This minimum MSE optimization is performed via the minimization of the so-called chi-square unbiased risk estimate ( CURE ) . Taking advantage of some acceleration techniques involving convolutions and parallel computation , we show that the proposed CURE-optimized NLM outperforms some state-of-the-art NLM algorithms with no increase in computation time . Convolutions are the fundamental building blocks of CNNs . The fact that their weights are spatially shared is one of the main reasons for their widespread use , but it is also a major limitation , as it makes convolutions content-agnostic . We propose a pixel-adaptive convolution ( PAC ) operation , a simple yet effective modification of standard convolutions , in which the filter weights are multiplied with a spatially varying kernel that depends on learnable , local pixel features . In this work , we explore the benefits of generalizing one step further into the hyper-complex numbers , quaternions specifically , and provide the architecture components needed to build deep quaternion networks . We develop the theoretical basis by reviewing quaternion convolutions , developing a novel quaternion weight initialization scheme , and developing novel algorithms for quaternion batch-normalization . These pieces are tested in a classification model by end-to-end training on the CIFAR −10 and CIFAR −100 data sets and a segmentation model by end-to-end training on the KITTI Road Segmentation data set . Different angles of rotation are a key features of the new filter such that horizontal , vertical , left , and right-diagonal LQS filter masks rotate pixels through angles π/2 , 5π/2 , 3π/2 , and 7π/2 , respectively . Although , the four LQS masks are combined parallel to make a single LQS mask but derived using four quaternion convolutions , one for each direction of edges , the LQS filter produces a result without the combination of results from four separate edge detectors . This methodology could be generalised to design more elaborate LQS filters to perform other geometric operations on colour image pixels . There are a number of string matching problems for which the best known algorithms rely on algebraic convolutions ( an approach pioneered by Fischer and Paterson [ FP74 ] ) . These include for instance the classical string matching with wild cards and the k-mismatches problem . Exploiting the abundant freedom of UWB signals can increase the Euclidean distance among codewords which will lead to an enhancement of the communication quality . In this paper , a coded modulation UWB system combining PPM , PAM and convolutions coding is proposed , which can significantly increase the power efficiency without degrading the data rate . The performance of this coded modulation system primarily depends on the free Euclidean distance and the number of corresponding error bits induced by the error paths . Thus , it has great potential to further increase efficiency through integrating the comb convolution to existing architectures . Experimental results demonstrate that by simply replacing standard convolutions with comb convolutions on state-of-the-art CNN architectures ( e.g. , VGGNets , Xception and SE-Net ) , we can achieve 50 % FLOPs reduction while still maintaining the accuracy . Additionally , it allows us to use common trainable layers , e.g. recurrent or convolutional operations . Specifically , we use a deep network of stacked dilated convolutions to model long range associations between any peaks within a tandem mass spectrum . We exemplify our approach by learning to detect post-translational modifications – in this case , protein phosphorylation – only based on a given mass spectrum in a fully data-driven manner . In pattern matching with character classes the goal is to find all occurrences of a pattern of length m in a text of length n , where each pattern position consists of an allowed set of characters from a finite alphabet @S. We present an FFT-based algorithm that uses a novel prime-numbers encoding scheme , which is logn/logm times faster than the fastest extant approaches , which are based on boolean convolutions . In particular , if m^|^@S^|=n^O^(^1^ ) , our algorithm runs in time O(nlogm ) , matching the complexity of the fastest techniques for wildcard matching , a special case of our problem . Our new framework is conceptually nonstandard , making no use of polynomial interpolation , nor any other expansion basis , such as typically considered in approximation theory . Our new method arises solely from the numerical manipulation of singular integrals , through an accurate quadrature for Cauchy Principal Value convolutions . The kernel is a distribution which gives rise to multi-resolution grid coefficients . Classical deep convolutional networks increase receptive field size by either gradual resolution reduction or application of hand-crafted dilated convolutions to prevent increase in the number of parameters . In this paper we propose a novel displaced aggregation unit ( DAU ) that does not require hand-crafting . Transforming a one dimensional convolution into a bidimensional one permits to increase the sequence length without increasing the word length . If we perform acyclic convolutions then we must partially overlap and add the resulting sequences in order to obtain the final sequence(polynomial ) . We overlap always the second dimension minus 1 . [ reference ] . Convolutions are applied bottom - up , so that the computations common to neighboring windows need only be done once . Note that the last layers of our architecture are fully connected linear layers . The decoder , which is stacked on top of the encoder , then learns an upscaling of these low - dimensional features via subsequent unpooling and deconvolution operations [ reference ] . Similarly , Badrinarayanan et al . [ reference ][ reference ] use convolutions instead of deconvolutions in the decoder network . In contrast , our approach preserves high - resolution information throughout the entire network by keeping a separate high - resolution processing stream . Dong adopted a deconvolution layer at the end of the network to perform upsampling . Lai proposed a Laplacian pyramid super - resolution network ( LapSRN ) that takes an LR image as input and progressively predicts the sub - band residuals with transposed convolutions in a coarse - to - fine manner . To improve the perceptual quality at a large scale factor , Ledig proposed a generative adversarial network based super - resolution ( SRGAN ) method . There are several past attempts to use convolutional encoders for neural machine translation , however , to our knowledge none of them were able to match the performance of recurrent encoders . ( Kalchbrenner and Blunsom , 2013 ) introduce a convolutional sentence encoder in which a multi - layer CNN generates a fixed sized embedding for a source sentence , or an n - gram representation followed by transposed convolutions for directly generating a per - token decoder input . The latter requires the length of the translation prior to generation and both models were evaluated by rescoring the output of an existing translation system . The resulting embeddings are concatenated into a tensor of size where is the number of inner channels in the network . subsection : Masked One - dimensional Convolutions The decoder applies masked one - dimensional convolutions to the input embedding tensor that have a masked kernel of size . The masking ensures that information from future tokens does not affect the prediction of the current token . The first layer is 3×3 convolutions . Then we use a stack of 6n layers with 3×3 convolutions on the feature maps of sizes { 32 , 16 , 8 } respectively , with 2n layers for each feature map size . The numbers of filters are { 16 , 32 , 64 } respectively . Table 1 ( d ) shows the results of our feature pyramid without the topdown pathway . With this modification , the 1×1 lateral connections followed by 3×3 convolutions are attached to the bottom - up pyramid . This architecture simulates the effect of reusing the pyramidal feature hierarchy ( Fig . 