Current research in convolutional neural networks ( CNN ) focuses mainly on changing the architecture of the networks , optimizing the hyper-parameters and improving the gradient descent . However , most work use only 3 standard families of operations inside the CNN , the convolution , the activation function , and the pooling . In this work , we propose a new family of operations based on the Green 's function of the Laplacian , which allows the network to solve the Laplacian , to integrate any vector field and to regularize the field by forcing it to be conservative . is a multilayer perceptron where each layer can be factorized into an affine transform and an element - wise activation function . Each activation function ; furthermore , has a finite number of discontinuities and . Input data to is continuous and its support is compact in with non - zero measure in each dimension and . This was due to numerical instabilities originating from the unbounded ReLU functions applied over long time series . However , coupling this activation function with batch normalization turned out to be helpful for taking advantage of ReLU neurons without numerical issues , as will be discussed in the next sub - section . subsection : Batch Normalization We provide human-accessible Buffon machines , which require a dozen coin flips or less , on average , and produce experiments whose probabilities of success are expressible in terms of numbers such as π , exp(−1 ) , log2 , √3 , cos(1/4 ) , ζ(5 ) . Generally , we develop a collection of constructions based on simple probabilistic mechanisms that enable one to design Buffon experiments involving compositions of exponentials and logarithms , polylogarithms , direct and inverse trigonometric functions , algebraic and hypergeometric functions , as well as functions defined by integrals , such as the Gaussian error function . A sufficiently smooth projection operator and Nussbaum function are used to overcome the parameter uncertainties and unknown direction of control gain respectively . An auxiliary design system and Gaussian error function are utilized to tackle the limitation on rudder angle . The proposed controller can make the course tracking error be arbitrarily small by selecting appropriate design parameters and guarantee all signals in system to be uniform ultimate boundedness . In this paper we propose a robust hypothesis verification algorithm , assuming data error is Gaussian . Previous approaches using gaussian error model start from an initial set of correspondences and try to extend it feature by feature . This solution is not optimal . To arrive at an characterization of the data structure contained in triplet data we investigate 2-dimensional planes being the only linear structures that can not be inferred from projections of the data . The key part of our methodology is the definition of a robust , Bayesian plane posterior under the assumption of an invariant prior and a Gaussian error model . A numerical representation of the plane posterior can be explored interactively . We propose the Gaussian Error Linear Unit ( GELU ) , a high-performing neural network activation function . The GELU nonlinearity is the expected transformation of a stochastic regularizer which randomly applies the identity or zero map to a neuron 's input . We found that the limits of the updated values constrain the assimilation results significantly and it is important to assess the measurement error variance to have a proper balance between preserving the prior information and the observation data misfit . Overshooting problems can be mitigated with the streamline based covariance localizations and normal score transformation of the parameters to support the Gaussian error statistics . The scale corresponds to the window covering the most amount of information . Gaussian and error functions are used to reveal entropy-scale relations . This study also introduces the entropy of functions and discusses its connection with differential entropy and Boltzmann 's entropy . Difficulties in source modeling arise from the fact that VBR video source traffic usually follows a gamma distribution with high correlation among adjacent data . Many researchers adopt autoregressive ( AR ) models driven by a Gaussian error process to account for such correlation . The problem is : due to the closure property of the Gaussian distribution , the traffic so generated is Gaussian rather than gamma . Expression Quantitative Trait Loci ( eQTL ) analysis enables characterisation of functional genetic variation influencing expression levels of individual genes . In outbread populations , including humans , eQTLs are commonly analysed using the conventional linear model , adjusting for relevant covariates , assuming an allelic dosage model and a Gaussian error term . However , gene expression data generally have noise that induces heavy-tailed errors relative to the Gaussian distribution and often include atypical observations , or outliers . Many online inference problems in computer vision and robotics are characterized by probability distributions whose factor graph representations are sparse and whose factors are all Gaussian functions of error residuals . Under these conditions , maximum likelihood estimation corresponds to solving a sequence of sparse least-squares minimization problems in which additional summands are added to the objective function over time . In this paper , a novel neural network activation function , called Symmetrical Gaussian Error Linear Unit ( SGELU ) , is proposed to obtain high performance . It is achieved by