Both are suitable for implementations of neurons in multilayer perceptron networks with an on-chip backpropagation learning algorithm . The activation function proposed shows minimal area and power consumption , can be considered as an approximation to the tanh(nx ) function , and can be programmed to achieve any slope at the origin that is equal to or greater than 2 . The derivative proposed also shows minimal area and maximizes its similarity , with the ideal derivative in the proximities of the origin being the best approximation for its degree of complexity . An improved ReLu segmentation correction Activate function is proposed , by improving the traditional convolution neural network , adding the local response normalization layer , and using the maximum stacking and so on . Based on the Google depth learning platform TensorFlow , the activation function is used to construct the modified convolution neural network structure model , using the CIFAR-10 data set as the neural network input for the model training and evaluation . We analyze effects of different neuron activation function on the neural network convergence speed and the accuracy of image recognition . subsection : System and Optimization strategies Let us assume that we have a system parameterized by , with activation function , which takes as input a data vector and produces an output vector . We use the same notation as in Section [ reference ] and define a data matrix composed of rows and columns , where is the input dimensionality . section : Introduction Currently the most popular activation function for neural networks is the rectified linear unit ( ReLU ) , which was first proposed for restricted Boltzmann machines and then successfully used for neural networks . The ReLU activation function is the identity for positive arguments and zero otherwise . A novel feature selection method using information theory was introduced which builds a feature set for classification by determining a group of class-informative features with low set co-information . An artificial neural network was built from the selected feature set using 10-hidden layer nodes and the tanh activation function . The resulting computer-aided diagnosis tool achieved a training accuracy of 96.2 % , sensitivity of 97.6 % , specificity of 95.2 % , and area-under-the-curve of 0.971 along with 97.1 % sensitivity and 94.9 % specificity a blinded validation set . The proposed neural network Bell Fuzzy Multi Layer Perceptron ( BF-MLP ) Neural network is constructed by introducing a fuzzy logic in hidden layer with the sugeno model and bell function . The proposed neural network consists of two layers with the first layer being a tanh activation function and the second layer containing the bell fuzzy activation function . The proposed FEDS method was implemented using Matlab and Modelsim . Abstract The ‘ tanh – coth expansion method ’ for finding solitary travelling-wave solutions to nonlinear evolution equations has been used extensively in the literature . It is a natural extension to the basic tanh-function expansion method which was developed in the 1990s . It usually delivers three types of solution , namely a tanh-function expansion , a coth-function expansion , and a tanh – coth expansion . We propose K-TanH , a novel , highly accurate , hardware efficient approximation of popular activation function Tanh for Deep Learning . K-TanH consists of a sequence of parameterized bit/integer operations , such as , masking , shift and add/subtract ( no floating point operation needed ) where parameters are stored in a very small look-up table ( bit-masking step can be eliminated ) . Activation function refers to the mathematical function implemented in multilayer perceptrons to limit the output signal of neurons . The objective of this project is to design a hyperbolic tangent activation function ( TANH ) for integrated circuit implementation using digital design approach . This paper compares the performances of area , speed and power between ring architecture and tree architecture of activation function using repetitive instantiation of multipliers and adders . This paper presents a new approach for training on neural networks by substituting a different activation function derivative to investigate its affects during back-propagation . We modify the derivation of hyperbolic tangent activation function ( TanH ) by adding a variable that depends on a linear model . Our modified function is called Linearized Hyperbolic Tangent function ( LRTanH ) . In this paper , we propose a general and effective Neural Network model for graph-based dependency parsing . Our model can automatically learn high-order feature combinations using only atomic features by exploiting a novel activation function tanhcube . Moreover , we propose a simple yet effective way to utilize phrase-level information that is expensive to use in conventional graph-based parsers . That is to say that each datum has a high attribute count and the unusual or abnormal data are sparse within the data set . Results suggest that the hyperbolic tangent ( tanh ) activation function outperforms other common activation functions by extracting a smaller , but more significant feature set . Furthermore , it was found that fitness evaluation sizes ranging from 20,000 to 40,000 within populations ranging from 200 to 300 , deliver optimum feature selection capability . Then , a 2048D image vector encoding the most interesting visual features for the premise ( hypothesis ) is obtained as a sum of the 36 image vectors weighted by the corresponding attention scores for the premise ( hypothesis ) . A fully - connected layer with a gated tanh activation function is applied to the image vector of the most interesting visual features for the premise and for the hypothesis to obtain a reduced 512D vector for each of them . A fully - connected layer with a gated tanh activation function is also applied to the premise and to the hypothesis in order to obtain a reduced 512D vector for each of them . The and functions are modeled by two different DNNs with the same architecture : two fully - connected layers with 64 hidden dimensions and the ReLU activation function . is two fully - connected layers with 16 hidden dimensions , where the first hidden layer uses a Tanh activation function and the output layer uses a linear activation function . is modeled by a GRU with hidden size 64 . The hyperparameters in PUCT are set to and . In RSP , a scale factor η is employed to mimic the stochasticity-adaptability of biological neurons , thereby enabling the antinoise capability of a DNN to be improved by