1 ( b ) ) . To perform local computation , we use modules of convolutions with ReLU non - linearities and layer normalization . A module of convolutions gets as input a tensor of shape [ sequence length , feature channels ] and returns a tensor of the same shape . Each step in our module consist of three components : a activation of the inputs , followed by a depthwise separable convolution , followed by layer normalization . Residual network consists of sequentially stacked residual blocks . In residual networks consisted of two type of blocks : basic - with two consecutive convolutions with batch normalization and ReLU preceding convolution : conv×33 - conv×33 Fig . [ reference ] bottleneck - with one convolution surrounded by dimensionality reducing and expanding convolution layers : Finally , we apply bilinear upsampling to the logits to obtain the original input crop resolution before computing the loss using an online bootstrapping strategy as described in ( setting and ) . We did not apply hybrid dilated convolutions nor added an auxiliary loss as proposed in . Training data is sampled in a uniform way ( by shuffling the database in each epoch ) and all Cityscapes experiments are run for 360 epochs using an initial learning rate of and polynomial learning rate decay , following . The decoder structure is similar to the encoder one , but with a single block per each spatial level . Each decoder level begins with upsizing : reducing the number of features by a factor of 2 ( using 1x1x1 convolutions ) and doubling the spatial dimension ( using 3D bilinear upsampling ) , followed by an addition of encoder output of the equivalent spatial level . The end of the decoder has the same spatial size as the original image , and the number of features equal to the initial input feature size , followed by 1x1x1 convolution into 3 channels and a sigmoid function . Spot noise lends itself well for the synthesis of texture over curved surfaces , and is therefore an alternative to solid texturing . The relations of spot noise with a variety of other techniques , such as radom faults , filtering , sparse convolution , and particle systems , are discussed . It appears that spot noise provides a new perspective on those techniques . To overcome this problem , additional single image is introduced and a multi-scale features fusion scheme to learn more correlations of the two different data is proposed . Furthermore , sparse convolution operation to improve feature robustness for sparse depth data is exploited . Experiments demonstrate that the approach obviously improves the performance for depth completion and outperforms all the previous published methods . We also show a specified version of DHM ( DSHM ) for efficiency , which inherits the sparse feature extraction process as in traditional decision tree with pixel-difference feature . To achieve sparse feature extraction , we propose to utilize sparse convolution operation in DSHM and show one possibility of introducing sparse convolution kernels by using local binary convolution layer . DHM can be applied to both classification and regression problems , and we validate it on standard image classification and face alignment tasks to show its advantages over past architectures . This paper designs a light convolution neural network ( CNN ) model with fewer parameters that detects surface defects and identifies their types in thin film transistor liquid crystal display ( TFT-LCD ) . We choose different sizes of small convolution kernels to extract the shallow features of the image , and introduce the sparse convolution structure to extract the multi-scale deep features . In addition , because there are few defects in actual industrial production lines , the defect sample numbers may be not sufficient for obtaining much more local features directly based on small sample learning . At last we train our models on the software named DIGITS which is provided by NVIDIA . The main contribution of this paper is to apply the convolutional neural network for the early screening of lung cancer and improve the screening accuracy by combining the AlexNet model with the sparse convolution structure . We make a series of experiments on the chest CT images using the proposed method , of which the sensitivity and specificity indicates that the method presented in this paper can effectively improve the accuracy of early screening of lung cancer and it has certain clinical significance at the same time . The success of these models in approximating nonlinear dynamical systems is tied to the effectiveness of the convolution map in accomplishing both ( a ) and ( b ) mentioned above . To assess this , we perform in-depth study of two classes of sparse convolution operators : ( i ) a pure data-driven POD-convolution that uses left singular vectors of the data snapshots - a staple of Koopman approximation methods and ( ii ) a sparse Gaussian Process ( sGP ) convolution that combines sparse sampling with a Gaussian kernel embedding an implicit feature map to an inner product reproducing kernel Hilbert space . In this paper , we demonstrate this property by explicitly introducing spatial variations . We do so by linking the sparse convolution process to the parameterization of the underlying surface . Using this approach , it is possible to provide control maps for the parameters in a natural and convenient way . However , the exhaustive computations limits the practical usage of semantic 3D perception for VR/AR applications in portable devices . In this paper , we identify that the efficiency bottleneck lies in the unorganized memory access of the sparse convolution steps , i.e. , the points are stored independently based on a predefined dictionary , which is inefficient due to the limited memory bandwidth of parallel computing devices ( GPU ) . With the insight that points are continuous as 2D surfaces in 3D space , a chunk-based sparse convolution scheme is proposed to reuse the neighboring points within each spatially organized chunk . ‘ dense ’ ’ implementations of convolutional networks are very inefficient when applied on such sparse data . We introduce a sparse convolutional operation tailored to processing sparse data that differs from prior work on sparse convolutional networks in that it operates strictly on submanifolds , rather than ‘ ‘ dilating ’ ’ the observation with every