effectively integrating the property of the stochastic regularizer in the Gaussian Error Linear Unit ( GELU ) with the symmetrical characteristics . Nonetheless , it is uncertain that SELU and neural network based detectors are compatible with one another . An evaluation of SELU incorporated networks would help clarify that uncertainty . Such evaluation is performed through series of tests on different neural networks . After the evaluation , it is concluded that , while indeed faster , SELU is still not as good as BN for building complex object detector networks . We present a fully automatic method using a convolutional neural network ( CNN ) to outline the levator hiatus in a two-dimensional image extracted from a three-dimensional ultrasound volume . In particular , our method uses a recently developed scaled exponential linear unit ( SELU ) as a nonlinear self-normalizing activation function , which for the first time has been applied in medical imaging with CNN . SELU has important advantages such as being parameter-free and mini-batch independent , which may help to overcome memory constraints during training . A dataset with 91 images from 35 patients during Valsalva , contraction , and rest , all labeled by three operators , is used for training and evaluation in a leave-one-patient-out cross validation . In this work , we present a fully automatic method using a convolutional neural network ( CNN ) to outline the levator hiatus in a 2D image extracted from a 3D ultrasound volume . In particular , our method uses a recently developed scaled exponential linear unit ( SELU ) as a nonlinear self-normalising activation function . SELU has important advantages such as being parameter-free and mini-batch independent . We propose a novel CNN architecture for automated robot-assisted skill assessment . We explore the use of the SELU activation function and a global mixed pooling approach based on the average and max-pooling layers . Finally , we examine two types of convolutional layers : real-value and quaternion-valued . We also conduct a sensitivity analysis to determine which estimator type is most robust to perturbations . An analysis of our findings shows that the most accurate and robust estimators are those based on feedforward neural networks with a SELU activation function and convolutional neural networks . They are rectified linear unit ( ReLU ) , exponential linear unit ( ELU ) and the newly proposed scaled exponential linear unit ( SELU ) . The results show that our method using CNN model can achieve better accuracy than the conventional method and SELU function shows superior ability for the network to convergence . Thus , we try to investigate the more suitable convolution and ReLU ratio for exploring the better network architectures . Specifically , inspired by Leaky ReLU , we focus on adopting the proportional module with N : M ( N$>$M ) convolution and ReLU ratio to design the better networks . From the perspective of ensemble learning , Leaky ReLU can be considered as an ensemble of networks with different convolution and ReLU ratio . Furthermore , our network uses Leaky Rectified Linear Units ( Leaky ReLU ) activation function . Compared with 10 multiplications in the hyperbolic tangent and rectified sigmoid activation functions utilized in the two networks , Leaky ReLU needs only one multiplication which makes it computationally much more efficient than the two other functions . Our experiments on the German Traffic Sign Benchmark dataset shows \(0.6\%\ ) improvement on the best reported classification accuracy while it reduces the overall number of parameters and the number of multiplications \(85\%\ ) and \(88\%\ ) , respectively , compared with the winner network in the competition . For the problems that the traditional mechanical parts identification algorithm needs to design and extract relevant features artificially , so that the process is complex and time consuming in the computation is larger as well as identification accuracy is easily affected by the diversity of parts morphology , a mechanical part identification algorithm based on convolutional neural network is proposed in this paper . The Leaky ReLU function algorithm as an activation function is used to improve the pooling method , and a SVM classifier is combined to construct a convolutional neural network WorkNet-2 for the recognition of mechanical parts . In the recognition experiments of common four kinds of mechanical parts , the trained WorkNet-2 network ’s recognition accuracy on the test set reached 97.82 % . It is also established on translation invariance features . In this paper , we have used rectified linear unit ( Relu ) and Leaky-Relu activation for inner CNN layer and softmax activation function for output layer to analyze its effect on MNIST dataset . In this paper , we propose a Hybrid Two-Track U-Net(HTTU-Net ) architecture for brain tumor segmentation . This architecture leverages the use of Leaky Relu activation and batch normalization . It includes two tracks ; each one has a different number of layers and utilizes a different kernel size . However , ReLU has a disadvantage that the gradient is zero whenever the unit is not active or saturated . To alleviate the potential problems due the zero gradient , Leaky ReLU ( LReLU ) was proposed . Recently , a parametrized form of ReLU ( PReLU ) was shown to give superior performance compared to ReLU on large scale computer vision tasks . Moreover , generalization guarantees are developed for ReLU networks trained with the novel SGD leveraging classic compression bounds . These guarantees