scholarly journals Overview of Configuring Adaptive Activation Functions for Deep Neural Networks - A Comparative Study

2021 ◽  
Vol 3 (1) ◽  
pp. 10-22
Author(s):  
Wang Haoxiang ◽  
Smys S
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Learning Process ◽  
Deep Neural Networks ◽  
Research Work ◽  
Nonlinear Function ◽  
Activation Function ◽  
Classification Error ◽  
Activation Functions ◽  
Research Article

Recently, the deep neural networks (DNN) have demonstrated many performances in the pattern recognition paradigm. The research studies on DNN include depth layer networks, filters, training and testing datasets. Deep neural network is providing many solutions for nonlinear partial differential equations (PDE). This research article comprises of many activation functions for each neuron. Besides, these activation networks are allowing many neurons within the neuron networks. In this network, the multitude of the functions will be selected between node by node to minimize the classification error. This is the reason for selecting the adaptive activation function for deep neural networks. Therefore, the activation functions are adapted with every neuron on the network, which is used to reduce the classification error during the process. This research article discusses the scaling factor for activation function that provides better optimization for the process in the dynamic changes of procedure. The proposed adaptive activation function has better learning capability than fixed activation function in any neural network. The research articles compare the convergence rate, early training function, and accuracy between existing methods. Besides, this research work provides improvements in debt ideas of the learning process of various neural networks. This learning process works and tests the solution available in the domain of various frequency bands. In addition to that, both forward and inverse problems of the parameters in the overriding equation will be identified. The proposed method is very simple architecture and efficiency, robustness, and accuracy will be high when considering the nonlinear function. The overall classification performance will be improved in the resulting networks, which have been trained with common datasets. The proposed work is compared with the recent findings in neuroscience research and proved better performance.

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

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 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.

scholarly journals Interval universal approximation for neural networks

2022 ◽  
Vol 6 (POPL) ◽  
pp. 1-29
Author(s):  
Zi Wang ◽  
Aws Albarghouthi ◽  
Gautam Prakriya ◽  
Somesh Jha
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Approximation Problem ◽  
Activation Function ◽  
Constructive Proof ◽  
Universal Approximation ◽  
Activation Functions ◽  
Complete Problems ◽  
Robust Network ◽  
Interval Approximation

To verify safety and robustness of neural networks, researchers have successfully applied abstract interpretation , primarily using the interval abstract domain. In this paper, we study the theoretical power and limits of the interval domain for neural-network verification. First, we introduce the interval universal approximation (IUA) theorem. IUA shows that neural networks not only can approximate any continuous function f (universal approximation) as we have known for decades, but we can find a neural network, using any well-behaved activation function, whose interval bounds are an arbitrarily close approximation of the set semantics of f (the result of applying f to a set of inputs). We call this notion of approximation interval approximation . Our theorem generalizes the recent result of Baader et al. from ReLUs to a rich class of activation functions that we call squashable functions . Additionally, the IUA theorem implies that we can always construct provably robust neural networks under ℓ ∞ -norm using almost any practical activation function. Second, we study the computational complexity of constructing neural networks that are amenable to precise interval analysis. This is a crucial question, as our constructive proof of IUA is exponential in the size of the approximation domain. We boil this question down to the problem of approximating the range of a neural network with squashable activation functions. We show that the range approximation problem (RA) is a Δ 2 -intermediate problem, which is strictly harder than NP -complete problems, assuming coNP ⊄ NP . As a result, IUA is an inherently hard problem : No matter what abstract domain or computational tools we consider to achieve interval approximation, there is no efficient construction of such a universal approximator. This implies that it is hard to construct a provably robust network, even if we have a robust network to start with.

scholarly journals Memristor crossbar architectures for implementing deep neural networks

2021 ◽  
Author(s):  
Xiaoyang Liu ◽  
Zhigang Zeng
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Pattern Recognition ◽  
Deep Neural Networks ◽  
Activation Functions ◽  
Simulation Results ◽  
Memristor Crossbars ◽  
Memristor Crossbar ◽  
Fully Connected

AbstractThe paper presents memristor crossbar architectures for implementing layers in deep neural networks, including the fully connected layer, the convolutional layer, and the pooling layer. The crossbars achieve positive and negative weight values and approximately realize various nonlinear activation functions. Then the layers constructed by the crossbars are adopted to build the memristor-based multi-layer neural network (MMNN) and the memristor-based convolutional neural network (MCNN). Two kinds of in-situ weight update schemes, which are the fixed-voltage update and the approximately linear update, respectively, are used to train the networks. Consider variations resulted from the inherent characteristics of memristors and the errors of programming voltages, the robustness of MMNN and MCNN to these variations is analyzed. The simulation results on standard datasets show that deep neural networks (DNNs) built by the memristor crossbars work satisfactorily in pattern recognition tasks and have certain robustness to memristor variations.

scholarly journals Differential Equation Units: Learning Functional Forms of Activation Functions from Data

2020 ◽  
Vol 34 (04) ◽  
pp. 6030-6037
Author(s):  
MohamadAli Torkamani ◽  
Shiv Shankar ◽  
Amirmohammad Rooshenas ◽  
Phillip Wallis
Keyword(s):  
Differential Equation ◽  
Neural Networks ◽  
Deep Neural Networks ◽  
Functional Form ◽  
Activation Function ◽  
The Other ◽  
Superior Performance ◽  
Activation Functions ◽  
Functional Forms ◽  
Nonlinear Activation Function

