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"abstract": "We present a method for registration and visualization of corresponding supine and prone virtual colonoscopy scans based on eigenfunction analysis and fold modeling. In virtual colonoscopy, CT scans are acquired with the patient in two positions, and their registration is desirable so that physicians can corroborate findings between scans. Our algorithm performs this registration efficiently through the use of Fiedler vector representation (the second eigenfunction of the Laplace-Beltrami operator). This representation is employed to first perform global registration of the two colon positions. The registration is then locally refined using the haustral folds, which are automatically segmented using the 3D level sets of the Fiedler vector. The use of Fiedler vectors and the segmented folds presents a precise way of visualizing corresponding regions across datasets and visual modalities. We present multiple methods of visualizing the results, including 2D flattened rendering and the corresponding 3D endoluminal views. The precise fold modeling is used to automatically find a suitable cut for the 2D flattening, which provides a less distorted visualization. Our approach is robust, and we demonstrate its efficiency and efficacy by showing matched views on both the 2D flattened colons and in the 3D endoluminal view. We analytically evaluate the results by measuring the distance between features on the registered colons, and we also assess our fold segmentation against 20 manually labeled datasets. We have compared our results analytically to previous methods, and have found our method to achieve superior results. We also prove the hot spots conjecture for modeling cylindrical topology using Fiedler vector representation, which allows our approach to be used for general cylindrical geometry modeling and feature extraction.",
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"content": "Over the past few decades, dimensionality reduction has been widely exploited in computer vision and pattern analysis. This paper proposes a simple but effective nonlinear dimensionality reduction algorithm, named Maximal Linear Embedding (MLE). MLE learns a parametric mapping to recover a single global low-dimensional coordinate space and yields an isometric embedding for the manifold. Inspired by geometric intuition, we introduce a reasonable definition of locally linear patch, Maximal Linear Patch (MLP), which seeks to maximize the local neighborhood in which linearity holds. The input data are first decomposed into a collection of local linear models, each depicting an MLP. These local models are then aligned into a global coordinate space, which is achieved by applying MDS to some randomly selected landmarks. The proposed alignment method, called Landmarks-based Global Alignment (LGA), can efficiently produce a closed-form solution with no risk of local optima. It just involves some small-scale eigenvalue problems, while most previous aligning techniques employ time-consuming iterative optimization. Compared with traditional methods such as ISOMAP and LLE, our MLE yields an explicit modeling of the intrinsic variation modes of the observation data. Extensive experiments on both synthetic and real data indicate the effectivity and efficiency of the proposed algorithm.",
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"surname": "Chen",
"fullName": "Xilin Chen",
"affiliation": "Chinese Academy of Sciences, Beijing",
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"givenName": "Jie",
"surname": "Chen",
"fullName": "Jie Chen",
"affiliation": "University of Oulu, Oulu",
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"givenName": "Wen",
"surname": "Gao",
"fullName": "Wen Gao",
"affiliation": "Peking University, Beijing",
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"content": "Abstract—Considerable evidence suggests that a viewer's perception of the 3D shape of a polygonally-defined object can be significantly affected (either masked or enhanced) by the presence of a surface texture pattern. However, investigations into the specific mechanisms of texture's effect on shape perception are still ongoing and the question of how to design and apply a texture pattern to a surface in order to best facilitate shape perception remains open. Recently, we have suggested that, for anisotropic texture patterns, the accuracy of shape judgments may be significantly affected by the orientation of the surface texture pattern anisotropy with respect to the principal directions of curvature over the surface. However, it has been difficult, until this time, to conduct controlled studies specifically investigating the effect of texture orientation on shape perception because there has been no simple and reliable method for texturing an arbitrary doubly curved surface with a specified input pattern such that the dominant orientation of the pattern everywhere follows a predefined directional vector field over the surface, while seams and projective distortion of the pattern are avoided. In this paper, we present a straightforward and highly efficient method for achieving such a texture and describe how it can potentially be used to enhance shape representation. Specifically, we describe a novel, efficient, automatic algorithm for seamlessly synthesizing, from a sample 2D pattern, a high resolution fitted surface texture in which the dominant orientation of the pattern locally follows a specified vector field over the surface at a per-pixel level and in which seams, projective distortion, and repetition artifacts in the texture pattern are nearly completely avoided. We demonstrate the robustness of our method with a variety of texture swatches applied to standard graphics data sets and we explain how our method can be used to facilitate research in the perception of shape from texture.",