highlight a key difference ( at least in the worst case ) between reliably learning a ReLU network as well as a leaky ReLU network in terms of sample complexity . Numerical tests using both synthetic data and real images validate the effectiveness of the algorithm and the practical merits of the theory . Abstract Based on the leaky rectified linear unit ( ReLU ) function , the paper proposes a modified leaky ReLU scheme ( MLRS ) for topology optimization with multiple materials . A continuous function formed by sequence of modified leaky ReLU functions are used for the material property interpolation . ( III ) The non - linearity used is Leaky - ReLU , [ reference ] , with leak coefficient α ∈ ( 0 , 1 ) . ( IV ) However , this operation is only possible if the activation function is invertible . Even though this requirement does not hold for ReLU , one of the most dominantly used activation functions , we show in § [ reference ] that an invertible function like Leaky ReLU with a small slope works well as a surrogate of ReLU without compromising on the model quality . We also need to invert the scale - and - shift operation , which is in general possible if . In our experiments we also compared the validation accuracy obtained when replacing ReLU with Leaky ReLU in a ResNeXt - 101 trained with ReLU . We also considered the opposite case , replacing Leaky ReLU with ReLU in a Leaky ReLU - trained network ( see Table [ reference ] ) . Our results are in line with , and never differ by more than a single point per training except for the center crop evaluation top - 1 results , probably also due to non - deterministic training behaviour . For the generator network , we use instance normalization in all layers except the last output layer . For the discriminator network , we use Leaky ReLU with a negative slope of 0.01 . There are some notations ; : the number of domain , : the dimension of domain labels ( when training with both the CelebA and RaFD datasets , otherwise same as ) , N : the number of output channels , K : kernel size , S : stride size , P : padding size , IN : instance normalization . 1 , stride 1 and outputs ni / 2 channels . This is followed by Batch Normalization and usage of Leaky ReLU activation . Another block takes in ni / 2 input channels and outputs ni channels with kernel size 3 and stride kept to 1 . The network consists of 5 convolution layers with kernel and stride of 2 , where the channel number is { 64 , 128 , 256 , 512 , 1 } , respectively . Except for the last layer , each convolution layer is followed by a leaky ReLU parameterized by . An up - sampling layer is added to the last convolution layer for re - scaling the output to the size of the input . Therefore has been preferred over logistic functions . 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 . The distribution is known in the statistics community , but we present in this paper a numerically stable method to compute its parameters . Although the Dirichlet distribution is known to be a good Bayesian prior for probabilities we believe this paper shows that the linear exponential model offers a good alternative in other contexts , such as when we want to use posterior probabilities as features for automatic speech recognition . We show how to incorporate posterior probabilities as additional features to an existing GMM , and show that the resulting model gives a 0.6 % relative gain on a broadcast news speech recognition system . Index Terms : Linear Exponential Family , Simplex , Divided Difference , Partition Function In this work , we lay the groundwork for this research by evaluating three models of pupillary light response in 2D , and in a virtual reality ( VR ) environment . Our results show that either a linear or an exponential model can be fit to an individual participant with an easy-to-use calibration procedure . This work opens several new research directions in VR relating to performance analysis and inspires the use of eye tracking beyond gaze as a pointer and foveated rendering . Estimating the equivalent dose ( ED ) value is critical to obtaining the burial dose for Optically Stimulated Luminescence ( OSL ) dating . In this study , a simple Bayesian method is used to assess the standard error of an ED value in a linear or an exponential model . An ED value is treated as a stochastic node that depends on a random variable whose posterior distribution can be constructed and sampled . It is known that the linear exponential operator in CLL can express a specific infinitely reusable resource , i.e. it is reusable not only for any number , but also many times . In contrast , the soft exponential operator in SLL , which is a weak version of the linear exponential operator , can express a specific usable resource , i.e. it is usable in any number , but only once ( i.e. it is consumed after use ) . In TSLL , the resource operators ( i.e. linear and soft exponentials ) and some temporal operators are combined based on the interpretation that “ time ” is regarded as a “ resource ” . In addition to its ability to reflect increasing appreciation for money , risk aversion , and decreasing risk aversion , it is consistent with a risk-return representation in which return is measured by expected value . In this paper we present a new condition , strong one-switch , that characterizes the linear plus exponential family . This note is concerned with performance prediction of multiple-target tracking systems , particularly in data-rich , high-target-density environments . Two simple but useful expressions are described : ( i ) the exponential law for