It turns out that our bound is consistent with the experimental results about ELM obtained before and predicts that overfitting can be avoided even when the number of hidden nodes approaches infinity . The prediction is confirmed by our experiments on 15 data sets using one kind of activation function with every parameter independently drawn from the same Guasssian distribution , which satisfies the assumption above . The experiments also showed that when the number of hidden nodes approaches infinity , the ELM kernel with the activation is insensitive to the kernel parameter . The system error is calculated based on some fuzzy measures in the output status of the neurons in the output layer of the network . An application of the proposed activation function for the extraction of objects using a three layer self-organizing neural network is demonstrated with two images . The standard correlation factor and the discrepancy index ( DI ) between the extracted images and the original images are used as the figures of merit to evaluate the quality of the extracted images . We use four kinds of building blocks in designing the V2V - PoseNet . The first one is the volumetric basic block that consists of a volumetric convolution , volumetric batch normalization [ reference ] , and the activation function ( i.e. , ReLU ) . This block is located in the first and last parts of the network . subsection : Data Adaptive Activation Function PReLU is a commonly used activation function where is one dimension of the input of activation function and is an indicator function which controls to switch between two channels of and . in the second channel is a learning parameter . Here we refer to as the control function . However , we can replace it with Leaky ReLU ( see , Figure [ reference ] ) with slope without impacting the quality of the trained models . This will be the activation function that we use in our experimental evaluation due to its affinity to standard ReLU , even though other activation functions could be used . The corresponding forward pass through the activation function with slope for negative inputs and its inverse used in our backward pass are given as follows : Leaky ReLU and its inverse share the same computational cost , an elementwise sign check and scaling operation . We establish optimal bounds in terms of network complexity and prove that rational neural networks approximate smooth functions more efficiently than ReLU networks . The flexibility and smoothness of rational activation functions make them an attractive alternative to ReLU , as we demonstrate with numerical experiments . In this paper we investigate the family of functions representable by deep neural networks ( DNN ) with rectified linear units ( ReLU ) . We give an algorithm to train a ReLU DNN with one hidden layer to * global optimality * with runtime polynomial in the data size albeit exponential in the input dimension . Further , we improve on the known lower bounds on size ( from exponential to super exponential ) for approximating a ReLU deep net function by a shallower ReLU net . It does not require extra-communications with the user . And , is based on the Rectified Linear Unit ( ReLU ) activation function that we secure with no approximation contrarily to actual SMLP solutions . To do so , we take advantage of two semi-honest non-colluding servers . We developed a 31-layer one-dimensional ( 1D ) residual convolutional neural network . The algorithm includes four residual blocks , each of which consists of three 1D convolution layers , three batch normalization ( BP ) layers , three rectified linear unit ( ReLU ) layers , and an " identity shortcut connections " structure . In addition , we propose to use 2-lead ECG signals in combination with deep learning methods to automatically identify five different types of heartbeats . Specifically , we first examine existing CNN models and observe an intriguing property that the filters in the lower layers form pairs ( i.e. , filters with opposite phase ) . Inspired by our observation , we propose a novel , simple yet effective activation scheme called concatenated ReLU ( CRelu ) and theoretically analyze its reconstruction property in CNNs . We integrate CRelu into several state-of-the-art CNN architectures and demonstrate improvement in their recognition performance on CIFAR-10/100 and ImageNet datasets with fewer trainable parameters . In this paper , we explore theoretical properties of training a two-layered ReLU network $ g(\mathbf{x } ; \mathbf{w } ) = \sum_{j=1}^K \sigma(\mathbf{w}_j^T\mathbf{x})$ with centered $ d$-dimensional spherical Gaussian input $ \mathbf{x}$ ( $ \sigma$=ReLU ) . We train our network with gradient descent on $ \mathbf{w}$ to mimic the output of a teacher network with the same architecture and fixed parameters $ \mathbf{w}^*$. We show that its population gradient has an analytical formula , leading to interesting theoretical analysis of critical points and convergence behaviors . Based on the output reachable set computation results , the safety verification for a ReLU neural network can be performed by checking the intersections of unsafe regions and output reachable set described by a union of polyhedra . A numerical example of a randomly generated ReLU neural network is provided to show the effectiveness of the approach developed in this paper . We provide exploitability bounds for $ f$-RCFR with the polynomial and exponential link functions in zero-sum imperfect information games and examine empirically how the link function interacts with the severity of the approximation . We find that the previously studied ReLU parameterization performs better when the