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"normalizedAbstract": "Abstract—Considerable evidence suggests that a viewer's perception of the 3D shape of a polygonally-defined object can be significantly affected (either masked or enhanced) by the presence of a surface texture pattern. However, investigations into the specific mechanisms of texture's effect on shape perception are still ongoing and the question of how to design and apply a texture pattern to a surface in order to best facilitate shape perception remains open. Recently, we have suggested that, for anisotropic texture patterns, the accuracy of shape judgments may be significantly affected by the orientation of the surface texture pattern anisotropy with respect to the principal directions of curvature over the surface. However, it has been difficult, until this time, to conduct controlled studies specifically investigating the effect of texture orientation on shape perception because there has been no simple and reliable method for texturing an arbitrary doubly curved surface with a specified input pattern such that the dominant orientation of the pattern everywhere follows a predefined directional vector field over the surface, while seams and projective distortion of the pattern are avoided. In this paper, we present a straightforward and highly efficient method for achieving such a texture and describe how it can potentially be used to enhance shape representation. Specifically, we describe a novel, efficient, automatic algorithm for seamlessly synthesizing, from a sample 2D pattern, a high resolution fitted surface texture in which the dominant orientation of the pattern locally follows a specified vector field over the surface at a per-pixel level and in which seams, projective distortion, and repetition artifacts in the texture pattern are nearly completely avoided. We demonstrate the robustness of our method with a variety of texture swatches applied to standard graphics data sets and we explain how our method can be used to facilitate research in the perception of shape from texture.",
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"abstract": "We propose a new method for recovering the 3D shape of a polyhedral object from its single 2D image using the shading information contained in the image and the prior information on the object. In a strict sense, we cannot recover the shape of a polyhedron from an incorrect line drawing, even if it is practically almost correct. In order to overcome this problem, we propose a flexible face positioning method that can permit inconsistencies in the recovered shape that arise from vertex-position errors contained in incorrect line drawings. Also, we propose to use prior information about the horizontality and verticality of special faces and the convex and concave properties of the edges in order to attain good solutions and present a method of formulating such prior information as physical constraints. The shape-from-shading method is formulated as a minimization problem of a nonlinear cost function with the nonlinear constraints and its solution is searched by a global optimization algorithm. In the experiments with a synthetic image and three kinds of real images, shapes that are similar to those of the actual objects were recovered in all cases. As a result, the proposed method has proven to be effective in the shape recovery of simple-shape polyhedral objects.",
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"content": "We propose a new method for recovering the 3D shape of a polyhedral object from its single 2D image using the shading information contained in the image and the prior information on the object. In a strict sense, we cannot recover the shape of a polyhedron from an incorrect line drawing, even if it is practically almost correct. In order to overcome this problem, we propose a flexible face positioning method that can permit inconsistencies in the recovered shape that arise from vertex-position errors contained in incorrect line drawings. Also, we propose to use prior information about the horizontality and verticality of special faces and the convex and concave properties of the edges in order to attain good solutions and present a method of formulating such prior information as physical constraints. The shape-from-shading method is formulated as a minimization problem of a nonlinear cost function with the nonlinear constraints and its solution is searched by a global optimization algorithm. In the experiments with a synthetic image and three kinds of real images, shapes that are similar to those of the actual objects were recovered in all cases. As a result, the proposed method has proven to be effective in the shape recovery of simple-shape polyhedral objects.",