the novel activation function . We validated the performance of RSP with a 19-layer residual network ( ResNet ) and a 19-layer visual geometry group ( VGG ) on facial expression recognition data sets and compared it with other popular activation functions , such as rectified linear units ( ReLU ) , softplus , leaky ReLU ( LReLU ) , exponential linear unit ( ELU ) , and noisy softplus ( NSP ) . The experimental results show that RSP is applied to VGG-19 or ResNet-19 , and the average recognition accuracy under five different noise levels exceeds the other functions on both of the two facial expression data sets ; in other words , RSP outperforms the other activation functions in noise resistance . It demonstrates the design features which can be implemented in other textbooks to support collaborative learning experiences for primary school children . The documentation of the co-design process provides a practical framework for co-designing an AR textbook with children , as well as an evidence of using the ELU framework in practice . 4 This research also contributes in bridging the gap between AR and Child-Computer Interaction ( CCI ) communities , through the use of common CCI methods in the AR development . Ease of Language Understanding model , ELU ) were more efficient for experienced than for less experienced users when perceiving speech . This study extends the existing ELU model that mismatch may also lead to the establishment of new phonological representations in the long-term memory . We study the problem of answering instance queries over non-Horn ontologies by rewriting them into Datalog programs or FirstOrder queries ( FOQs ) . We consider the basic non-Horn language ELU , which extends EL with disjunctions . Both Datalog-rewritability and FOrewritability of instance queries have been recently shown to be decidable for ALC ontologies ( and hence also for ELU ) ; however , existing decision methods are mainly of theoretical interest . It is based on the preconditioned Richardson method with the incomplete LU decomposition as the preconditioner , and the decomposition is updated with ensparsing . The average number of the ELU relaxations is about 1.01 with the optimum choice of the ensparsing threshold , and the ELU relaxation process can be omitted at the cost of about 1 % increase of the Newton iteration ( the lazy ELU method ) . The lazy ELU method is about twice as fast as the direct method for simulations of ECL adders . In this paper , we aimed to improve the SNR of seismic data , and proposed an intelligent convolutional neural network noise reduction framework to adaptively capture seismic signals from seismic data with noise . The eponential linear unit ( ELU ) activation function and the Adam optimization algorithm were used to train the network , which increased the effective information extraction of the network in the negative interval . In order to speed up network training , we added residual learning and batch normalization methods to the network . In this study , we consider a location-based location update ( LU ) scheme . We propose an enhanced LU ( ELU ) scheme that can store more cells to reduce the location update cost of the LU scheme and show that the ELU scheme always outperforms the LU scheme . Our scheme can be easily implemented in actual cellular systems . We propose the Ensparsed LU decomposition ( ELU ) method as a linear solver for large-scale circuit transient analysis . Ensparsing is an algorithmic technique of ignoring small values in computation . In this paper , we propose learning a parameterization of ELU in order to learn the proper activation shape at each layer in the CNNs . Our results on the MNIST , CIFAR-10/100 and ImageNet datasets using the NiN , Overfeat , All-CNN and ResNet networks indicate that our proposed Parametric ELU ( PELU ) has better performances than the non-parametric ELU . We have observed as much as a 7.28 % relative error improvement on ImageNet with the NiN network , with only 0.0003 % parameter increase . MAIN RESULTS The CNN model and the LDA classifier achieved comparable accuracy on the lower-dimensional dataset , but CNN exceeded LDA performance significantly on the higher-dimensional dataset ( without hypothesis-driven preprocessing ) , achieving an average decoding accuracy of 90.7 % ( chance level = 8.3 % ) . Parallel convolutions , tanh or ELU activation functions , and dropout regularization proved valuable for model performance , whereas the sequential convolutions , ReLU activation function , and batch normalization components , reduced accuracy or yielded no significant difference . Saliency maps revealed meaningful features , displaying the typical spatial distribution and latency of the P300 component expected during this task . These problems have been reduced in practice through normalized initialization and most recently , Batch Normalization . Exponential linear unit ( ELU ) also reduces the vanishing gradient problem . ELUs introduce negative values which push the mean activation towards zero . In experiments , ELUs lead not only to faster learning , but also to significantly better generalization performance than ReLUs and LReLUs on networks with more than 5 layers . On CIFAR - 100 ELUs networks significantly outperform ReLU networks with batch normalization while batch normalization does not improve ELU networks . ELU networks are among the top 10 reported CIFAR - 10 results and yield the best published result on CIFAR - 100 , without resorting to multi - view evaluation or model averaging . ELUs achieve both lower training loss and lower test error than ReLUs , LReLUs , and SReLUs . Both the ELU training and test performance is significantly better than for other activation functions ( Wilcoxon signed - rank test with - value 0.001 ) . Batch normalization improved ReLU and LReLU networks , but did not improve ELU and [ reference ] . ELU - networks are the second best on CIFAR - 10 with a test error of 6.55 % but still they are among the top 10 best results reported for CIFAR - 10 . ELU networks performed best on CIFAR - 100 with a test error of 24.28 % . The single - model performance was evaluated on the single center crop with no further augmentation and yielded a top - 5 validation error below 10 % . Currently ELU nets are 5 % slower on ImageNet than ReLU nets . The difference is small because activation functions generally have only minor influence on the overall training time . In terms of wall clock time , ELUs require 12.15h vs. ReLUs with 11.48h for 10k iterations . We expect that ELU implementations can be improved , e.g. by faster exponential functions . section : Conclusion appendix : Variance of Mean Activations in ELU and ReLU Networks To compare the variance of median activation in ReLU and ELU networks , we trained a neural network with 5 hidden layers of 256 hidden units for 200 epochs using a learning rate of 0.01 , once using ReLU and once using ELU activation functions on the MNIST dataset . After each epoch , we calculated the median activation of each hidden unit on the whole training set . Inductive learning For the inductive learning task , we apply a three - layer GAT model . Both of the first two layers consist of K = 4 attention heads computing F = 256 features ( for a total of 1024 features ) , followed by an ELU nonlinearity . The final layer is used for ( multi - label ) classification : Abstract A review is given about shielding computational methods starting from a simple exponential formula and ending up with very sophisticated 3-D computational methods dealing with complicated geometries and performing dose rate calculations at deep penetrations . This review aims to illustrate : ( a ) the types of problems that can be treated with simple methods within reasonable accuracy ; ( b ) the sources of errors in the calculated and measured dose rates ; ( c ) the methods that can be used to improve the accuracy of routinely used methods using either experimental results or results of complicated calculational methods ; ( d ) the requirements and the experience needed to run sophisticated codes ; and ( e ) finally , to demonstrate the experience in the National Center of Safety and Radiation Control in the area of shielding calculations . PSD was well represented by Hino ’s formula by changing the scaling parameter . Spatial correlation at two points was well represented not by the exponential formula but by an alternative coherence function based on isotropic turbulence theory . Decay factor in the exponential formula showed a weakly increasing trend with the increase in distance and wind speed . Abstract Heat kernel pagerank is a variation of Personalized PageRank given in an exponential formulation . In this work , we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph . The winner determination problem in this auction poses a challenge to the auctioneer . We present an exponential formulation and a polynomial formulation for this problem , both based on integer linear programming . The polynomial formulation proves to find the optimal set of bids in a matter of seconds . The frequency of verbal interactions among members of small discussion groups has been carefully studied in experiments by Bales and his associates at Harvard and by Stephan and Mishler at Princeton . Stephan suggested that the data could be described by a simple exponential equation , which has intrigued several mathematical sociologists because of its apparent generality in providing a concise statement of experimental results . The present paper suggests that this result could be generated by a simple probabilistic process , which may have uses in other types of group interaction studies where an analogous structure prevails . This work attempts to approach this problem through the implementation of a nondestructive technique known as indentation by Shore A ( hardness measure ) , that can be relate with deformation ( Young 's Modulus ) through analytical models . This research reports that the relationship between the Young 's Modulus and the electrosurgical pencils hardness follows a parabolic model among other models , including a multivariate model , a logarithmic model and an exponential one . We conclude that it is possible to obtain the value of the deformation of a MD through the measure of hardness , achieving to validate the mechanical behavior without destroying it , increasing the cost to benefit ratio of the health care institution and securing the patient 's integrity during a medical procedure . Motivated by the problem of customer wallet estimation , we propose a new setting for multi-view regression , where we learn a completely unobserved target ( in our case , customer wallet ) by modeling it as a " central link " in a directed graphical model , connecting multiple sets of observed variables . The resulting conditional independence allows us to reduce the maximum discriminative likelihood estimation problem to a convex optimization problem for exponential linear models . We show that under certain modeling assumptions , in particular , when there exist two conditionally independent views and the noise is Gaussian , this problem can be reduced to a single least squares regression . Explicit exponential integrators based on general linear methods are studied for the time discretization of quasi-linear parabolic initial-boundary value problems . Compared to other exponential integrators encountering rather severe order reductions , in general , the considered class of exponential general linear methods provides the possibility to construct schemes that retain higher-order accuracy in time when applied to quasi-linear parabolic problems . Employing an abstract framework , the considered problems take the form of initial value problems on Banach spaces : $ u'(t ) = Q(u(t ) ) u(t ) , t \in ( 0,T ) , u(0)$ given . In this work , the convergence analysis of explicit exponential time integrators based on general linear methods for quasi-linear parabolic initial boundary value problems is pursued . Compared to other types of exponential integrators encountering rather severe order reductions , in general , the considered class of exponential general linear methods provides the possibility of constructing schemes that retain higher-order accuracy in time when applied to quasi-linear parabolic problems . In view of practical applications , the case of variable time step sizes is incorporated . For such solution sets we prove that finding a maximal inner box is an NP-hard problem . This justifies our exponential linear programming methods for computing maximal inner boxes . We also propose a polynomial heuristic that yields a large , but not necessarily the maximal , inner box . To shape a coarse-to-fine object perception , a hierarchical convolutional neural network ( CNN ) denoting the skip-connections convolutional neural network ( S-CCNN ) was proposed , focusing on a butterfly domain at sub-species level due to the fine-grained structure of the category taxonomy . Specifically , based on the serial backbone , three skip-connections with Grating layers are established to link the earlier layers and upper layers of network , and integrated with DropConnect , exponential linear unit ( ELU ) , and local response