approximation error is small while the softmax parameterization can perform better when the approximation error is large . In practice , Bayesian neural networks rely on poorly understood approximations for computational tractability . We prove that two commonly used approximation methods , the factorised Gaussian assumption and Monte Carlo dropout , lead to pathological estimates of the predictive uncertainty in single hidden layer ReLU networks . This indicates that more flexible approximations are needed to obtain reliable uncertainty estimates . More importantly , we show that the same characterization can also be applied to deep ReLU networks with rank-one inputs , where we prove that strong duality still holds and optimal layer weight matrices are rank-one for scalar output networks . As a corollary , we prove that norm regularized deep ReLU networks yield spline interpolation for one-dimensional datasets which was previously known only for two-layer networks . We then verify our theoretical results via several numerical experiments . that we find in modern deep architectures . The activation function ( ReLU ) is denoted by . Computations occurring during the forward pass are shown in green and involve the entire minibatch ( we omit the subscript ) . We experimented with 1 - and 2 - layer LSTMNs . For the latter model , we predict the sentiment label of the sentence based on the averaged hidden vector passed to a 2 - layer neural network classifier with ReLU as the activation function . The memory size for both LSTMN models was set to 168 to be compatible with previous LSTM models applied to the same task . The encoder converts a character sequence into a hidden feature representation which the decoder consumes to predict a spectrogram . Input characters are represented using a learned 512 - dimensional character embedding , which are passed through a stack of 3 convolutional layers each containing 512 filters with shape , i.e. , where each filter spans 5 characters , followed by batch normalization and ReLU activations . As in Tacotron , these convolutional layers model longer - term context ( e.g. , - grams ) in the input character sequence . The decoder is an autoregressive recurrent neural network which predicts a mel spectrogram from the encoded input sequence one frame at a time . The prediction from the previous time step is first passed through a small pre - net containing 2 fully connected layers of 256 hidden ReLU units . We found that the pre - net acting as an information bottleneck was essential for learning attention . We then compute an attended vector for each context token as : We also compute a query - to - context vector : The final vector computed for each token is built by concatenating , , , and . In our model we subsequently pass the result through a linear layer with ReLU activations . Self - Attention : Srivastava2014DropoutAS at the input to the final two fully connected layers . All feed forward layers use ReLU activations . Parameters were optimized using Adam Kingma2014AdamAM with gradient norms clipped at 5.0 and initial learning rate 0.0004 , decreasing by half each time accuracy on the development set did not increase in subsequent epochs . Suppose multiple U - Nets are stacked together , for the top - down and bottom - up blocks in the U - Net , we use and to denote their non - linear transformations . Their outputs are represented by and . and comprise operations of Convolution ( Conv ) , Batch Normalization ( BN ) , rectified linear units ( ReLU ) , and pooling . Stacked U - Nets . The size of the result tensor is . The Rectified Linear Unit ( ReLU ) is not added after this convolution . Similar to conventional multi - class recognition approaches , we use the cross - entropy loss for identity prediction , which is Here denotes the convolutional operation . In our experiments , we use siamese architecture described in [ reference ] ( Deep Metric Learning or DML ) for learning deep image descriptors on the source data set . This architecture incorporates two convolution layers ( with 7 × 7 and 5 × 5 filter banks ) , followed by ReLU and max pooling , and one fully - connected layer , which gives 500 - dimensional descriptors as an output . There are three parallel flows within the CNN for processing three part of an image : the upper , the middle , and the lower one . Followed by an element - wise ‘ sum ’ layer and a ‘ ReLU ’ layer , we obtain the fused feature as . Let us now compare the pooling operation defined by Eq . [ reference ] to the standard definition of a convolutional layer applied to feature map given as : where are the convolutional weights ( or the kernel weights , or filters ) , is the activation function , typically a rectified linear activation ReLU , and is the number of output feature ( or channel ) of the convolutional layer . When formalized like this it becomes clear that both operations depend on the same elements of the previous layer feature map . A cross - entropy loss is used to train model by backpropagating the error through multiple memory layers , in the same manner as the QA tasks . To aid training , we apply ReLU operations to half of the units in each layer . We use layer - wise ( RNN - like ) weight sharing , i.e. the query weights of each layer are the same ; the output weights of each layer are the same . and CycleGAN . Let c7s1 - k denote a Convolution - InstanceNorm - ReLU layer with filters and stride . dk denotes a Convolution - InstanceNorm - ReLU layer with filters , and stride . Nowadays , applications based on digits recognition and characters recognition have become much more reliable thanks to the rapid development of the DNN(deep