predicting average probability of correct data association , and ( ii ) the linear-times-exponential law for calculating the effective measurement error variances with possible data misassociation . Estimation of two key multiple-target tracking performance measures , i.e. , track purity and track accuracy , are then derived using these two laws . In this paper , we show that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is a universal approximator of convex functions . Such a network represents a family of scaled log-sum exponential functions , here named log-sum-exp ( < inline-formula > < tex-math notation="LaTeX">$\mathrm {LSE}_{T}$ < /tex-math></inline-formula > ) . Under a suitable exponential transformation , the class of < inline-formula > < tex-math notation="LaTeX">$\mathrm {LSE}_{T}$ < /tex-math></inline-formula > functions maps to a family of generalized posynomials < inline-formula > < tex-math notation="LaTeX">$\mathrm {GPOS}_{T}$ < /tex-math></inline-formula > , which we similarly show to be universal approximators for log-log-convex functions . document : Deep Residual Networks with Exponential Linear Unit Very deep convolutional neural networks introduced new problems like vanishing gradient and degradation . These very deep models have lead to a considerable decrease in test errors , on benchmarks like ImageNet and COCO . In this paper , we propose the use of exponential linear unit instead of the combination of ReLU and Batch Normalization in Residual Networks . We show that this not only speeds up learning in Residual Networks but also improves the accuracy as the depth increases . 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 . We propose the Gaussian Error Linear Unit ( GELU ) , a high-performing neural network activation function . The GELU nonlinearity is the expected transformation of a stochastic regularizer which randomly applies the identity or zero map to a neuron 's input . This stochastic regularizer is comparable to nonlinearities aided by dropout , but it removes the need for a traditional nonlinearity . The connection between the GELU and the stochastic regularizer suggests a new probabilistic understanding of nonlinearities . We perform an empirical evaluation of the GELU nonlinearity against the ReLU and ELU activations and find performance improvements across all tasks . We propose the Gaussian Error Linear Unit ( GELU ) , a high-performing neural network activation function . The GELU nonlinearity is the expected transformation of a stochastic regularizer which randomly applies the identity or zero map to a neuron 's input . The GELU nonlinearity weights inputs by their magnitude , rather than gates inputs by their sign as in ReLUs . We perform an empirical evaluation of the GELU nonlinearity against the ReLU and ELU activations and find performance improvements across all considered computer vision , natural language processing , and speech tasks . Variations on GLU are possible , using different nonlinear ( or even linear ) functions in place of sigmoid . We test these variants in the feed-forward sublayers of the Transformer ( arXiv:1706.03762 ) sequence-to-sequence model , and find that some of them yield quality improvements over the typically-used ReLU or GELU activations .
Current research in convolutional neural networks ( CNN ) focuses mainly on changing the architecture of the networks , optimizing the hyper-parameters and improving the gradient descent . However , most work use only 3 standard families of operations inside the CNN , the convolution , the activation function , and the pooling . In this work , we propose a new family of operations based on the Green 's function of the Laplacian , which allows the network to solve the Laplacian , to integrate any vector field and to regularize the field by forcing it to be conservative .
is a multilayer perceptron where each layer can be factorized into an affine transform and an element - wise activation function . Each activation function ; furthermore , has a finite number of discontinuities and . Input data to is continuous and its support is compact in with non - zero measure in each dimension and .
This was due to numerical instabilities originating from the unbounded ReLU functions applied over long time series . However , coupling this activation function with batch normalization turned out to be helpful for taking advantage of ReLU neurons without numerical issues , as will be discussed in the next sub - section . subsection : Batch Normalization
We provide human-accessible Buffon machines , which require a dozen coin flips or less , on average , and produce experiments whose probabilities of success are expressible in terms of numbers such as π , exp(−1 ) , log2 , √3 , cos(1/4 ) , ζ(5 ) . Generally , we develop a collection of constructions based on simple probabilistic mechanisms that enable one to design Buffon experiments involving compositions of exponentials and logarithms , polylogarithms , direct and inverse trigonometric functions , algebraic and hypergeometric functions , as well as functions defined by integrals , such as the Gaussian error function .
A sufficiently smooth projection operator and Nussbaum function are used to overcome the parameter uncertainties and unknown direction of control gain respectively . An auxiliary design system and Gaussian error function are utilized to tackle the limitation on rudder angle . The proposed controller can make the course tracking error be arbitrarily small by selecting appropriate design parameters and guarantee all signals in system to be uniform ultimate boundedness .