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"abstractUrl": "/journal/tp/1999/12/i1250/13rRUwwsltF",
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"abstract": "Abstract—We introduce adaptive scale filtering, a general method for deriving shape from texture under perspective projection without recourse to prior segmentation of the image into geometric texture elements (texels), and without thresholding of filtered images.If texels on a given surface can be identified in an image then the orientation of that surface can be obtained [11]. However, there is no general characterization of texels for arbitrary textures. Furthermore, even if the size and shape of texels on the surface is invariant with regard to position, perspective projection ensures that the size and shape of the corresponding image texels vary by orders of magnitude.Commencing with an initial set F0 of identical image filters, adaptive scale filtering iteratively derives a set FN which contains a unique filter for each image position. Each element of FN is tuned to the three-dimensional structure of the surface; that is, all image filters in FN back-project to an identical shape and size on the surface. Thus image texels of various sizes, but associated with a single spatial scale on the surface, can be identified in different parts of the image. When combined with conventional shape from texture methods, edges derived using FN provide accurate estimates of surface orientation. Results for planar surfaces are presented.",
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"abstract": "For some applications, triangulated irregular networks are superior to rectangular grids in modeling complex surfaces. The radial sweep algorithm is an improvement of TIN techniques.",
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"abstract": "Abstract—This paper extends Lounsbery's multiresolution analysis wavelet-based theory for triangular 3D meshes, which can only be applied to regularly subdivided meshes and thus involves a remeshing of the existing 3D data. Based on a new irregular subdivision scheme, the proposed algorithm can be applied directly to irregular meshes, which can be very interesting when one wants to keep the connectivity and geometry of the processed mesh completely unchanged. This is very convenient in CAD (Computer-Assisted Design), when the mesh has attributes such as texture and color information, or when the 3D mesh is used for simulations, and where a different connectivity could lead to simulation errors. The algorithm faces an inverse problem for which a solution is proposed. For each level of resolution, the simplification is processed in order to keep the mesh as regular as possible. In addition, a geometric criterion is used to keep the geometry of the approximations as close as possible to the original mesh. Several examples on various reference meshes are shown to prove the efficiency of our proposal.",
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"abstract": "Most investigations into near-memory hardware accelerators for deep neural networks have primarily focused on inference, while the potential of accelerating training has received relatively little attention so far. Based on an in-depth analysis of the key computational patterns in state-of-the-art gradient-based training methods, we propose an efficient near-memory acceleration engine called NTX that can be used to train state-of-the-art deep convolutional neural networks at scale. Our main contributions are: (i) a loose coupling of RISC-V cores and NTX co-processors reducing offloading overhead by <inline-formula><tex-math notation=\"LaTeX\">Z_$7\\times$_Z</tex-math></inline-formula> over previously published results; (ii) an optimized IEEE 754 compliant data path for fast high-precision convolutions and gradient propagation; (iii) evaluation of near-memory computing with NTX embedded into residual area on the Logic Base die of a Hybrid Memory Cube; and (iv) a scaling analysis to meshes of HMCs in a data center scenario. We demonstrate a <inline-formula><tex-math notation=\"LaTeX\">Z_$2.7\\times$_Z</tex-math></inline-formula> energy efficiency improvement of NTX over contemporary GPUs at <inline-formula><tex-math notation=\"LaTeX\">Z_$4.4\\times$_Z</tex-math></inline-formula> less silicon area, and a compute performance of 1.2 Tflop/s for training large state-of-the-art networks with full floating-point precision. At the data center scale, a mesh of NTX achieves above 95 percent parallel and energy efficiency, while providing <inline-formula><tex-math notation=\"LaTeX\">Z_$2.1\\times$_Z</tex-math></inline-formula> energy savings or <inline-formula><tex-math notation=\"LaTeX\">Z_$3.1\\times$_Z</tex-math></inline-formula> performance improvement over a GPU-based system.",