neural network ) architecture and constantly increasing the efficiency to the computing resources . A lot of methods have been proposed to improve the performance of DNNs , such as the ReLU ( Rectified Linear Unit ) which is a widely used alternative of the sigmoid activation function , Local Response Normalization and Batch Normalization . What 's more , some methods , OHEM ( Online Hard Sample Mining ) for instance , aims to augment the capability of generalization of DNNs in certain scenarios . A CNN model was designed with six optimized convolution layers including activation , pooling , and dropout layers . One-dimensional ( 1D ) convolution , rectified linear units ( ReLU ) , and max pooling were applied to the convolution , activation , and pooling layers , respectively . For training and evaluation of the CNN model , a single-lead ECG dataset was collected from 82 subjects with OSA and was divided into training ( including data from 63 patients with 34,281 events ) and testing ( including data from 19 patients with 8571 events ) datasets . Our method is comprised of two ingredients : first a negative log-log ordinal classifier is devised in the last layer of the network , which can improve the ordinal discriminative ability of the model . Second , as a variant of the Rectified Linear Units ( ReLU ) , a modified activation function is developed for photo based air pollution estimation . This function has been shown it can alleviate the vanishing gradient issue effectively . In this paper we review work on distant speech recognition , with an emphasis on approaches which combine multichannel signal processing with acoustic modelling , and investigate the use of hybrid neural network / hidden Markov model acoustic models for distant speech recognition of meetings recorded using microphone arrays . In particular we investigate the use of convolutional and fully-connected neural networks with different activation functions ( sigmoid , rectified linear , and maxout ) . We performed experiments on the AMI and ICSI meeting corpora , with results indicating that neural network models are capable of significant improvements in accuracy compared with discriminatively trained Gaussian mixture models . Rectified linear activation units are important components for state-of-the-art deep convolutional networks . In this paper , we propose a novel S-shaped rectified linear activation unit ( SReLU ) to learn both convex and non-convex functions , imitating the multiple function forms given by the two fundamental laws , namely the Webner-Fechner law and the Stevens law , in psychophysics and neural sciences . To improve the identification accuracy of maize leaf diseases and reduce the number of network parameters , the improved GoogLeNet and Cifar10 models based on deep learning are proposed for leaf disease recognition in this paper . Two improved models that are used to train and test nine kinds of maize leaf images are obtained by adjusting the parameters , changing the pooling combinations , adding dropout operations and rectified linear unit functions , and reducing the number of classifiers . In addition , the number of parameters of the improved models is significantly smaller than that of the VGG and AlexNet structures . In addition , we found that on average , across all datasets , the Rectified Linear Unit activation function performs better than any maxout activation when the number of convolutional filters is increased . Furthermore , adding more filters enhances the classification accuracy of the Rectified Linear Unit networks , without adversely affecting their advantage over maxout activations with respect to network-training speed . This article proposes “ Hexpo ” , an activation function that has ability to scale the gradient and hence overcome the vanishing gradient problem . Unlike rectified linear units family which produces identity mapping on positive inputs , Hexpo has scalable limits on both positive and negative values . With parametrization , the active domain of Hexpo and the output it maps to is flexible . In this paper , a novel framework is proposed for classification and reconstruction of airborne laser scanning point cloud data . To label point clouds , we present a rectified linear units neural network named ReLu-NN where the rectified linear units ( ReLu ) instead of the traditional sigmoid are taken as the activation function in order to speed up the convergence . Since the features of the point cloud are sparse , we reduce the number of neurons by the dropout to avoid over-fitting of the training process . The following convolutional layer has the set of 96 filters . The subsampling layer contains the rectified linear units ( RELU ) layers and pooling layers . The final level is the fully connected layer with 4 neurons . Given the input feature vector , the - th hidden layer of the network is denoted as , which is a nonlinear function of the previous hidden layer defined as : where and are parameters of the - th layer , and . We adopt rectified linear unit as the nonlinear function in this work . The loss function of our framework can be expressed as where is a supervised loss of predicting the labels , and is an unsupervised loss of predicting the graph context . We use leaky rectified linear units ( lRELU ) [ reference ] with leaky rate 0.1 as the nonlinearity applied to hidden layers of the discrminator networks , and normal rectified linear units ( RELU ) for the generator networks . Unless noted otherwise , learning rate is 2e - 4 for D and 1e - 3 for G ; λ is set to 1 . Recently “ Leaky ReLUs ” ( LReLUs ) that replace the negative part of the ReLU with a linear function have been shown