In this paper we propose a robust hypothesis verification algorithm , assuming data error is Gaussian . Previous approaches using gaussian error model start from an initial set of correspondences and try to extend it feature by feature . This solution is not optimal .
To arrive at an characterization of the data structure contained in triplet data we investigate 2-dimensional planes being the only linear structures that can not be inferred from projections of the data . The key part of our methodology is the definition of a robust , Bayesian plane posterior under the assumption of an invariant prior and a Gaussian error model . A numerical representation of the plane posterior can be explored interactively .
We propose the Gaussian Error Linear Unit ( GELU ) , a high-performing neural network activation function . The GELU nonlinearity is the expected transformation of a stochastic regularizer which randomly applies the identity or zero map to a neuron 's input .
We found that the limits of the updated values constrain the assimilation results significantly and it is important to assess the measurement error variance to have a proper balance between preserving the prior information and the observation data misfit . Overshooting problems can be mitigated with the streamline based covariance localizations and normal score transformation of the parameters to support the Gaussian error statistics .
The scale corresponds to the window covering the most amount of information . Gaussian and error functions are used to reveal entropy-scale relations . This study also introduces the entropy of functions and discusses its connection with differential entropy and Boltzmann 's entropy .
Difficulties in source modeling arise from the fact that VBR video source traffic usually follows a gamma distribution with high correlation among adjacent data . Many researchers adopt autoregressive ( AR ) models driven by a Gaussian error process to account for such correlation . The problem is : due to the closure property of the Gaussian distribution , the traffic so generated is Gaussian rather than gamma .
Expression Quantitative Trait Loci ( eQTL ) analysis enables characterisation of functional genetic variation influencing expression levels of individual genes . In outbread populations , including humans , eQTLs are commonly analysed using the conventional linear model , adjusting for relevant covariates , assuming an allelic dosage model and a Gaussian error term . However , gene expression data generally have noise that induces heavy-tailed errors relative to the Gaussian distribution and often include atypical observations , or outliers .
Many online inference problems in computer vision and robotics are characterized by probability distributions whose factor graph representations are sparse and whose factors are all Gaussian functions of error residuals . Under these conditions , maximum likelihood estimation corresponds to solving a sequence of sparse least-squares minimization problems in which additional summands are added to the objective function over time .
In this paper , a novel neural network activation function , called Symmetrical Gaussian Error Linear Unit ( SGELU ) , is proposed to obtain high performance . It is achieved by effectively integrating the property of the stochastic regularizer in the Gaussian Error Linear Unit ( GELU ) with the symmetrical characteristics .
Nonetheless , it is uncertain that SELU and neural network based detectors are compatible with one another . An evaluation of SELU incorporated networks would help clarify that uncertainty . Such evaluation is performed through series of tests on different neural networks . After the evaluation , it is concluded that , while indeed faster , SELU is still not as good as BN for building complex object detector networks .
We present a fully automatic method using a convolutional neural network ( CNN ) to outline the levator hiatus in a two-dimensional image extracted from a three-dimensional ultrasound volume . In particular , our method uses a recently developed scaled exponential linear unit ( SELU ) as a nonlinear self-normalizing activation function , which for the first time has been applied in medical imaging with CNN . SELU has important advantages such as being parameter-free and mini-batch independent , which may help to overcome memory constraints during training . A dataset with 91 images from 35 patients during Valsalva , contraction , and rest , all labeled by three operators , is used for training and evaluation in a leave-one-patient-out cross validation .
In this work , we present a fully automatic method using a convolutional neural network ( CNN ) to outline the levator hiatus in a 2D image extracted from a 3D ultrasound volume . In particular , our method uses a recently developed scaled exponential linear unit ( SELU ) as a nonlinear self-normalising activation function . SELU has important advantages such as being parameter-free and mini-batch independent .
We propose a novel CNN architecture for automated robot-assisted skill assessment . We explore the use of the SELU activation function and a global mixed pooling approach based on the average and max-pooling layers . Finally , we examine two types of convolutional layers : real-value and quaternion-valued .
We also conduct a sensitivity analysis to determine which estimator type is most robust to perturbations . An analysis of our findings shows that the most accurate and robust estimators are those based on feedforward neural networks with a SELU activation function and convolutional neural networks .