layer in the network . OctNets slightly modify the convolution operator to produce ‘ ‘ averaged ’ ’ hidden states in parts of the grid that are away from regions of interest . One of the downsides of prior sparse implementations of convolutional networks is that they ‘ In this work , we show that it is possible to successfully train convolutional networks that keep the same sparsity pattern throughout the layers of the network , without dilating the feature maps . To this end , we explore two novel convolution operators : sparse convolution ( SC ) and valid sparse convolution ( VSC ) . In our experiments with recognizing handwritten digits and 3D shapes , networks using SC and VSC achieve state - of - the - art performance whilst reducing the computation and memory requirements by . The success of very deep ResNets , ResNeXt models , and DenseNets with bottleneck connections shows that it can be useful to calculate a relatively small number of features at a time and amalgamate these features into a larger state variable , either by vector - addition or feature - vector concatenation . Unfortunately , these techniques are impractical using existing sparse convolutional network implementations . One problem is that networks with multiple paths will tend to generate different sets of active paths , which would have to be merged to reconnect the outputs . section : ( Valid ) Sparse Convolutions : SC and VSC We define a sparse convolution SC ( with input feature planes , output feature planes , a filter size of , and stride . We assume and to be odd integers , but we can allow generalization to non - square filters , e.g. , or , if we want to implement Inception - style factorised convolutions . There are several issues with the traditional workflow , e.g. , ambiguities in standards may lead to incorrect design and implementation of real-world systems ; the conformance of real-world systems to standards is difficult to check ; and bug fixing after implementation is costly . To remedy the situation , in this paper , we present a unified executable formal automobile kernel under OSEK/VDX standard by defining the operational semantics of the system services in the standard using a rewrite-based executable semantic framework called $ \mathbb {K}$. The formal kernel is unified in that it serves multiple purposes such as : 1 ) formal modeling of the OSEK/VDX standard helps detect ambiguities in the standard ; 2 ) the executable kernel is essentially a formal model of the standard , which can be used to verify the correctness of automobile applications ; and 3 ) verified applications can be used as test cases to check the conformance of a real-world automobile operating system against the OSEK/VDX standard . Using the formal kernel , we identify several ambiguities in the OSEK/VDX standard and a potential deadlock vulnerability in an industrial automobile application . For practical implementations , one can think of using a discrete family of filters , and then to interpolate from their outputs to produce the desired filtered version of the image . We propose a multirate implementation of deformable kernels , capable to further reduce the computational weight . The " basis " filters are applied to the different levels of a pyramidal decomposition . The methods rely on building a graph or hypergraph Laplacian with both the labeled and unlabeled data , which is further used to deform the training kernel matrix . The deformed kernel is then used for support vector regression ( SVR ) . The semi-supervised SVR methods are sucessfully tested in LAI estimation and ocean chlorophyll concentration prediction from remotely sensed images . The methods rely on building a graph or hypergraph Laplacian with both the available labeled and unlabeled data , which is further used to deform the training kernel matrix . The deformed kernel is then used for support vector regression ( SVR ) . Given the high computational burden involved , we present two alternative formulations based on the Nystrom method and the incomplete Cholesky factorization to achieve operational processing times . A reformative kernel algorithm , which can deal with two-class problems as well as those with more than two classes , on Fisher discriminant analysis is proposed . In the novel algorithm the supposition that in feature space discriminant vector can be approximated by some linear combination of a part of training samples , called " significant nodes " , is made . We instead learn explicitly sparse and spatially-variant kernels for this task . To this end , we propose a CNN architecture and its efficient implementation , called the deformable kernel network ( DKN ) , that outputs sparse sets of neighbors and the corresponding weights adaptively for each pixel . We also propose a fast version of DKN ( FDKN ) that runs about 17 times faster ( 0.01 seconds for a HR image of size 640 x 480 ) . It is thus natural to design other approaches to adapt the ERF directly during runtime . In this work , we instantiate one possible solution as Deformable Kernels ( DKs ) , a family of novel and generic convolutional operators for handling object deformations by directly adapting the ERF while leaving the receptive field untouched . At the heart of our method is the ability to resample the original kernel space towards recovering the deformation of objects . For microbiome data , the phylogenetic tree provides important prior information about how these bacterial species are related , and incorporating the phylogenetic tree into analysis can potentially improve the efficiency and power of the analysis . While there are methods for converting the phylogeny-based distance measures into kernels , a formal kernel function that allows flexible integration of the tree does not exist . Here we provide a three-parameter phylogeny-based kernel , which allows modeling a wide range of nonlinear relationships . The objective criterion can be proved to have a determined global minimum point . Then , we use the on-line learning algorithm to optimize the formulated kernel function . In addition , in order to get an appropriate learning rate for the algorithm to accelerate the convergence rate , we use an adaptive rate learning method to optimize the kernel function . We use legal texts as a source of knowledge to analyze and to construct the IS ontology level of an institutional domain . The objective of the ontology level is to build an informational kernel founded on stable concepts . This kernel evolves to integrate the organizational aspects not described in the legal texts . The main component is the temporal convolutional module , which simply computes a 1 - D convolution . Suppose we have a discrete input function and a discrete kernel function . The convolution between and with stride is defined as where is an offset constant . We choose star , while is chosen so that the transfer function is already very close to for . This means that our model is equivalent to an inf - NN graph with the same exponential kernel . Note that the final reconstruction error is better than star in RMS , which justifies that distances that are smaller than that are trusted . To be specific , we associate each Spectral Multiplication layer with a dilation