normalization ( LRN ) to alleviate over-fitting and vanishing gradient . Benefitting from the long-span skip-connections , coarse-grained context with orientation descriptions and finer-grained context with semantic representations can be both took into consideration , and they are jointly incorporated into framework . On experiments involving MNIST hand digit recognition dataset , Hexpo outperforms rectified linear units family(rectified linear unit and exponential linear unit ) by the accuracy and speed of learning . On the experiments involving CIFAR-10 tiny image recognition dataset and convolutional layers , Hexpo outperforms rectified linear unit and performs similar in comparison with exponential linear unit . One main reason is called Batch Normalization ( BN ) [ 1 ] , which is an important method for building these detectors . Recent studies present a potential replacement called Self-normalizing Neural Network ( SNN ) [ 2 ] , which at its core is a special activation function named Scaled Exponential Linear Unit ( SELU ) . This replacement seems to have most of BNs benefits while requiring less computational power . For this purpose , enhanced deep transfer auto-encoder is proposed for fault diagnosis of bearing installed in different machines . First , scaled exponential linear unit is used to improve the quality of the mapped vibration data collected from bearing . Second , nonnegative constraint is adopted for modifying the loss function to improve reconstruction effect . Weak positive relationship was found between VIs and dead materials where the cover was less than 50 % , and a significant high negative relationship was evident when cover was greater than 50 % . When the combined exponential and linear model was applied to fit the negative relationships , more than 90 % variation in dead material cover could be explained by VIs . Sensitivity analysis was further applied to the developed models , indicating that sensitivities of all VIs were significant over the entire range of dead material cover except for the triangular vegetation index ( TVI ) , which has insignificant sensitivity when dead material cover was greater than 94 % . Its architectural hyperparameters have been optimized on the Cora dataset and are then reused for Citeseer . The first layer consists of K = 8 attention heads computing F = 8 features each ( for a total of 64 features ) , followed by an exponential linear unit ( ELU ) [ reference ] nonlinearity . The second layer is used for classification : a single attention head that computes C features ( where C is the number of classes ) , followed by a softmax activation . SNM estimation is closely related to all n - gram LM smoothing techniques that rely on mixing relative frequencies at various orders . Unlike most of those , it combines the predictors at various orders without relying on a hierarchical nesting of the contexts , setting it closer to the family of maximum entropy ( ME ) [ reference ] , or exponential models . We are not the first ones to highlight the effectiveness of skip n - grams at capturing dependencies across longer contexts , similar to RNN LMs ; previous such results were reported in [ reference ] . [ reference ] Another positive aspect is the relatively cheap computation . No exponential function has to be calculated . This function also prevents the vanishing gradient error , since the gradients are linear functions or zero These hierarchical attention maps could decrease the correlation among them . Different from traditional usage of attention map , which naively multiple it with the feature maps , our attention maps are first feed to an exponential operation and then dot with feature maps . It is able to keep more context information , and meanwhile highlight the detection information . Lightweight or mobile neural networks used for real-time computer vision tasks contain fewer parameters than normal networks , which lead to a constrained performance . In this work , we proposed a novel activation function named Tanh Exponential Activation Function ( TanhExp ) which can improve the performance for these networks on image classification task significantly . The definition of TanhExp is f(x ) = xtanh(e^x ) .
Both are suitable for implementations of neurons in multilayer perceptron networks with an on-chip backpropagation learning algorithm . The activation function proposed shows minimal area and power consumption , can be considered as an approximation to the tanh(nx ) function , and can be programmed to achieve any slope at the origin that is equal to or greater than 2 . The derivative proposed also shows minimal area and maximizes its similarity , with the ideal derivative in the proximities of the origin being the best approximation for its degree of complexity .
An improved ReLu segmentation correction Activate function is proposed , by improving the traditional convolution neural network , adding the local response normalization layer , and using the maximum stacking and so on . Based on the Google depth learning platform TensorFlow , the activation function is used to construct the modified convolution neural network structure model , using the CIFAR-10 data set as the neural network input for the model training and evaluation . We analyze effects of different neuron activation function on the neural network convergence speed and the accuracy of image recognition .
subsection : System and Optimization strategies Let us assume that we have a system parameterized by , with activation function , which takes as input a data vector and produces an output vector . We use the same notation as in Section [ reference ] and define a data matrix composed of rows and columns , where is the input dimensionality .
section : Introduction Currently the most popular activation function for neural networks is the rectified linear unit ( ReLU ) , which was first proposed for restricted Boltzmann machines and then successfully used for neural networks . The ReLU activation function is the identity for positive arguments and zero otherwise .
A novel feature selection method using information theory was introduced which builds a feature set for classification by determining a group of class-informative features with low set co-information . An artificial neural network was built from the selected feature set using 10-hidden layer nodes and the tanh activation function . The resulting computer-aided diagnosis tool achieved a training accuracy of 96.2 % , sensitivity of 97.6 % , specificity of 95.2 % , and area-under-the-curve of 0.971 along with 97.1 % sensitivity and 94.9 % specificity a blinded validation set .