They are rectified linear unit ( ReLU ) , exponential linear unit ( ELU ) and the newly proposed scaled exponential linear unit ( SELU ) . The results show that our method using CNN model can achieve better accuracy than the conventional method and SELU function shows superior ability for the network to convergence .
Thus , we try to investigate the more suitable convolution and ReLU ratio for exploring the better network architectures . Specifically , inspired by Leaky ReLU , we focus on adopting the proportional module with N : M ( N$>$M ) convolution and ReLU ratio to design the better networks . From the perspective of ensemble learning , Leaky ReLU can be considered as an ensemble of networks with different convolution and ReLU ratio .
Furthermore , our network uses Leaky Rectified Linear Units ( Leaky ReLU ) activation function . Compared with 10 multiplications in the hyperbolic tangent and rectified sigmoid activation functions utilized in the two networks , Leaky ReLU needs only one multiplication which makes it computationally much more efficient than the two other functions . Our experiments on the German Traffic Sign Benchmark dataset shows \(0.6\%\ ) improvement on the best reported classification accuracy while it reduces the overall number of parameters and the number of multiplications \(85\%\ ) and \(88\%\ ) , respectively , compared with the winner network in the competition .
For the problems that the traditional mechanical parts identification algorithm needs to design and extract relevant features artificially , so that the process is complex and time consuming in the computation is larger as well as identification accuracy is easily affected by the diversity of parts morphology , a mechanical part identification algorithm based on convolutional neural network is proposed in this paper . The Leaky ReLU function algorithm as an activation function is used to improve the pooling method , and a SVM classifier is combined to construct a convolutional neural network WorkNet-2 for the recognition of mechanical parts . In the recognition experiments of common four kinds of mechanical parts , the trained WorkNet-2 network ’s recognition accuracy on the test set reached 97.82 % .
It is also established on translation invariance features . In this paper , we have used rectified linear unit ( Relu ) and Leaky-Relu activation for inner CNN layer and softmax activation function for output layer to analyze its effect on MNIST dataset .
In this paper , we propose a Hybrid Two-Track U-Net(HTTU-Net ) architecture for brain tumor segmentation . This architecture leverages the use of Leaky Relu activation and batch normalization . It includes two tracks ; each one has a different number of layers and utilizes a different kernel size .
However , ReLU has a disadvantage that the gradient is zero whenever the unit is not active or saturated . To alleviate the potential problems due the zero gradient , Leaky ReLU ( LReLU ) was proposed . Recently , a parametrized form of ReLU ( PReLU ) was shown to give superior performance compared to ReLU on large scale computer vision tasks .
Moreover , generalization guarantees are developed for ReLU networks trained with the novel SGD leveraging classic compression bounds . These guarantees highlight a key difference ( at least in the worst case ) between reliably learning a ReLU network as well as a leaky ReLU network in terms of sample complexity . Numerical tests using both synthetic data and real images validate the effectiveness of the algorithm and the practical merits of the theory .
Abstract Based on the leaky rectified linear unit ( ReLU ) function , the paper proposes a modified leaky ReLU scheme ( MLRS ) for topology optimization with multiple materials . A continuous function formed by sequence of modified leaky ReLU functions are used for the material property interpolation .
( III ) The non - linearity used is Leaky - ReLU , [ reference ] , with leak coefficient α ∈ ( 0 , 1 ) . ( IV )
However , this operation is only possible if the activation function is invertible . Even though this requirement does not hold for ReLU , one of the most dominantly used activation functions , we show in § [ reference ] that an invertible function like Leaky ReLU with a small slope works well as a surrogate of ReLU without compromising on the model quality . We also need to invert the scale - and - shift operation , which is in general possible if .
In our experiments we also compared the validation accuracy obtained when replacing ReLU with Leaky ReLU in a ResNeXt - 101 trained with ReLU . We also considered the opposite case , replacing Leaky ReLU with ReLU in a Leaky ReLU - trained network ( see Table [ reference ] ) . Our results are in line with , and never differ by more than a single point per training except for the center crop evaluation top - 1 results , probably also due to non - deterministic training behaviour .
For the generator network , we use instance normalization in all layers except the last output layer . For the discriminator network , we use Leaky ReLU with a negative slope of 0.01 . There are some notations ; : the number of domain , : the dimension of domain labels ( when training with both the CelebA and RaFD datasets , otherwise same as ) , N : the number of output channels , K : kernel size , S : stride size , P : padding size , IN : instance normalization .