parameter and parameterize as a combination of some modulated exponential window functions , namely Here is a set of learnable parameters , is a hyper - parameter controlling the number of learnable parameters . Large corresponds to rapidly changing multipliers with small bandwidth , thus a smooth kernel with large spatial support . On the other hand , small corresponds to slowly changing multipliers with large bandwidth , corresponding to kernels with small spatial support . It is demonstrated that this lossless filter bank method is an excellent choice for implementing many signal processing functions in real-time high rate systems . These filter bank architectures incorporate vector processing , the discrete Fourier transform-inverse discrete Fourier transform ( DFT-IDFT ) overlap-and-save convolution method , and the sub-convolution method . The parallel processing architectures presented facilitate processing for very high rate sampled systems ( multi-giga-samples per second ) with lower rate CMOS hardware with relatively low complexity ( low transistor count ) . To achieve this goal , we must generalize the basic building block of traditional CNN architectures , namely , the weighted combinations operation . To this end , we develop a tangent space combination operation which is used to define a convolution operation on manifold-valued images that we call , the Manifold-Valued Convolution ( MVC ) . We prove theoretical properties of the MVC operation , including equivariance to the action of the isometry group admitted by the manifold and characterizing when compositions of MVC layers collapse to a single layer . This paper devises a new means of filter diversification , dubbed multi-fold filter convolution ( < inline-formula > < tex-math notation="LaTeX">$\mathcal {M}$ < /tex-math></inline-formula>-FFC ) , for face recognition . On the assumption that < inline-formula > < tex-math notation="LaTeX">$\mathcal {M}$ < /tex-math></inline-formula>-FFC receives single-scale Gabor filters of varying orientations as input , these filters are self-cross convolved by < inline-formula > < tex-math notation="LaTeX">$\mathcal {M}$ < /tex-math></inline-formula>-fold to instantiate a filter offspring set . Pure 3D CNNs require a lot of memory and computing time , therefore most related approaches project ALS point clouds into two-dimensional images . Sparse Submanifold Convolutional Networks ( SSCNs ) address this issue by exploiting the sparsity often inherent in 3D data . In this work , we propose the application of SSCNs for efficient semantic segmentation of voxelized ALS point clouds in an end-to-end encoder-decoder architecture . We propose a new approach for 3D instance segmentation based on sparse convolution and point affinity prediction , which indicates the likelihood of two points belonging to the same instance . The proposed network , built upon submanifold sparse convolution [ 3 ] , processes a voxelized point cloud and predicts semantic scores for each occupied voxel as well as the affinity between neighboring voxels at different scales . A simple yet effective clustering algorithm segments points into instances based on the predicted affinity and the mesh topology . This paper introduces a novel approach for 3D semantic instance segmentation on point clouds . A 3D convolutional neural network called submanifold sparse convolutional network is used to generate semantic predictions and instance embeddings simultaneously . To obtain discriminative embeddings for each 3D instance , a structure-aware loss function is proposed which considers both the structure information and the embedding information . document : Submanifold Sparse Convolutional Networks Convolutional network are the de - facto standard for analysing spatio - temporal data such as images , videos , 3D shapes , etc . ‘ dilating ’ ’ the observation with every layer in the network . Our empirical analysis of the resulting submanifold sparse convolutional networks shows that they perform on par with state - of - the - art methods whilst requiring substantially less computation . section : Introduction The set of connections between input - output sites is simply inverted . subsection : Submanifold Convolutional Networks We use a combination of VSC convolutions , strided SC convolutions , and sparse pooling operations to build sparse versions of the popular VGG , ResNet , and DenseNet convolutional networks . The blocks we use in our networks are presented in Figure [ reference ] . We refer to our networks as submanifold convolutional networks , because they are optimised to process low - dimensional data living in a space of higher dimensionality . We use the name VGG to refer to networks that contain a number of VSC ( , , 3 , 1 ) convolutions , separated by max - pooling . We have shown that this makes it practical to train deep and efficient VGG and ResNet models . Submanifold convolutional networks are also much sparser than OctNets . OctNet stores data in oct - trees : a data structure in which the grid cube is progressively subdivided into smaller sub - cubes until the sub - cubes are either empty or contain a single active site .
This minimum MSE optimization is performed via the minimization of the so-called chi-square unbiased risk estimate ( CURE ) . Taking advantage of some acceleration techniques involving convolutions and parallel computation , we show that the proposed CURE-optimized NLM outperforms some state-of-the-art NLM algorithms with no increase in computation time .
Convolutions are the fundamental building blocks of CNNs . The fact that their weights are spatially shared is one of the main reasons for their widespread use , but it is also a major limitation , as it makes convolutions content-agnostic . We propose a pixel-adaptive convolution ( PAC ) operation , a simple yet effective modification of standard convolutions , in which the filter weights are multiplied with a spatially varying kernel that depends on learnable , local pixel features .
In this work , we explore the benefits of generalizing one step further into the hyper-complex numbers , quaternions specifically , and provide the architecture components needed to build deep quaternion networks . We develop the theoretical basis by reviewing quaternion convolutions , developing a novel quaternion weight initialization scheme , and developing novel algorithms for quaternion batch-normalization . These pieces are tested in a classification model by end-to-end training on the CIFAR −10 and CIFAR −100 data sets and a segmentation model by end-to-end training on the KITTI Road Segmentation data set .
Different angles of rotation are a key features of the new filter such that horizontal , vertical , left , and right-diagonal LQS filter masks rotate pixels through angles π/2 , 5π/2 , 3π/2 , and 7π/2 , respectively . Although , the four LQS masks are combined parallel to make a single LQS mask but derived using four quaternion convolutions , one for each direction of edges , the LQS filter produces a result without the combination of results from four separate edge detectors . This methodology could be generalised to design more elaborate LQS filters to perform other geometric operations on colour image pixels .