The proposed neural network Bell Fuzzy Multi Layer Perceptron ( BF-MLP ) Neural network is constructed by introducing a fuzzy logic in hidden layer with the sugeno model and bell function . The proposed neural network consists of two layers with the first layer being a tanh activation function and the second layer containing the bell fuzzy activation function . The proposed FEDS method was implemented using Matlab and Modelsim .
Abstract The ‘ tanh – coth expansion method ’ for finding solitary travelling-wave solutions to nonlinear evolution equations has been used extensively in the literature . It is a natural extension to the basic tanh-function expansion method which was developed in the 1990s . It usually delivers three types of solution , namely a tanh-function expansion , a coth-function expansion , and a tanh – coth expansion .
We propose K-TanH , a novel , highly accurate , hardware efficient approximation of popular activation function Tanh for Deep Learning . K-TanH consists of a sequence of parameterized bit/integer operations , such as , masking , shift and add/subtract ( no floating point operation needed ) where parameters are stored in a very small look-up table ( bit-masking step can be eliminated ) .
Activation function refers to the mathematical function implemented in multilayer perceptrons to limit the output signal of neurons . The objective of this project is to design a hyperbolic tangent activation function ( TANH ) for integrated circuit implementation using digital design approach . This paper compares the performances of area , speed and power between ring architecture and tree architecture of activation function using repetitive instantiation of multipliers and adders .
This paper presents a new approach for training on neural networks by substituting a different activation function derivative to investigate its affects during back-propagation . We modify the derivation of hyperbolic tangent activation function ( TanH ) by adding a variable that depends on a linear model . Our modified function is called Linearized Hyperbolic Tangent function ( LRTanH ) .
In this paper , we propose a general and effective Neural Network model for graph-based dependency parsing . Our model can automatically learn high-order feature combinations using only atomic features by exploiting a novel activation function tanhcube . Moreover , we propose a simple yet effective way to utilize phrase-level information that is expensive to use in conventional graph-based parsers .
That is to say that each datum has a high attribute count and the unusual or abnormal data are sparse within the data set . Results suggest that the hyperbolic tangent ( tanh ) activation function outperforms other common activation functions by extracting a smaller , but more significant feature set . Furthermore , it was found that fitness evaluation sizes ranging from 20,000 to 40,000 within populations ranging from 200 to 300 , deliver optimum feature selection capability .
Then , a 2048D image vector encoding the most interesting visual features for the premise ( hypothesis ) is obtained as a sum of the 36 image vectors weighted by the corresponding attention scores for the premise ( hypothesis ) . A fully - connected layer with a gated tanh activation function is applied to the image vector of the most interesting visual features for the premise and for the hypothesis to obtain a reduced 512D vector for each of them . A fully - connected layer with a gated tanh activation function is also applied to the premise and to the hypothesis in order to obtain a reduced 512D vector for each of them .
The and functions are modeled by two different DNNs with the same architecture : two fully - connected layers with 64 hidden dimensions and the ReLU activation function . is two fully - connected layers with 16 hidden dimensions , where the first hidden layer uses a Tanh activation function and the output layer uses a linear activation function . is modeled by a GRU with hidden size 64 . The hyperparameters in PUCT are set to and .
In RSP , a scale factor η is employed to mimic the stochasticity-adaptability of biological neurons , thereby enabling the antinoise capability of a DNN to be improved by the novel activation function . We validated the performance of RSP with a 19-layer residual network ( ResNet ) and a 19-layer visual geometry group ( VGG ) on facial expression recognition data sets and compared it with other popular activation functions , such as rectified linear units ( ReLU ) , softplus , leaky ReLU ( LReLU ) , exponential linear unit ( ELU ) , and noisy softplus ( NSP ) . The experimental results show that RSP is applied to VGG-19 or ResNet-19 , and the average recognition accuracy under five different noise levels exceeds the other functions on both of the two facial expression data sets ; in other words , RSP outperforms the other activation functions in noise resistance .
It demonstrates the design features which can be implemented in other textbooks to support collaborative learning experiences for primary school children . The documentation of the co-design process provides a practical framework for co-designing an AR textbook with children , as well as an evidence of using the ELU framework in practice . 4 This research also contributes in bridging the gap between AR and Child-Computer Interaction ( CCI ) communities , through the use of common CCI methods in the AR development .
Ease of Language Understanding model , ELU ) were more efficient for experienced than for less experienced users when perceiving speech . This study extends the existing ELU model that mismatch may also lead to the establishment of new phonological representations in the long-term memory .
We study the problem of answering instance queries over non-Horn ontologies by rewriting them into Datalog programs or FirstOrder queries ( FOQs ) . We consider the basic non-Horn language ELU , which extends EL with disjunctions . Both Datalog-rewritability and FOrewritability of instance queries have been recently shown to be decidable for ALC ontologies ( and hence also for ELU ) ; however , existing decision methods are mainly of theoretical interest .