to be superior to ReLUs . Parametric Rectified Linear Units ( PReLUs ) generalize LReLUs by learning the slope of the negative part which yielded improved learning behavior on large image benchmark data sets . Another variant are Randomized Leaky Rectified Linear Units ( RReLUs ) which randomly sample the slope of the negative part which raised the performance on image benchmark datasets and convolutional networks . The remaining non - recurrent layers operate on independent data for each time step . Thus , for each time , the first 3 layers are computed by : where is the clipped rectified - linear ( ReLu ) activation function and are the weight matrix and bias parameters for layer . The fourth layer is a bi - directional recurrent layer . For example , Graves et al . have previously introduced the “ Connectionist Temporal Classification ” ( CTC ) loss function for scoring transcriptions produced by RNNs and , with LSTM networks , have previously applied this approach to speech . We similarly adopt the CTC loss for part of our training procedure but use much simpler recurrent networks with rectified - linear activations . Our recurrent network is similar to the bidirectional RNN used by Hannun et al . , but with multiple changes to enhance its scalability . : To obtain features that are non - linear transformations of the input , an element - wise non - linearity is applied to the result of the kernel convolution . There are multiple choices for this non - linearity , such as the sigmoid , hyperbolic tangent and rectified linear functions , . Recently , proposed a Maxout non - linearity , which has been shown to be particularly effective at modeling useful features . This work introduces a novel activation unit that can be efficiently employed in deep neural nets ( DNNs ) and performs significantly better than the traditional Rectified Linear Units ( ReLU ) . The function developed is a two parameter version of the specialized Richard 's Curve and we call it Adaptive Richard 's Curve weighted Activation ( ARiA ) . This function is non-monotonous , analogous to the newly introduced Swish , however allows a precise control over its non-monotonous convexity by varying the hyper-parameters . The benchmark database used for the evaluation was BRAST 2015 dataset . The results showed that the HardELiSH activation function outperformed the standard ReLU activation function . This proves that the deep learning model performance in brain tumour segmentation can be enhanced with the choice of the activation function . This work introduces a novel activation unit that can be efficiently employed in deep neural nets ( DNNs ) and performs significantly better than the traditional Rectified Linear Units ( ReLU ) . The function developed is a two parameter version of the specialized Richard 's Curve and we call it Adaptive Richard 's Curve weighted Activation ( ARiA ) . This function is non-monotonous , analogous to the newly introduced Swish , however allows a precise control over its non-monotonous convexity by varying the hyper-parameters .
It turns out that our bound is consistent with the experimental results about ELM obtained before and predicts that overfitting can be avoided even when the number of hidden nodes approaches infinity . The prediction is confirmed by our experiments on 15 data sets using one kind of activation function with every parameter independently drawn from the same Guasssian distribution , which satisfies the assumption above . The experiments also showed that when the number of hidden nodes approaches infinity , the ELM kernel with the activation is insensitive to the kernel parameter .
The system error is calculated based on some fuzzy measures in the output status of the neurons in the output layer of the network . An application of the proposed activation function for the extraction of objects using a three layer self-organizing neural network is demonstrated with two images . The standard correlation factor and the discrepancy index ( DI ) between the extracted images and the original images are used as the figures of merit to evaluate the quality of the extracted images .
We use four kinds of building blocks in designing the V2V - PoseNet . The first one is the volumetric basic block that consists of a volumetric convolution , volumetric batch normalization [ reference ] , and the activation function ( i.e. , ReLU ) . This block is located in the first and last parts of the network .
subsection : Data Adaptive Activation Function PReLU is a commonly used activation function where is one dimension of the input of activation function and is an indicator function which controls to switch between two channels of and . in the second channel is a learning parameter . Here we refer to as the control function .
However , we can replace it with Leaky ReLU ( see , Figure [ reference ] ) with slope without impacting the quality of the trained models . This will be the activation function that we use in our experimental evaluation due to its affinity to standard ReLU , even though other activation functions could be used . The corresponding forward pass through the activation function with slope for negative inputs and its inverse used in our backward pass are given as follows : Leaky ReLU and its inverse share the same computational cost , an elementwise sign check and scaling operation .
We establish optimal bounds in terms of network complexity and prove that rational neural networks approximate smooth functions more efficiently than ReLU networks . The flexibility and smoothness of rational activation functions make them an attractive alternative to ReLU , as we demonstrate with numerical experiments .