1 , stride 1 and outputs ni / 2 channels . This is followed by Batch Normalization and usage of Leaky ReLU activation . Another block takes in ni / 2 input channels and outputs ni channels with kernel size 3 and stride kept to 1 .
The network consists of 5 convolution layers with kernel and stride of 2 , where the channel number is { 64 , 128 , 256 , 512 , 1 } , respectively . Except for the last layer , each convolution layer is followed by a leaky ReLU parameterized by . An up - sampling layer is added to the last convolution layer for re - scaling the output to the size of the input .
Therefore has been preferred over logistic functions . 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 .
The distribution is known in the statistics community , but we present in this paper a numerically stable method to compute its parameters . Although the Dirichlet distribution is known to be a good Bayesian prior for probabilities we believe this paper shows that the linear exponential model offers a good alternative in other contexts , such as when we want to use posterior probabilities as features for automatic speech recognition . We show how to incorporate posterior probabilities as additional features to an existing GMM , and show that the resulting model gives a 0.6 % relative gain on a broadcast news speech recognition system . Index Terms : Linear Exponential Family , Simplex , Divided Difference , Partition Function
In this work , we lay the groundwork for this research by evaluating three models of pupillary light response in 2D , and in a virtual reality ( VR ) environment . Our results show that either a linear or an exponential model can be fit to an individual participant with an easy-to-use calibration procedure . This work opens several new research directions in VR relating to performance analysis and inspires the use of eye tracking beyond gaze as a pointer and foveated rendering .
Estimating the equivalent dose ( ED ) value is critical to obtaining the burial dose for Optically Stimulated Luminescence ( OSL ) dating . In this study , a simple Bayesian method is used to assess the standard error of an ED value in a linear or an exponential model . An ED value is treated as a stochastic node that depends on a random variable whose posterior distribution can be constructed and sampled .
It is known that the linear exponential operator in CLL can express a specific infinitely reusable resource , i.e. it is reusable not only for any number , but also many times . In contrast , the soft exponential operator in SLL , which is a weak version of the linear exponential operator , can express a specific usable resource , i.e. it is usable in any number , but only once ( i.e. it is consumed after use ) . In TSLL , the resource operators ( i.e. linear and soft exponentials ) and some temporal operators are combined based on the interpretation that “ time ” is regarded as a “ resource ” .
In addition to its ability to reflect increasing appreciation for money , risk aversion , and decreasing risk aversion , it is consistent with a risk-return representation in which return is measured by expected value . In this paper we present a new condition , strong one-switch , that characterizes the linear plus exponential family .
This note is concerned with performance prediction of multiple-target tracking systems , particularly in data-rich , high-target-density environments . Two simple but useful expressions are described : ( i ) the exponential law for predicting average probability of correct data association , and ( ii ) the linear-times-exponential law for calculating the effective measurement error variances with possible data misassociation . Estimation of two key multiple-target tracking performance measures , i.e. , track purity and track accuracy , are then derived using these two laws .
In this paper , we show that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is a universal approximator of convex functions . Such a network represents a family of scaled log-sum exponential functions , here named log-sum-exp ( < inline-formula > < tex-math notation="LaTeX">$\mathrm {LSE}_{T}$ < /tex-math></inline-formula > ) . Under a suitable exponential transformation , the class of < inline-formula > < tex-math notation="LaTeX">$\mathrm {LSE}_{T}$ < /tex-math></inline-formula > functions maps to a family of generalized posynomials < inline-formula > < tex-math notation="LaTeX">$\mathrm {GPOS}_{T}$ < /tex-math></inline-formula > , which we similarly show to be universal approximators for log-log-convex functions .
document : Deep Residual Networks with Exponential Linear Unit Very deep convolutional neural networks introduced new problems like vanishing gradient and degradation .
These very deep models have lead to a considerable decrease in test errors , on benchmarks like ImageNet and COCO . In this paper , we propose the use of exponential linear unit instead of the combination of ReLU and Batch Normalization in Residual Networks . We show that this not only speeds up learning in Residual Networks but also improves the accuracy as the depth increases .
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 .