Most deep neural networks use simple, fixed activation functions, such as sigmoids or rectified linear units, regardless of domain or network structure. We introduce differential equation units (DEUs), an improvement to modern neural networks, which enables each neuron to learn a particular nonlinear activation function from a family of solutions to an ordinary differential equation. Specifically, each neuron may change its functional form during training based on the behavior of the other parts of the network. We show that using neurons with DEU activation functions results in a more compact network capable of achieving comparable, if not superior, performance when compared to much larger networks.

scholarly journals On Transformative Adaptive Activation Functions in Neural Networks for Gene Expression Inference

2019 ◽  
Author(s):  
Vladimír Kunc ◽  
Jiří Kléma
Keyword(s):  
Neural Network ◽  
Gene Expression ◽  
Neural Networks ◽  
Expression Profiling ◽  
Mean Absolute Error ◽  
Absolute Error ◽  
Activation Function ◽  
Activation Functions ◽  
Hyperbolic Tangent ◽  
Sigmoid Activation Function

AbstractMotivationGene expression profiling was made cheaper by the NIH LINCS program that profiles only ~1, 000 selected landmark genes and uses them to reconstruct the whole profile. The D–GEX method employs neural networks to infer the whole profile. However, the original D–GEX can be further significantly improved.ResultsWe have analyzed the D–GEX method and determined that the inference can be improved using a logistic sigmoid activation function instead of the hyperbolic tangent. Moreover, we propose a novel transformative adaptive activation function that improves the gene expression inference even further and which generalizes several existing adaptive activation functions. Our improved neural network achieves average mean absolute error of 0.1340 which is a significant improvement over our reimplementation of the original D–GEX which achieves average mean absolute error 0.1637

scholarly journals Broad Autoencoder Features Learning for Classification Problem

2021 ◽  
Vol 15 (4) ◽  
pp. 0-0
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
Classification Problem ◽  
Activation Function ◽  
Activation Functions ◽  
Classification Problems ◽  
Stacked Autoencoders ◽  
Learned Features ◽  
Sigmoid Functions ◽  
Nonlinear Mappings

Activation functions such as Tanh and Sigmoid functions are widely used in Deep Neural Networks (DNNs) and pattern classification problems. To take advantages of different activation functions, the Broad Autoencoder Features (BAF) is proposed in this work. The BAF consists of four parallel-connected Stacked Autoencoders (SAEs) and each of them uses a different activation function, including Sigmoid, Tanh, ReLU, and Softplus. The final learned features can merge such features by various nonlinear mappings from original input features with such a broad setting. This helps to excavate more information from the original input features. Experimental results show that the BAF yields better-learned features and classification performances.

scholarly journals Stochastic Selection of Activation Layers for Convolutional Neural Networks

Sensors ◽  
2020 ◽  
Vol 20 (6) ◽  
pp. 1626 ◽  
Author(s):  
Loris Nanni ◽  
Alessandra Lumini ◽  
Stefano Ghidoni ◽  
Gianluca Maguolo
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Deep Neural Networks ◽  
Activation Function ◽  
Computational Time ◽  
Activation Functions ◽  
Practical Applications ◽  
Functional Blocks ◽  
Stochastic Selection ◽  
Selection Of

In recent years, the field of deep learning has achieved considerable success in pattern recognition, image segmentation, and many other classification fields. There are many studies and practical applications of deep learning on images, video, or text classification. Activation functions play a crucial role in discriminative capabilities of the deep neural networks and the design of new “static” or “dynamic” activation functions is an active area of research. The main difference between “static” and “dynamic” functions is that the first class of activations considers all the neurons and layers as identical, while the second class learns parameters of the activation function independently for each layer or even each neuron. Although the “dynamic” activation functions perform better in some applications, the increased number of trainable parameters requires more computational time and can lead to overfitting. In this work, we propose a mixture of “static” and “dynamic” activation functions, which are stochastically selected at each layer. Our idea for model design is based on a method for changing some layers along the lines of different functional blocks of the best performing CNN models, with the aim of designing new models to be used as stand-alone networks or as a component of an ensemble. We propose to replace each activation layer of a CNN (usually a ReLU layer) by a different activation function stochastically drawn from a set of activation functions: in this way, the resulting CNN has a different set of activation function layers.

scholarly journals Identification of Covid’19 Vaccinator by Deep Learning Approach Using Contactless Palmprints

2021 ◽  
Vol 3 (3) ◽  
pp. 178-193
Author(s):  
B. Vivekanandam
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Deep Learning ◽  
Convolutional Neural Network ◽  
Research Study ◽  
Research Work ◽  
Digital Camera ◽  
Activation Function ◽  
User Participation ◽  
Learning Platform

The invention of the first vaccine has also raised several anti-vaccination views among people. Vaccine reluctance may be exacerbated by the growing reliance on social media, which is considered as a source of health information. During this COVID'19 scenario, the verification of non-vaccinators via the use of biometric characteristics has received greater attention, especially in areas such as vaccination monitoring and other emergency medical services, among other things. The traditional digital camera utilizes the middle-resolution images for commercial applications in a regulated or contact-based environment with user participation, while the latter uses high-resolution latent palmprints. This research study attempts to utilize convolutional neural networks (CNN) for the first time to perform contactless recognition. To identify the COVID '19 vaccine using the CNN technique, this research work has used the contactless palmprint method. Further, this research study utilizes the PalmNet structure of convolutional neural network to resolve the issue. First, the ROI region of the palmprint was extracted from the input picture based on the geometric form of the print. After image registration, the ROI region is sent into a convolutional neural network as an input. The softmax activation function is then used to train the network so that it can choose the optimal learning rate and super parameters for the given learning scenario. The neural networks of the deep learning platform were then compared and summarized.

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