There are a number of string matching problems for which the best known algorithms rely on algebraic convolutions ( an approach pioneered by Fischer and Paterson [ FP74 ] ) . These include for instance the classical string matching with wild cards and the k-mismatches problem .
Exploiting the abundant freedom of UWB signals can increase the Euclidean distance among codewords which will lead to an enhancement of the communication quality . In this paper , a coded modulation UWB system combining PPM , PAM and convolutions coding is proposed , which can significantly increase the power efficiency without degrading the data rate . The performance of this coded modulation system primarily depends on the free Euclidean distance and the number of corresponding error bits induced by the error paths .
Thus , it has great potential to further increase efficiency through integrating the comb convolution to existing architectures . Experimental results demonstrate that by simply replacing standard convolutions with comb convolutions on state-of-the-art CNN architectures ( e.g. , VGGNets , Xception and SE-Net ) , we can achieve 50 % FLOPs reduction while still maintaining the accuracy .
Additionally , it allows us to use common trainable layers , e.g. recurrent or convolutional operations . Specifically , we use a deep network of stacked dilated convolutions to model long range associations between any peaks within a tandem mass spectrum . We exemplify our approach by learning to detect post-translational modifications – in this case , protein phosphorylation – only based on a given mass spectrum in a fully data-driven manner .
In pattern matching with character classes the goal is to find all occurrences of a pattern of length m in a text of length n , where each pattern position consists of an allowed set of characters from a finite alphabet @S. We present an FFT-based algorithm that uses a novel prime-numbers encoding scheme , which is logn/logm times faster than the fastest extant approaches , which are based on boolean convolutions . In particular , if m^|^@S^|=n^O^(^1^ ) , our algorithm runs in time O(nlogm ) , matching the complexity of the fastest techniques for wildcard matching , a special case of our problem .
Our new framework is conceptually nonstandard , making no use of polynomial interpolation , nor any other expansion basis , such as typically considered in approximation theory . Our new method arises solely from the numerical manipulation of singular integrals , through an accurate quadrature for Cauchy Principal Value convolutions . The kernel is a distribution which gives rise to multi-resolution grid coefficients .
Classical deep convolutional networks increase receptive field size by either gradual resolution reduction or application of hand-crafted dilated convolutions to prevent increase in the number of parameters . In this paper we propose a novel displaced aggregation unit ( DAU ) that does not require hand-crafting .
Transforming a one dimensional convolution into a bidimensional one permits to increase the sequence length without increasing the word length . If we perform acyclic convolutions then we must partially overlap and add the resulting sequences in order to obtain the final sequence(polynomial ) . We overlap always the second dimension minus 1 .
[ reference ] . Convolutions are applied bottom - up , so that the computations common to neighboring windows need only be done once . Note that the last layers of our architecture are fully connected linear layers .
The decoder , which is stacked on top of the encoder , then learns an upscaling of these low - dimensional features via subsequent unpooling and deconvolution operations [ reference ] . Similarly , Badrinarayanan et al . [ reference ][ reference ] use convolutions instead of deconvolutions in the decoder network . In contrast , our approach preserves high - resolution information throughout the entire network by keeping a separate high - resolution processing stream .
Dong adopted a deconvolution layer at the end of the network to perform upsampling . Lai proposed a Laplacian pyramid super - resolution network ( LapSRN ) that takes an LR image as input and progressively predicts the sub - band residuals with transposed convolutions in a coarse - to - fine manner . To improve the perceptual quality at a large scale factor , Ledig proposed a generative adversarial network based super - resolution ( SRGAN ) method .
There are several past attempts to use convolutional encoders for neural machine translation , however , to our knowledge none of them were able to match the performance of recurrent encoders . ( Kalchbrenner and Blunsom , 2013 ) introduce a convolutional sentence encoder in which a multi - layer CNN generates a fixed sized embedding for a source sentence , or an n - gram representation followed by transposed convolutions for directly generating a per - token decoder input . The latter requires the length of the translation prior to generation and both models were evaluated by rescoring the output of an existing translation system .
The resulting embeddings are concatenated into a tensor of size where is the number of inner channels in the network . subsection : Masked One - dimensional Convolutions The decoder applies masked one - dimensional convolutions to the input embedding tensor that have a masked kernel of size . The masking ensures that information from future tokens does not affect the prediction of the current token .
The first layer is 3×3 convolutions . Then we use a stack of 6n layers with 3×3 convolutions on the feature maps of sizes { 32 , 16 , 8 } respectively , with 2n layers for each feature map size . The numbers of filters are { 16 , 32 , 64 } respectively .
Table 1 ( d ) shows the results of our feature pyramid without the topdown pathway . With this modification , the 1×1 lateral connections followed by 3×3 convolutions are attached to the bottom - up pyramid . This architecture simulates the effect of reusing the pyramidal feature hierarchy ( Fig . 1 ( b ) ) .
To perform local computation , we use modules of convolutions with ReLU non - linearities and layer normalization . A module of convolutions gets as input a tensor of shape [ sequence length , feature channels ] and returns a tensor of the same shape . Each step in our module consist of three components : a activation of the inputs , followed by a depthwise separable convolution , followed by layer normalization .
Residual network consists of sequentially stacked residual blocks . In residual networks consisted of two type of blocks : basic - with two consecutive convolutions with batch normalization and ReLU preceding convolution : conv×33 - conv×33 Fig . [ reference ] bottleneck - with one convolution surrounded by dimensionality reducing and expanding convolution layers :
Finally , we apply bilinear upsampling to the logits to obtain the original input crop resolution before computing the loss using an online bootstrapping strategy as described in ( setting and ) . We did not apply hybrid dilated convolutions nor added an auxiliary loss as proposed in . Training data is sampled in a uniform way ( by shuffling the database in each epoch ) and all Cityscapes experiments are run for 360 epochs using an initial learning rate of and polynomial learning rate decay , following .