In this paper we investigate the family of functions representable by deep neural networks ( DNN ) with rectified linear units ( ReLU ) . We give an algorithm to train a ReLU DNN with one hidden layer to * global optimality * with runtime polynomial in the data size albeit exponential in the input dimension . Further , we improve on the known lower bounds on size ( from exponential to super exponential ) for approximating a ReLU deep net function by a shallower ReLU net .
It does not require extra-communications with the user . And , is based on the Rectified Linear Unit ( ReLU ) activation function that we secure with no approximation contrarily to actual SMLP solutions . To do so , we take advantage of two semi-honest non-colluding servers .
We developed a 31-layer one-dimensional ( 1D ) residual convolutional neural network . The algorithm includes four residual blocks , each of which consists of three 1D convolution layers , three batch normalization ( BP ) layers , three rectified linear unit ( ReLU ) layers , and an " identity shortcut connections " structure . In addition , we propose to use 2-lead ECG signals in combination with deep learning methods to automatically identify five different types of heartbeats .
Specifically , we first examine existing CNN models and observe an intriguing property that the filters in the lower layers form pairs ( i.e. , filters with opposite phase ) . Inspired by our observation , we propose a novel , simple yet effective activation scheme called concatenated ReLU ( CRelu ) and theoretically analyze its reconstruction property in CNNs . We integrate CRelu into several state-of-the-art CNN architectures and demonstrate improvement in their recognition performance on CIFAR-10/100 and ImageNet datasets with fewer trainable parameters .
In this paper , we explore theoretical properties of training a two-layered ReLU network $ g(\mathbf{x } ; \mathbf{w } ) = \sum_{j=1}^K \sigma(\mathbf{w}_j^T\mathbf{x})$ with centered $ d$-dimensional spherical Gaussian input $ \mathbf{x}$ ( $ \sigma$=ReLU ) . We train our network with gradient descent on $ \mathbf{w}$ to mimic the output of a teacher network with the same architecture and fixed parameters $ \mathbf{w}^*$. We show that its population gradient has an analytical formula , leading to interesting theoretical analysis of critical points and convergence behaviors .
Based on the output reachable set computation results , the safety verification for a ReLU neural network can be performed by checking the intersections of unsafe regions and output reachable set described by a union of polyhedra . A numerical example of a randomly generated ReLU neural network is provided to show the effectiveness of the approach developed in this paper .
We provide exploitability bounds for $ f$-RCFR with the polynomial and exponential link functions in zero-sum imperfect information games and examine empirically how the link function interacts with the severity of the approximation . We find that the previously studied ReLU parameterization performs better when the approximation error is small while the softmax parameterization can perform better when the approximation error is large .
In practice , Bayesian neural networks rely on poorly understood approximations for computational tractability . We prove that two commonly used approximation methods , the factorised Gaussian assumption and Monte Carlo dropout , lead to pathological estimates of the predictive uncertainty in single hidden layer ReLU networks . This indicates that more flexible approximations are needed to obtain reliable uncertainty estimates .
More importantly , we show that the same characterization can also be applied to deep ReLU networks with rank-one inputs , where we prove that strong duality still holds and optimal layer weight matrices are rank-one for scalar output networks . As a corollary , we prove that norm regularized deep ReLU networks yield spline interpolation for one-dimensional datasets which was previously known only for two-layer networks . We then verify our theoretical results via several numerical experiments .
that we find in modern deep architectures . The activation function ( ReLU ) is denoted by . Computations occurring during the forward pass are shown in green and involve the entire minibatch ( we omit the subscript ) .
We experimented with 1 - and 2 - layer LSTMNs . For the latter model , we predict the sentiment label of the sentence based on the averaged hidden vector passed to a 2 - layer neural network classifier with ReLU as the activation function . The memory size for both LSTMN models was set to 168 to be compatible with previous LSTM models applied to the same task .
The encoder converts a character sequence into a hidden feature representation which the decoder consumes to predict a spectrogram . Input characters are represented using a learned 512 - dimensional character embedding , which are passed through a stack of 3 convolutional layers each containing 512 filters with shape , i.e. , where each filter spans 5 characters , followed by batch normalization and ReLU activations . As in Tacotron , these convolutional layers model longer - term context ( e.g. , - grams ) in the input character sequence .