It is based on the preconditioned Richardson method with the incomplete LU decomposition as the preconditioner , and the decomposition is updated with ensparsing . The average number of the ELU relaxations is about 1.01 with the optimum choice of the ensparsing threshold , and the ELU relaxation process can be omitted at the cost of about 1 % increase of the Newton iteration ( the lazy ELU method ) . The lazy ELU method is about twice as fast as the direct method for simulations of ECL adders .
In this paper , we aimed to improve the SNR of seismic data , and proposed an intelligent convolutional neural network noise reduction framework to adaptively capture seismic signals from seismic data with noise . The eponential linear unit ( ELU ) activation function and the Adam optimization algorithm were used to train the network , which increased the effective information extraction of the network in the negative interval . In order to speed up network training , we added residual learning and batch normalization methods to the network .
In this study , we consider a location-based location update ( LU ) scheme . We propose an enhanced LU ( ELU ) scheme that can store more cells to reduce the location update cost of the LU scheme and show that the ELU scheme always outperforms the LU scheme . Our scheme can be easily implemented in actual cellular systems .
We propose the Ensparsed LU decomposition ( ELU ) method as a linear solver for large-scale circuit transient analysis . Ensparsing is an algorithmic technique of ignoring small values in computation .
In this paper , we propose learning a parameterization of ELU in order to learn the proper activation shape at each layer in the CNNs . Our results on the MNIST , CIFAR-10/100 and ImageNet datasets using the NiN , Overfeat , All-CNN and ResNet networks indicate that our proposed Parametric ELU ( PELU ) has better performances than the non-parametric ELU . We have observed as much as a 7.28 % relative error improvement on ImageNet with the NiN network , with only 0.0003 % parameter increase .
MAIN RESULTS The CNN model and the LDA classifier achieved comparable accuracy on the lower-dimensional dataset , but CNN exceeded LDA performance significantly on the higher-dimensional dataset ( without hypothesis-driven preprocessing ) , achieving an average decoding accuracy of 90.7 % ( chance level = 8.3 % ) . Parallel convolutions , tanh or ELU activation functions , and dropout regularization proved valuable for model performance , whereas the sequential convolutions , ReLU activation function , and batch normalization components , reduced accuracy or yielded no significant difference . Saliency maps revealed meaningful features , displaying the typical spatial distribution and latency of the P300 component expected during this task .
These problems have been reduced in practice through normalized initialization and most recently , Batch Normalization . Exponential linear unit ( ELU ) also reduces the vanishing gradient problem . ELUs introduce negative values which push the mean activation towards zero .
In experiments , ELUs lead not only to faster learning , but also to significantly better generalization performance than ReLUs and LReLUs on networks with more than 5 layers . On CIFAR - 100 ELUs networks significantly outperform ReLU networks with batch normalization while batch normalization does not improve ELU networks . ELU networks are among the top 10 reported CIFAR - 10 results and yield the best published result on CIFAR - 100 , without resorting to multi - view evaluation or model averaging .
ELUs achieve both lower training loss and lower test error than ReLUs , LReLUs , and SReLUs . Both the ELU training and test performance is significantly better than for other activation functions ( Wilcoxon signed - rank test with - value 0.001 ) . Batch normalization improved ReLU and LReLU networks , but did not improve ELU and
[ reference ] . ELU - networks are the second best on CIFAR - 10 with a test error of 6.55 % but still they are among the top 10 best results reported for CIFAR - 10 . ELU networks performed best on CIFAR - 100 with a test error of 24.28 % .
The single - model performance was evaluated on the single center crop with no further augmentation and yielded a top - 5 validation error below 10 % . Currently ELU nets are 5 % slower on ImageNet than ReLU nets . The difference is small because activation functions generally have only minor influence on the overall training time . In terms of wall clock time , ELUs require 12.15h vs. ReLUs with 11.48h for 10k iterations . We expect that ELU implementations can be improved , e.g. by faster exponential functions . section : Conclusion
appendix : Variance of Mean Activations in ELU and ReLU Networks To compare the variance of median activation in ReLU and ELU networks , we trained a neural network with 5 hidden layers of 256 hidden units for 200 epochs using a learning rate of 0.01 , once using ReLU and once using ELU activation functions on the MNIST dataset . After each epoch , we calculated the median activation of each hidden unit on the whole training set .
Inductive learning For the inductive learning task , we apply a three - layer GAT model . Both of the first two layers consist of K = 4 attention heads computing F = 256 features ( for a total of 1024 features ) , followed by an ELU nonlinearity . The final layer is used for ( multi - label ) classification :
Abstract A review is given about shielding computational methods starting from a simple exponential formula and ending up with very sophisticated 3-D computational methods dealing with complicated geometries and performing dose rate calculations at deep penetrations . This review aims to illustrate : ( a ) the types of problems that can be treated with simple methods within reasonable accuracy ; ( b ) the sources of errors in the calculated and measured dose rates ; ( c ) the methods that can be used to improve the accuracy of routinely used methods using either experimental results or results of complicated calculational methods ; ( d ) the requirements and the experience needed to run sophisticated codes ; and ( e ) finally , to demonstrate the experience in the National Center of Safety and Radiation Control in the area of shielding calculations .