The decoder structure is similar to the encoder one , but with a single block per each spatial level . Each decoder level begins with upsizing : reducing the number of features by a factor of 2 ( using 1x1x1 convolutions ) and doubling the spatial dimension ( using 3D bilinear upsampling ) , followed by an addition of encoder output of the equivalent spatial level . The end of the decoder has the same spatial size as the original image , and the number of features equal to the initial input feature size , followed by 1x1x1 convolution into 3 channels and a sigmoid function .
Spot noise lends itself well for the synthesis of texture over curved surfaces , and is therefore an alternative to solid texturing . The relations of spot noise with a variety of other techniques , such as radom faults , filtering , sparse convolution , and particle systems , are discussed . It appears that spot noise provides a new perspective on those techniques .
To overcome this problem , additional single image is introduced and a multi-scale features fusion scheme to learn more correlations of the two different data is proposed . Furthermore , sparse convolution operation to improve feature robustness for sparse depth data is exploited . Experiments demonstrate that the approach obviously improves the performance for depth completion and outperforms all the previous published methods .
We also show a specified version of DHM ( DSHM ) for efficiency , which inherits the sparse feature extraction process as in traditional decision tree with pixel-difference feature . To achieve sparse feature extraction , we propose to utilize sparse convolution operation in DSHM and show one possibility of introducing sparse convolution kernels by using local binary convolution layer . DHM can be applied to both classification and regression problems , and we validate it on standard image classification and face alignment tasks to show its advantages over past architectures .
This paper designs a light convolution neural network ( CNN ) model with fewer parameters that detects surface defects and identifies their types in thin film transistor liquid crystal display ( TFT-LCD ) . We choose different sizes of small convolution kernels to extract the shallow features of the image , and introduce the sparse convolution structure to extract the multi-scale deep features . In addition , because there are few defects in actual industrial production lines , the defect sample numbers may be not sufficient for obtaining much more local features directly based on small sample learning .
At last we train our models on the software named DIGITS which is provided by NVIDIA . The main contribution of this paper is to apply the convolutional neural network for the early screening of lung cancer and improve the screening accuracy by combining the AlexNet model with the sparse convolution structure . We make a series of experiments on the chest CT images using the proposed method , of which the sensitivity and specificity indicates that the method presented in this paper can effectively improve the accuracy of early screening of lung cancer and it has certain clinical significance at the same time .
The success of these models in approximating nonlinear dynamical systems is tied to the effectiveness of the convolution map in accomplishing both ( a ) and ( b ) mentioned above . To assess this , we perform in-depth study of two classes of sparse convolution operators : ( i ) a pure data-driven POD-convolution that uses left singular vectors of the data snapshots - a staple of Koopman approximation methods and ( ii ) a sparse Gaussian Process ( sGP ) convolution that combines sparse sampling with a Gaussian kernel embedding an implicit feature map to an inner product reproducing kernel Hilbert space .
In this paper , we demonstrate this property by explicitly introducing spatial variations . We do so by linking the sparse convolution process to the parameterization of the underlying surface . Using this approach , it is possible to provide control maps for the parameters in a natural and convenient way .
However , the exhaustive computations limits the practical usage of semantic 3D perception for VR/AR applications in portable devices . In this paper , we identify that the efficiency bottleneck lies in the unorganized memory access of the sparse convolution steps , i.e. , the points are stored independently based on a predefined dictionary , which is inefficient due to the limited memory bandwidth of parallel computing devices ( GPU ) . With the insight that points are continuous as 2D surfaces in 3D space , a chunk-based sparse convolution scheme is proposed to reuse the neighboring points within each spatially organized chunk .
‘ dense ’ ’ implementations of convolutional networks are very inefficient when applied on such sparse data . We introduce a sparse convolutional operation tailored to processing sparse data that differs from prior work on sparse convolutional networks in that it operates strictly on submanifolds , rather than ‘ ‘ dilating ’ ’ the observation with every layer in the network .
OctNets slightly modify the convolution operator to produce ‘ ‘ averaged ’ ’ hidden states in parts of the grid that are away from regions of interest . One of the downsides of prior sparse implementations of convolutional networks is that they ‘
In this work , we show that it is possible to successfully train convolutional networks that keep the same sparsity pattern throughout the layers of the network , without dilating the feature maps . To this end , we explore two novel convolution operators : sparse convolution ( SC ) and valid sparse convolution ( VSC ) . In our experiments with recognizing handwritten digits and 3D shapes , networks using SC and VSC achieve state - of - the - art performance whilst reducing the computation and memory requirements by .
The success of very deep ResNets , ResNeXt models , and DenseNets with bottleneck connections shows that it can be useful to calculate a relatively small number of features at a time and amalgamate these features into a larger state variable , either by vector - addition or feature - vector concatenation . Unfortunately , these techniques are impractical using existing sparse convolutional network implementations . One problem is that networks with multiple paths will tend to generate different sets of active paths , which would have to be merged to reconnect the outputs .
section : ( Valid ) Sparse Convolutions : SC and VSC We define a sparse convolution SC ( with input feature planes , output feature planes , a filter size of , and stride . We assume and to be odd integers , but we can allow generalization to non - square filters , e.g. , or , if we want to implement Inception - style factorised convolutions .