The decoder is an autoregressive recurrent neural network which predicts a mel spectrogram from the encoded input sequence one frame at a time . The prediction from the previous time step is first passed through a small pre - net containing 2 fully connected layers of 256 hidden ReLU units . We found that the pre - net acting as an information bottleneck was essential for learning attention .
We then compute an attended vector for each context token as : We also compute a query - to - context vector : The final vector computed for each token is built by concatenating , , , and . In our model we subsequently pass the result through a linear layer with ReLU activations . Self - Attention :
Srivastava2014DropoutAS at the input to the final two fully connected layers . All feed forward layers use ReLU activations . Parameters were optimized using Adam Kingma2014AdamAM with gradient norms clipped at 5.0 and initial learning rate 0.0004 , decreasing by half each time accuracy on the development set did not increase in subsequent epochs .
Suppose multiple U - Nets are stacked together , for the top - down and bottom - up blocks in the U - Net , we use and to denote their non - linear transformations . Their outputs are represented by and . and comprise operations of Convolution ( Conv ) , Batch Normalization ( BN ) , rectified linear units ( ReLU ) , and pooling . Stacked U - Nets .
The size of the result tensor is . The Rectified Linear Unit ( ReLU ) is not added after this convolution . Similar to conventional multi - class recognition approaches , we use the cross - entropy loss for identity prediction , which is Here denotes the convolutional operation .
In our experiments , we use siamese architecture described in [ reference ] ( Deep Metric Learning or DML ) for learning deep image descriptors on the source data set . This architecture incorporates two convolution layers ( with 7 × 7 and 5 × 5 filter banks ) , followed by ReLU and max pooling , and one fully - connected layer , which gives 500 - dimensional descriptors as an output . There are three parallel flows within the CNN for processing three part of an image : the upper , the middle , and the lower one .
Followed by an element - wise ‘ sum ’ layer and a ‘ ReLU ’ layer , we obtain the fused feature as .
Let us now compare the pooling operation defined by Eq . [ reference ] to the standard definition of a convolutional layer applied to feature map given as : where are the convolutional weights ( or the kernel weights , or filters ) , is the activation function , typically a rectified linear activation ReLU , and is the number of output feature ( or channel ) of the convolutional layer . When formalized like this it becomes clear that both operations depend on the same elements of the previous layer feature map .
A cross - entropy loss is used to train model by backpropagating the error through multiple memory layers , in the same manner as the QA tasks . To aid training , we apply ReLU operations to half of the units in each layer . We use layer - wise ( RNN - like ) weight sharing , i.e. the query weights of each layer are the same ; the output weights of each layer are the same .
and CycleGAN . Let c7s1 - k denote a Convolution - InstanceNorm - ReLU layer with filters and stride . dk denotes a Convolution - InstanceNorm - ReLU layer with filters , and stride .
Nowadays , applications based on digits recognition and characters recognition have become much more reliable thanks to the rapid development of the DNN(deep neural network ) architecture and constantly increasing the efficiency to the computing resources . A lot of methods have been proposed to improve the performance of DNNs , such as the ReLU ( Rectified Linear Unit ) which is a widely used alternative of the sigmoid activation function , Local Response Normalization and Batch Normalization . What 's more , some methods , OHEM ( Online Hard Sample Mining ) for instance , aims to augment the capability of generalization of DNNs in certain scenarios .
A CNN model was designed with six optimized convolution layers including activation , pooling , and dropout layers . One-dimensional ( 1D ) convolution , rectified linear units ( ReLU ) , and max pooling were applied to the convolution , activation , and pooling layers , respectively . For training and evaluation of the CNN model , a single-lead ECG dataset was collected from 82 subjects with OSA and was divided into training ( including data from 63 patients with 34,281 events ) and testing ( including data from 19 patients with 8571 events ) datasets .
Our method is comprised of two ingredients : first a negative log-log ordinal classifier is devised in the last layer of the network , which can improve the ordinal discriminative ability of the model . Second , as a variant of the Rectified Linear Units ( ReLU ) , a modified activation function is developed for photo based air pollution estimation . This function has been shown it can alleviate the vanishing gradient issue effectively .
In this paper we review work on distant speech recognition , with an emphasis on approaches which combine multichannel signal processing with acoustic modelling , and investigate the use of hybrid neural network / hidden Markov model acoustic models for distant speech recognition of meetings recorded using microphone arrays . In particular we investigate the use of convolutional and fully-connected neural networks with different activation functions ( sigmoid , rectified linear , and maxout ) . We performed experiments on the AMI and ICSI meeting corpora , with results indicating that neural network models are capable of significant improvements in accuracy compared with discriminatively trained Gaussian mixture models .
