  
Paulo Vitor de Campos Souza ◽  
Luiz Carlos Bambirra Torres ◽  
Augusto Junio Guimarães ◽  
Vanessa Souza Araujo
Keyword(s):  
Neural Networks ◽  
Large Scale ◽  
Activation Function ◽  
Fuzzy Neural Networks ◽  
Activation Functions ◽  
Large Scale Problems ◽  
Proposed Model ◽  
Fuzzy Neural ◽  
Learning Machine ◽  
Intelligent Models

The use of intelligent models may be slow because of the number of samples involved in the problem. The identification of pulsars (stars that emit Earth-catchable signals) involves collecting thousands of signals by professionals of astronomy and their identification may be hampered by the nature of the problem, which requires many dimensions and samples to be analyzed. This paper proposes the use of hybrid models based on concepts of regularized fuzzy neural networks that use the representativeness of input data to define the groupings that make up the neurons of the initial layers of the model. The andneurons are used to aggregate the neurons of the first layer and can create fuzzy rules. The training uses fast extreme learning machine concepts to generate the weights of neurons that use robust activation functions to perform pattern classification. To solve large-scale problems involving the nature of pulsar detection problems, the model proposes a fast and highly accurate approach to address complex issues. In the execution of the tests with the proposed model, experiments were conducted explanation in two databases of pulsars, and the results prove the viability of the fast and interpretable approach in identifying such involved stars.

scholarly journals Application of Artificial Neural Networks to Assess the Mycological State of Bulk Stored Rapeseeds

Agriculture ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 567
Author(s):  
Jolanta Wawrzyniak
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Control Systems ◽  
Multilayer Perceptron ◽  
Activation Function ◽  
Fungal Population ◽  
Support Tool ◽  
Artificial Neural ◽  
Hidden Layer ◽  
And Storage

Artificial neural networks (ANNs) constitute a promising modeling approach that may be used in control systems for postharvest preservation and storage processes. The study investigated the ability of multilayer perceptron and radial-basis function ANNs to predict fungal population levels in bulk stored rapeseeds with various temperatures (T = 12–30 °C) and water activity in seeds (aw = 0.75–0.90). The neural network model input included aw, temperature, and time, whilst the fungal population level was the model output. During the model construction, networks with a different number of hidden layer neurons and different configurations of activation functions in neurons of the hidden and output layers were examined. The best architecture was the multilayer perceptron ANN, in which the hyperbolic tangent function acted as an activation function in the hidden layer neurons, while the linear function was the activation function in the output layer neuron. The developed structure exhibits high prediction accuracy and high generalization capability. The model provided in the research may be readily incorporated into control systems for postharvest rapeseed preservation and storage as a support tool, which based on easily measurable on-line parameters can estimate the risk of fungal development and thus mycotoxin accumulation.

Descartes' Rule of Signs for Radial Basis Function Neural Networks

2002 ◽  
Vol 14 (12) ◽  
pp. 2997-3011 ◽  
Author(s):  
Michael Schmitt
Keyword(s):  
Neural Networks ◽  
Radial Basis Function ◽  
Lower Bounds ◽  
Basis Function ◽  
Rbf Neural Networks ◽  
Vc Dimension ◽  
Network Parameters ◽  
Number Of Zeros ◽  
Radial Basis

We establish versions of Descartes' rule of signs for radial basis function (RBF) neural networks. The RBF rules of signs provide tight bounds for the number of zeros of univariate networks with certain parameter restrictions. Moreover, they can be used to infer that the Vapnik-Chervonenkis (VC) dimension and pseudodimension of these networks are no more than linear. This contrasts with previous work showing that RBF neural networks with two or more input nodes have superlinear VC dimension. The rules also give rise to lower bounds for network sizes, thus demonstrating the relevance of network parameters for the complexity of computing with RBF neural networks.

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