There are several issues with the traditional workflow , e.g. , ambiguities in standards may lead to incorrect design and implementation of real-world systems ; the conformance of real-world systems to standards is difficult to check ; and bug fixing after implementation is costly . To remedy the situation , in this paper , we present a unified executable formal automobile kernel under OSEK/VDX standard by defining the operational semantics of the system services in the standard using a rewrite-based executable semantic framework called $ \mathbb {K}$. The formal kernel is unified in that it serves multiple purposes such as : 1 ) formal modeling of the OSEK/VDX standard helps detect ambiguities in the standard ; 2 ) the executable kernel is essentially a formal model of the standard , which can be used to verify the correctness of automobile applications ; and 3 ) verified applications can be used as test cases to check the conformance of a real-world automobile operating system against the OSEK/VDX standard . Using the formal kernel , we identify several ambiguities in the OSEK/VDX standard and a potential deadlock vulnerability in an industrial automobile application .
For practical implementations , one can think of using a discrete family of filters , and then to interpolate from their outputs to produce the desired filtered version of the image . We propose a multirate implementation of deformable kernels , capable to further reduce the computational weight . The " basis " filters are applied to the different levels of a pyramidal decomposition .
The methods rely on building a graph or hypergraph Laplacian with both the labeled and unlabeled data , which is further used to deform the training kernel matrix . The deformed kernel is then used for support vector regression ( SVR ) . The semi-supervised SVR methods are sucessfully tested in LAI estimation and ocean chlorophyll concentration prediction from remotely sensed images .
The methods rely on building a graph or hypergraph Laplacian with both the available labeled and unlabeled data , which is further used to deform the training kernel matrix . The deformed kernel is then used for support vector regression ( SVR ) . Given the high computational burden involved , we present two alternative formulations based on the Nystrom method and the incomplete Cholesky factorization to achieve operational processing times .
A reformative kernel algorithm , which can deal with two-class problems as well as those with more than two classes , on Fisher discriminant analysis is proposed . In the novel algorithm the supposition that in feature space discriminant vector can be approximated by some linear combination of a part of training samples , called " significant nodes " , is made .
We instead learn explicitly sparse and spatially-variant kernels for this task . To this end , we propose a CNN architecture and its efficient implementation , called the deformable kernel network ( DKN ) , that outputs sparse sets of neighbors and the corresponding weights adaptively for each pixel . We also propose a fast version of DKN ( FDKN ) that runs about 17 times faster ( 0.01 seconds for a HR image of size 640 x 480 ) .
It is thus natural to design other approaches to adapt the ERF directly during runtime . In this work , we instantiate one possible solution as Deformable Kernels ( DKs ) , a family of novel and generic convolutional operators for handling object deformations by directly adapting the ERF while leaving the receptive field untouched . At the heart of our method is the ability to resample the original kernel space towards recovering the deformation of objects .
For microbiome data , the phylogenetic tree provides important prior information about how these bacterial species are related , and incorporating the phylogenetic tree into analysis can potentially improve the efficiency and power of the analysis . While there are methods for converting the phylogeny-based distance measures into kernels , a formal kernel function that allows flexible integration of the tree does not exist . Here we provide a three-parameter phylogeny-based kernel , which allows modeling a wide range of nonlinear relationships .
The objective criterion can be proved to have a determined global minimum point . Then , we use the on-line learning algorithm to optimize the formulated kernel function . In addition , in order to get an appropriate learning rate for the algorithm to accelerate the convergence rate , we use an adaptive rate learning method to optimize the kernel function .
We use legal texts as a source of knowledge to analyze and to construct the IS ontology level of an institutional domain . The objective of the ontology level is to build an informational kernel founded on stable concepts . This kernel evolves to integrate the organizational aspects not described in the legal texts .
The main component is the temporal convolutional module , which simply computes a 1 - D convolution . Suppose we have a discrete input function and a discrete kernel function . The convolution between and with stride is defined as where is an offset constant .
We choose star , while is chosen so that the transfer function is already very close to for . This means that our model is equivalent to an inf - NN graph with the same exponential kernel . Note that the final reconstruction error is better than star in RMS , which justifies that distances that are smaller than that are trusted .
To be specific , we associate each Spectral Multiplication layer with a dilation parameter and parameterize as a combination of some modulated exponential window functions , namely Here is a set of learnable parameters , is a hyper - parameter controlling the number of learnable parameters . Large corresponds to rapidly changing multipliers with small bandwidth , thus a smooth kernel with large spatial support . On the other hand , small corresponds to slowly changing multipliers with large bandwidth , corresponding to kernels with small spatial support .
It is demonstrated that this lossless filter bank method is an excellent choice for implementing many signal processing functions in real-time high rate systems . These filter bank architectures incorporate vector processing , the discrete Fourier transform-inverse discrete Fourier transform ( DFT-IDFT ) overlap-and-save convolution method , and the sub-convolution method . The parallel processing architectures presented facilitate processing for very high rate sampled systems ( multi-giga-samples per second ) with lower rate CMOS hardware with relatively low complexity ( low transistor count ) .
To achieve this goal , we must generalize the basic building block of traditional CNN architectures , namely , the weighted combinations operation . To this end , we develop a tangent space combination operation which is used to define a convolution operation on manifold-valued images that we call , the Manifold-Valued Convolution ( MVC ) . We prove theoretical properties of the MVC operation , including equivariance to the action of the isometry group admitted by the manifold and characterizing when compositions of MVC layers collapse to a single layer .
This paper devises a new means of filter diversification , dubbed multi-fold filter convolution ( < inline-formula > < tex-math notation="LaTeX">$\mathcal {M}$ < /tex-math></inline-formula>-FFC ) , for face recognition . On the assumption that < inline-formula > < tex-math notation="LaTeX">$\mathcal {M}$ < /tex-math></inline-formula>-FFC receives single-scale Gabor filters of varying orientations as input , these filters are self-cross convolved by < inline-formula > < tex-math notation="LaTeX">$\mathcal {M}$ < /tex-math></inline-formula>-fold to instantiate a filter offspring set .