We propose the Gaussian Error Linear Unit ( GELU ) , a high-performing neural network activation function . The GELU nonlinearity is the expected transformation of a stochastic regularizer which randomly applies the identity or zero map to a neuron 's input . This stochastic regularizer is comparable to nonlinearities aided by dropout , but it removes the need for a traditional nonlinearity . The connection between the GELU and the stochastic regularizer suggests a new probabilistic understanding of nonlinearities . We perform an empirical evaluation of the GELU nonlinearity against the ReLU and ELU activations and find performance improvements across all tasks .
We propose the Gaussian Error Linear Unit ( GELU ) , a high-performing neural network activation function . The GELU nonlinearity is the expected transformation of a stochastic regularizer which randomly applies the identity or zero map to a neuron 's input . The GELU nonlinearity weights inputs by their magnitude , rather than gates inputs by their sign as in ReLUs . We perform an empirical evaluation of the GELU nonlinearity against the ReLU and ELU activations and find performance improvements across all considered computer vision , natural language processing , and speech tasks .
Variations on GLU are possible , using different nonlinear ( or even linear ) functions in place of sigmoid . We test these variants in the feed-forward sublayers of the Transformer ( arXiv:1706.03762 ) sequence-to-sequence model , and find that some of them yield quality improvements over the typically-used ReLU or GELU activations .
Improving Convolutional Neural Networks Via Conservative Field Regularisation and Integration Improving MMD-GAN Training with Repulsive Loss Function Light Gated Recurrent Units for Speech Recognition On Buffon machines and numbers Adaptive Ship Course Following Control Based on Sufficiently Smooth Projection Operator Hypothesis Verification in Model-Based Object Recognition with a Gaussian Error Method ExPlanes: Exploring Planes in Triplet Data Gaussian Error Linear Units (GELUs). A Hybrid Ensemble Kalman Filter for Nonlinear Dynamics Scale Detection Based on Maximum Entropy Principle A general AR-based technique for the generation of arbitrary gamma VBR video traffic in ATM networks Robust Linear Models for Cis-eQTL Analysis An incremental trust-region method for Robust online sparse least-squares estimation Symmetrical Gaussian Error Linear Units (SGELUs) Generalization of SELU to CNN Automatic segmentation method of pelvic floor levator hiatus in ultrasound using a self-normalizing neural network Technical note: automatic segmentation method of pelvic floor levator hiatus in ultrasound using a self-normalising neural network Towards Optimizing Convolutional Neural Networks for Robotic Surgery Skill Evaluation Using Deep Learning to Predict Complex Systems: A Case Study in Wind Farm Generation Deep convolutional neural network for decoding motor imagery based brain computer interface Training Better CNNs Requires to Rethink ReLU Recognizing Traffic Signs Using a Practical Deep Neural Network Recognition Algorithm Based on Convolution Neural Network for the Mechanical Parts Comparative Study of Convolution Neural Network’s Relu and Leaky-Relu Activation Functions HTTU-Net: Hybrid Two Track U-Net for Automatic Brain Tumor Segmentation Investigation of parametric rectified linear units for noise robust speech recognition Learning ReLU Networks on Linearly Separable Data: Algorithm, Optimality, and Generalization A modified leaky ReLU scheme (MLRS) for topology optimization with multiple materials On gradient regularizers for MMD GANs In-place Activated BatchNorm for Memory-Optimized Training of DNNs StarGAN: Unified Generative Adversarial Networks for Multi-domain Image-to-Image Translation Incremental Learning in Person Re-Identification Learning to Adapt Structured Output Space for Semantic Segmentation Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs) Modeling posterior probabilities using the linear exponential family An evaluation of pupillary light response models for 2D screens and VR HMDs A simple Bayesian method for assessing the standard error of equivalent dose estimates Towards a theory of resource: an approach based on soft exponentials Strong One-Switch Utility Prediction of track purity and track accuracy in dense target environments Log-Sum-Exp Neural Networks and Posynomial Models for Convex and Log-Log-Convex Data Deep Residual Networks with Exponential Linear Unit Bridging Nonlinearities and Stochastic Regularizers with Gaussian Error Linear Units Gaussian Error Linear Units (GELUs). GLU Variants Improve Transformer
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ICLR IEEE Transactions on Emerging Topics in Computational Intelligence SODA ECCV (2) ICAC ICRA Medical Imaging: Image-Guided Procedures IJCNN ROBOT (1) INTERSPEECH NeurIPS 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition ArXiv 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition ICLR INTERSPEECH VRST VisionNet'16
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