PSD was well represented by Hino ’s formula by changing the scaling parameter . Spatial correlation at two points was well represented not by the exponential formula but by an alternative coherence function based on isotropic turbulence theory . Decay factor in the exponential formula showed a weakly increasing trend with the increase in distance and wind speed .
Abstract Heat kernel pagerank is a variation of Personalized PageRank given in an exponential formulation . In this work , we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph .
The winner determination problem in this auction poses a challenge to the auctioneer . We present an exponential formulation and a polynomial formulation for this problem , both based on integer linear programming . The polynomial formulation proves to find the optimal set of bids in a matter of seconds .
The frequency of verbal interactions among members of small discussion groups has been carefully studied in experiments by Bales and his associates at Harvard and by Stephan and Mishler at Princeton . Stephan suggested that the data could be described by a simple exponential equation , which has intrigued several mathematical sociologists because of its apparent generality in providing a concise statement of experimental results . The present paper suggests that this result could be generated by a simple probabilistic process , which may have uses in other types of group interaction studies where an analogous structure prevails .
This work attempts to approach this problem through the implementation of a nondestructive technique known as indentation by Shore A ( hardness measure ) , that can be relate with deformation ( Young 's Modulus ) through analytical models . This research reports that the relationship between the Young 's Modulus and the electrosurgical pencils hardness follows a parabolic model among other models , including a multivariate model , a logarithmic model and an exponential one . We conclude that it is possible to obtain the value of the deformation of a MD through the measure of hardness , achieving to validate the mechanical behavior without destroying it , increasing the cost to benefit ratio of the health care institution and securing the patient 's integrity during a medical procedure .
Motivated by the problem of customer wallet estimation , we propose a new setting for multi-view regression , where we learn a completely unobserved target ( in our case , customer wallet ) by modeling it as a " central link " in a directed graphical model , connecting multiple sets of observed variables . The resulting conditional independence allows us to reduce the maximum discriminative likelihood estimation problem to a convex optimization problem for exponential linear models . We show that under certain modeling assumptions , in particular , when there exist two conditionally independent views and the noise is Gaussian , this problem can be reduced to a single least squares regression .
Explicit exponential integrators based on general linear methods are studied for the time discretization of quasi-linear parabolic initial-boundary value problems . Compared to other exponential integrators encountering rather severe order reductions , in general , the considered class of exponential general linear methods provides the possibility to construct schemes that retain higher-order accuracy in time when applied to quasi-linear parabolic problems . Employing an abstract framework , the considered problems take the form of initial value problems on Banach spaces : $ u'(t ) = Q(u(t ) ) u(t ) , t \in ( 0,T ) , u(0)$ given .
In this work , the convergence analysis of explicit exponential time integrators based on general linear methods for quasi-linear parabolic initial boundary value problems is pursued . Compared to other types of exponential integrators encountering rather severe order reductions , in general , the considered class of exponential general linear methods provides the possibility of constructing schemes that retain higher-order accuracy in time when applied to quasi-linear parabolic problems . In view of practical applications , the case of variable time step sizes is incorporated .
For such solution sets we prove that finding a maximal inner box is an NP-hard problem . This justifies our exponential linear programming methods for computing maximal inner boxes . We also propose a polynomial heuristic that yields a large , but not necessarily the maximal , inner box .
To shape a coarse-to-fine object perception , a hierarchical convolutional neural network ( CNN ) denoting the skip-connections convolutional neural network ( S-CCNN ) was proposed , focusing on a butterfly domain at sub-species level due to the fine-grained structure of the category taxonomy . Specifically , based on the serial backbone , three skip-connections with Grating layers are established to link the earlier layers and upper layers of network , and integrated with DropConnect , exponential linear unit ( ELU ) , and local response normalization ( LRN ) to alleviate over-fitting and vanishing gradient . Benefitting from the long-span skip-connections , coarse-grained context with orientation descriptions and finer-grained context with semantic representations can be both took into consideration , and they are jointly incorporated into framework .
On experiments involving MNIST hand digit recognition dataset , Hexpo outperforms rectified linear units family(rectified linear unit and exponential linear unit ) by the accuracy and speed of learning . On the experiments involving CIFAR-10 tiny image recognition dataset and convolutional layers , Hexpo outperforms rectified linear unit and performs similar in comparison with exponential linear unit .
One main reason is called Batch Normalization ( BN ) [ 1 ] , which is an important method for building these detectors . Recent studies present a potential replacement called Self-normalizing Neural Network ( SNN ) [ 2 ] , which at its core is a special activation function named Scaled Exponential Linear Unit ( SELU ) . This replacement seems to have most of BNs benefits while requiring less computational power .
For this purpose , enhanced deep transfer auto-encoder is proposed for fault diagnosis of bearing installed in different machines . First , scaled exponential linear unit is used to improve the quality of the mapped vibration data collected from bearing . Second , nonnegative constraint is adopted for modifying the loss function to improve reconstruction effect .
Weak positive relationship was found between VIs and dead materials where the cover was less than 50 % , and a significant high negative relationship was evident when cover was greater than 50 % . When the combined exponential and linear model was applied to fit the negative relationships , more than 90 % variation in dead material cover could be explained by VIs . Sensitivity analysis was further applied to the developed models , indicating that sensitivities of all VIs were significant over the entire range of dead material cover except for the triangular vegetation index ( TVI ) , which has insignificant sensitivity when dead material cover was greater than 94 % .