Rectified linear activation units are important components for state-of-the-art deep convolutional networks . In this paper , we propose a novel S-shaped rectified linear activation unit ( SReLU ) to learn both convex and non-convex functions , imitating the multiple function forms given by the two fundamental laws , namely the Webner-Fechner law and the Stevens law , in psychophysics and neural sciences .
To improve the identification accuracy of maize leaf diseases and reduce the number of network parameters , the improved GoogLeNet and Cifar10 models based on deep learning are proposed for leaf disease recognition in this paper . Two improved models that are used to train and test nine kinds of maize leaf images are obtained by adjusting the parameters , changing the pooling combinations , adding dropout operations and rectified linear unit functions , and reducing the number of classifiers . In addition , the number of parameters of the improved models is significantly smaller than that of the VGG and AlexNet structures .
In addition , we found that on average , across all datasets , the Rectified Linear Unit activation function performs better than any maxout activation when the number of convolutional filters is increased . Furthermore , adding more filters enhances the classification accuracy of the Rectified Linear Unit networks , without adversely affecting their advantage over maxout activations with respect to network-training speed .
This article proposes “ Hexpo ” , an activation function that has ability to scale the gradient and hence overcome the vanishing gradient problem . Unlike rectified linear units family which produces identity mapping on positive inputs , Hexpo has scalable limits on both positive and negative values . With parametrization , the active domain of Hexpo and the output it maps to is flexible .
In this paper , a novel framework is proposed for classification and reconstruction of airborne laser scanning point cloud data . To label point clouds , we present a rectified linear units neural network named ReLu-NN where the rectified linear units ( ReLu ) instead of the traditional sigmoid are taken as the activation function in order to speed up the convergence . Since the features of the point cloud are sparse , we reduce the number of neurons by the dropout to avoid over-fitting of the training process .
The following convolutional layer has the set of 96 filters . The subsampling layer contains the rectified linear units ( RELU ) layers and pooling layers . The final level is the fully connected layer with 4 neurons .
Given the input feature vector , the - th hidden layer of the network is denoted as , which is a nonlinear function of the previous hidden layer defined as : where and are parameters of the - th layer , and . We adopt rectified linear unit as the nonlinear function in this work . The loss function of our framework can be expressed as where is a supervised loss of predicting the labels , and is an unsupervised loss of predicting the graph context .
We use leaky rectified linear units ( lRELU ) [ reference ] with leaky rate 0.1 as the nonlinearity applied to hidden layers of the discrminator networks , and normal rectified linear units ( RELU ) for the generator networks . Unless noted otherwise , learning rate is 2e - 4 for D and 1e - 3 for G ; λ is set to 1 .
Recently “ Leaky ReLUs ” ( LReLUs ) that replace the negative part of the ReLU with a linear function have been shown to be superior to ReLUs . Parametric Rectified Linear Units ( PReLUs ) generalize LReLUs by learning the slope of the negative part which yielded improved learning behavior on large image benchmark data sets . Another variant are Randomized Leaky Rectified Linear Units ( RReLUs ) which randomly sample the slope of the negative part which raised the performance on image benchmark datasets and convolutional networks .
The remaining non - recurrent layers operate on independent data for each time step . Thus , for each time , the first 3 layers are computed by : where is the clipped rectified - linear ( ReLu ) activation function and are the weight matrix and bias parameters for layer . The fourth layer is a bi - directional recurrent layer .
For example , Graves et al . have previously introduced the “ Connectionist Temporal Classification ” ( CTC ) loss function for scoring transcriptions produced by RNNs and , with LSTM networks , have previously applied this approach to speech . We similarly adopt the CTC loss for part of our training procedure but use much simpler recurrent networks with rectified - linear activations . Our recurrent network is similar to the bidirectional RNN used by Hannun et al . , but with multiple changes to enhance its scalability .
: To obtain features that are non - linear transformations of the input , an element - wise non - linearity is applied to the result of the kernel convolution . There are multiple choices for this non - linearity , such as the sigmoid , hyperbolic tangent and rectified linear functions , . Recently , proposed a Maxout non - linearity , which has been shown to be particularly effective at modeling useful features .