Pure 3D CNNs require a lot of memory and computing time , therefore most related approaches project ALS point clouds into two-dimensional images . Sparse Submanifold Convolutional Networks ( SSCNs ) address this issue by exploiting the sparsity often inherent in 3D data . In this work , we propose the application of SSCNs for efficient semantic segmentation of voxelized ALS point clouds in an end-to-end encoder-decoder architecture .
We propose a new approach for 3D instance segmentation based on sparse convolution and point affinity prediction , which indicates the likelihood of two points belonging to the same instance . The proposed network , built upon submanifold sparse convolution [ 3 ] , processes a voxelized point cloud and predicts semantic scores for each occupied voxel as well as the affinity between neighboring voxels at different scales . A simple yet effective clustering algorithm segments points into instances based on the predicted affinity and the mesh topology .
This paper introduces a novel approach for 3D semantic instance segmentation on point clouds . A 3D convolutional neural network called submanifold sparse convolutional network is used to generate semantic predictions and instance embeddings simultaneously . To obtain discriminative embeddings for each 3D instance , a structure-aware loss function is proposed which considers both the structure information and the embedding information .
document : Submanifold Sparse Convolutional Networks Convolutional network are the de - facto standard for analysing spatio - temporal data such as images , videos , 3D shapes , etc .
‘ dilating ’ ’ the observation with every layer in the network . Our empirical analysis of the resulting submanifold sparse convolutional networks shows that they perform on par with state - of - the - art methods whilst requiring substantially less computation . section : Introduction
The set of connections between input - output sites is simply inverted . subsection : Submanifold Convolutional Networks We use a combination of VSC convolutions , strided SC convolutions , and sparse pooling operations to build sparse versions of the popular VGG , ResNet , and DenseNet convolutional networks . The blocks we use in our networks are presented in Figure [ reference ] . We refer to our networks as submanifold convolutional networks , because they are optimised to process low - dimensional data living in a space of higher dimensionality . We use the name VGG to refer to networks that contain a number of VSC ( , , 3 , 1 ) convolutions , separated by max - pooling .
We have shown that this makes it practical to train deep and efficient VGG and ResNet models . Submanifold convolutional networks are also much sparser than OctNets . OctNet stores data in oct - trees : a data structure in which the grid cube is progressively subdivided into smaller sub - cubes until the sub - cubes are either empty or contain a single active site .
Magnitude MR image denoising via CURE-optimized non-local means Pixel-Adaptive Convolutional Neural Networks Deep Quaternion Networks Multi-directional colour edge detector using LQS convolution New Results and Open Problems Related to Non-Standard Stringology Coded Modulation in UWB Communications Comb Convolution for Efficient Convolutional Architecture AHLF: ad hoc learning of fragmentation patterns in mass spectra detects post-translationally modified peptides prior to database search Faster pattern matching with character classes using prime number encoding Singular integration towards a spectrally accurate finite difference operator Spatially-Adaptive Filter Units for Deep Neural Networks An algebraic approach to multidimensional convolution (abstract only) OverFeat: Integrated Recognition, Localization and Detection using Convolutional Networks Full-Resolution Residual Networks for Semantic Segmentation in Street Scenes Learning a Single Convolutional Super-Resolution Network for Multiple Degradations A Convolutional Encoder Model for Neural Machine Translation Neural Machine Translation in Linear Time Deep Residual Learning for Image Recognition Feature Pyramid Networks for Object Detection Depthwise Separable Convolutions for Neural Machine Translation Wide Residual Networks In-place Activated BatchNorm for Memory-Optimized Training of DNNs 3D MRI brain tumor segmentation using autoencoder regularization Spot noise texture synthesis for data visualization Multi-scale features fusion from sparse LiDAR data and single image for depth completion Deep Hierarchical Machine: a Flexible Divide-and-Conquer Architecture A Light CNN Model for Defect Detection of LCD A deep learning method for early screening of lung cancer Sparse Convolution-based Markov Models for Nonlinear Fluid Flows Sampling Gabor noise in the spatial domain Live Semantic 3D Perception for Immersive Augmented Reality Submanifold Sparse Convolutional Networks Toward a Unified Executable Formal Automobile OS Kernel and Its Applications Pyramidal implementation of deformable kernels Semi-Supervised Support Vector Biophysical Parameter Estimation Biophysical Parameter Estimation With a Semisupervised Support Vector Machine An efficient renovation on kernel Fisher discriminant analysis and face recognition experiments Deformable kernel networks for guided depth map upsampling Deformable Kernels: Adapting Effective Receptive Fields for Object Deformation Phylogeny-Based Kernels with Application to Microbiome Association Studies Adaptive on-line optimizing the Gaussian kernel for classification based on the kernel target alignment Information Systems Engineering for e-government : Strategy, Concepts and Foundations Character-level Convolutional Networks for Text Classification Matrix Completion on Graphs SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation Parallel sub-convolution filter bank architectures MVC-Net: A Convolutional Neural Network Architecture for Manifold-Valued Images With Applications Multi-Fold Gabor, PCA, and ICA Filter Convolution Descriptor for Face Recognition SUBMANIFOLD SPARSE CONVOLUTIONAL NETWORKS FOR SEMANTIC SEGMENTATION OF LARGE-SCALE ALS POINT CLOUDS MASC: Multi-scale Affinity with Sparse Convolution for 3D Instance Segmentation 3D Graph Embedding Learning with a Structure-aware Loss Function for Point Cloud Semantic Instance Segmentation Submanifold Sparse Convolutional Networks
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