Its architectural hyperparameters have been optimized on the Cora dataset and are then reused for Citeseer . The first layer consists of K = 8 attention heads computing F = 8 features each ( for a total of 64 features ) , followed by an exponential linear unit ( ELU ) [ reference ] nonlinearity . The second layer is used for classification : a single attention head that computes C features ( where C is the number of classes ) , followed by a softmax activation .
SNM estimation is closely related to all n - gram LM smoothing techniques that rely on mixing relative frequencies at various orders . Unlike most of those , it combines the predictors at various orders without relying on a hierarchical nesting of the contexts , setting it closer to the family of maximum entropy ( ME ) [ reference ] , or exponential models . We are not the first ones to highlight the effectiveness of skip n - grams at capturing dependencies across longer contexts , similar to RNN LMs ; previous such results were reported in [ reference ] . [ reference ]
Another positive aspect is the relatively cheap computation . No exponential function has to be calculated . This function also prevents the vanishing gradient error , since the gradients are linear functions or zero
These hierarchical attention maps could decrease the correlation among them . Different from traditional usage of attention map , which naively multiple it with the feature maps , our attention maps are first feed to an exponential operation and then dot with feature maps . It is able to keep more context information , and meanwhile highlight the detection information .
Lightweight or mobile neural networks used for real-time computer vision tasks contain fewer parameters than normal networks , which lead to a constrained performance . In this work , we proposed a novel activation function named Tanh Exponential Activation Function ( TanhExp ) which can improve the performance for these networks on image classification task significantly . The definition of TanhExp is f(x ) = xtanh(e^x ) .
A Novel Minimum-Size Activation Function and Its Derivative Research on convolutional neural network based on improved Relu piecewise activation function No more meta-parameter tuning in unsupervised sparse feature learning Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs) Information theory optimization based feature selection in breast mammography lesion classification AN FUZZY NEURAL APPROACH FOR MEDICAL IMAGE RETRIEVAL Observations on the basic (G'/G)-expansion method for finding solutions to nonlinear evolution equations K-TanH: Hardware Efficient Activations For Deep Learning Hyperbolic tangent activation function integrated circuit implementation for perceptrons LRTanH: Substitution for the Activation Function Derivative during Back Propagation An Effective Neural Network Model for Graph-based Dependency Parsing Genetic Algorithm-Neural Network (GANN): a study of neural network activation functions and depth of genetic algorithm search applied to feature selection Grounded Textual Entailment M-Walk: Learning to Walk over Graphs using Monte Carlo Tree Search Improving the Antinoise Ability of DNNs via a Bio-Inspired Noise Adaptive Activation Function Rand Softplus Co-design of augmented reality textbook for children’s collaborative learning experience in primary schools Hearing aid experience and background noise affect the robust relationship between working memory and speech recognition in noise Sufficient Conditions for First-Order and Datalog Rewritability in ELU New Iterative Linear Solvers For Parallel Circuit Simulation Random Noise Attenuation Based on Residual Convolutional Neural Network in Seismic Datasets An Enhanced Location-Based Location Update Scheme in Mobile Cellular Networks The ensparsed LU decomposition method for large scale circuit transient analysis Parametric Exponential Linear Unit for Deep Convolutional Neural Networks Convolutional neural networks for decoding of covert attention focus and saliency maps for EEG feature visualization. Deep Residual Networks with Exponential Linear Unit Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs) Graph Attention Networks Review of shielding computation methodology with emphasis on the experience in the national center of nuclear safety and radiation control Full-Scale Measurement of Akashi-Kaikyo Bridge during Typhoon Computing heat kernel pagerank and a local clustering algorithm An asymmetric multi-item auction with quantity discounts applied to Internet service procurement in Buenos Aires public schools A MATHEMATICAL MODEL OF PARTICIPATION IN SMALL GROUP DISCUSSIONS. Comparing different mechanical models for the evaluation of mechanical behavior of reuse in PVC electrosurgical pencils through their hardness and Young's Modulus relation A new multi-view regression approach with an application to customer wallet estimation Higher-Order Exponential Integrators for Quasi-Linear Parabolic Problems. Part I: Stability Higher-Order Exponential Integrators for Quasi-Linear Parabolic Problems. Part II: Convergence Maximal inner boxes in parametric AE-solution sets with linear shape Fine-grained visual categorization of butterfly specimens at sub-species level via a convolutional neural network with skip-connections Hexpo: A vanishing-proof activation function Generalization of SELU to CNN Transfer fault diagnosis of bearing installed in different machines using enhanced deep auto-encoder Quantifying Responses of Spectral Vegetation Indices to Dead Materials in Mixed Grasslands Graph Attention Networks Skip-gram Language Modeling Using Sparse Non-negative Matrix Probability Estimation DeXpression: Deep Convolutional Neural Network for Expression Recognition Face Attention Network: An Effective Face Detector for the Occluded Faces TanhExp: A Smooth Activation Function with High Convergence Speed for Lightweight Neural Networks
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