This work introduces a novel activation unit that can be efficiently employed in deep neural nets ( DNNs ) and performs significantly better than the traditional Rectified Linear Units ( ReLU ) . The function developed is a two parameter version of the specialized Richard 's Curve and we call it Adaptive Richard 's Curve weighted Activation ( ARiA ) . This function is non-monotonous , analogous to the newly introduced Swish , however allows a precise control over its non-monotonous convexity by varying the hyper-parameters .
The benchmark database used for the evaluation was BRAST 2015 dataset . The results showed that the HardELiSH activation function outperformed the standard ReLU activation function . This proves that the deep learning model performance in brain tumour segmentation can be enhanced with the choice of the activation function .
This work introduces a novel activation unit that can be efficiently employed in deep neural nets ( DNNs ) and performs significantly better than the traditional Rectified Linear Units ( ReLU ) . The function developed is a two parameter version of the specialized Richard 's Curve and we call it Adaptive Richard 's Curve weighted Activation ( ARiA ) . This function is non-monotonous , analogous to the newly introduced Swish , however allows a precise control over its non-monotonous convexity by varying the hyper-parameters .
An oscillation bound of the generalization performance of extreme learning machine and corresponding analysis Multi-scale object extraction using a self organizing neural network with a multi-level beta activation function V2V-PoseNet: Voxel-to-Voxel Prediction Network for Accurate 3D Hand and Human Pose Estimation from a Single Depth Map Deep Interest Network for Click-Through Rate Prediction In-place Activated BatchNorm for Memory-Optimized Training of DNNs Rational neural networks Understanding Deep Neural Networks with Rectified Linear Units Secure Multilayer Perceptron Based On Homomorphic Encryption Heartbeat classification using deep residual convolutional neural network from 2-lead electrocardiogram. Understanding and Improving Convolutional Neural Networks via Concatenated Rectified Linear Units An Analytical Formula of Population Gradient for two-layered ReLU network and its Applications in Convergence and Critical Point Analysis Reachable Set Computation and Safety Verification for Neural Networks with ReLU Activations Alternative Function Approximation Parameterizations for Solving Games: An Analysis of f-Regression Counterfactual Regret Minimization Pathologies of Factorised Gaussian and MC Dropout Posteriors in Bayesian Neural Networks Convex Duality of Deep Neural Networks In-place Activated BatchNorm for Memory-Optimized Training of DNNs Long Short-Term Memory-Networks for Machine Reading Natural TTS Synthesis by Conditioning Wavenet on MEL Spectrogram Predictions Simple and Effective Multi-Paragraph Reading Comprehension Deep contextualized word representations Quantized Densely Connected U-Nets for Efficient Landmark Localization A Discriminatively Learned CNN Embedding for Person Reidentification Domain-Adversarial Training of Neural Networks ICNet for Real-Time Semantic Segmentation on High-Resolution Images Striving for Simplicity: The All Convolutional Net End-To-End Memory Networks High-Resolution Image Synthesis and Semantic Manipulation with Conditional GANs Improving the lenet with batch normalization and online hard example mining for digits recognition Automated Detection of Obstructive Sleep Apnea Events from a Single-Lead Electrocardiogram Using a Convolutional Neural Network On Estimating Air Pollution from Photos Using Convolutional Neural Network Neural networks for distant speech recognition Deep Learning with S-Shaped Rectified Linear Activation Units Identification of Maize Leaf Diseases Using Improved Deep Convolutional Neural Networks Evaluation of maxout activations in deep learning across several big data domains Hexpo: A vanishing-proof activation function Large-scale urban point cloud labeling and reconstruction Convolutional Neural Networks for Comprehending Geographical Features of International Important Ramsar Wetland Ecological Habitat Scenes in China Revisiting Semi-Supervised Learning with Graph Embeddings InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs) Deep Speech: Scaling up end-to-end speech recognition Brain tumor segmentation with Deep Neural Networks ARiA: Utilizing Richard's Curve for Controlling the Non-monotonicity of the Activation Function in Deep Neural Nets Enhancement of U-Net Performance in MRI Brain Tumour Segmentation using HardELiSH Activation Function ARiA: Utilizing Richard's Curve for Controlling the Non-monotonicity of the Activation Function in Deep Neural Nets
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2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition KDD 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition IWDW ICML 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition EMNLP 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) ACL NAACL-HLT ECCV ACM Trans. Multim. Comput. Commun. Appl. J. Mach. Learn. Res. ECCV ICLR NIPS 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition ACM Multimedia HSCMA IJCNN ISCID (1) ICML NIPS ICLR ArXiv Medical Image Anal.
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