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"content": "Most investigations into near-memory hardware accelerators for deep neural networks have primarily focused on inference, while the potential of accelerating training has received relatively little attention so far. Based on an in-depth analysis of the key computational patterns in state-of-the-art gradient-based training methods, we propose an efficient near-memory acceleration engine called NTX that can be used to train state-of-the-art deep convolutional neural networks at scale. Our main contributions are: (i) a loose coupling of RISC-V cores and NTX co-processors reducing offloading overhead by <inline-formula><tex-math notation=\"LaTeX\">$7\\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>7</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"schuiki-ieq1-2876312.gif\"/></alternatives></inline-formula> over previously published results; (ii) an optimized IEEE 754 compliant data path for fast high-precision convolutions and gradient propagation; (iii) evaluation of near-memory computing with NTX embedded into residual area on the Logic Base die of a Hybrid Memory Cube; and (iv) a scaling analysis to meshes of HMCs in a data center scenario. We demonstrate a <inline-formula><tex-math notation=\"LaTeX\">$2.7\\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>2</mml:mn><mml:mo>.</mml:mo><mml:mn>7</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"schuiki-ieq2-2876312.gif\"/></alternatives></inline-formula> energy efficiency improvement of NTX over contemporary GPUs at <inline-formula><tex-math notation=\"LaTeX\">$4.4\\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>4</mml:mn><mml:mo>.</mml:mo><mml:mn>4</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"schuiki-ieq3-2876312.gif\"/></alternatives></inline-formula> less silicon area, and a compute performance of 1.2 Tflop/s for training large state-of-the-art networks with full floating-point precision. At the data center scale, a mesh of NTX achieves above 95 percent parallel and energy efficiency, while providing <inline-formula><tex-math notation=\"LaTeX\">$2.1\\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>2</mml:mn><mml:mo>.</mml:mo><mml:mn>1</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"schuiki-ieq4-2876312.gif\"/></alternatives></inline-formula> energy savings or <inline-formula><tex-math notation=\"LaTeX\">$3.1\\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>3</mml:mn><mml:mo>.</mml:mo><mml:mn>1</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"schuiki-ieq5-2876312.gif\"/></alternatives></inline-formula> performance improvement over a GPU-based system.",
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"abstract": "Extracting information from large-scale high-dimensional data is a fundamentally important task in high performance computing, where the hierarchical Tucker (HT) tensor learning approach (learning a tensor-tree structure) has been widely used in many applications. However, HT tensor learning algorithms are compute-intensive due to the “<italic>curse of dimensionality</italic>,” i.e., the time complexity grows exponentially with the order of the data tensor. The computation of HT tensor learning algorithms boils down to tensor primitives, which are amenable to computing on GPU tensor cores. Existing work does not support HT tensor learning using GPU tensor cores. There are three main challenges to address: 1) to accelerate tensor learning primitives using GPU tensor cores; 2) to implement the tensor learning algorithms using GPU tensor cores and multiple GPUs; 3) to support large-scale data tensors exceeding the GPU memory capacity. In this paper, we present efficient HT tensor learning primitives using GPU tensor cores and demonstrate three applications. First, we utilize GPU tensor cores to optimize HT tensor learning primitives, including tensor contractions, tensor matricizations and tensor singular value decomposition (SVD). We employ the optimized primitives to optimize HT tensor decomposition algorithms for Big Data analysis. Second, we propose a novel HT tensor layer for deep neural networks, whose training process only involves a forward pass without back propagation. The forward pass consists of tensor operations, thus further exploiting the computing power of GPU tensor cores. Third, we apply the optimized primitives to develop a tensor-tree structured quantum machine learning algorithm <italic>tree-tensor network (TTN)</italic>. Compared with TensorLy and TensorNetwork on NVIDIA A100 GPUs, our third-order HT tensor decomposition algorithm achieves up to <inline-formula><tex-math notation=\"LaTeX\">Z_$8.92 \\times$_Z</tex-math></inline-formula> and <inline-formula><tex-math notation=\"LaTeX\">Z_$6.42 \\times$_Z</tex-math></inline-formula> speedups, respectively, and our high-order case achieves up to <inline-formula><tex-math notation=\"LaTeX\">Z_$32.67 \\times$_Z</tex-math></inline-formula> and <inline-formula><tex-math notation=\"LaTeX\">Z_$23.97 \\times$_Z</tex-math></inline-formula> speedups, respectively. Our HT tensor layer for a fully connected neural network achieves <inline-formula><tex-math notation=\"LaTeX\">Z_$49.2 \\times$_Z</tex-math></inline-formula> compression at the cost of 0.5% drops in accuracy and <inline-formula><tex-math notation=\"LaTeX\">Z_$1.42 \\times$_Z</tex-math></inline-formula> speedup compared with the implementation on CUDA cores; for the AlexNet, our HT tensor layer achieves <inline-formula><tex-math notation=\"LaTeX\">Z_$9.45 \\times$_Z</tex-math></inline-formula> compression at the cost of 0.8% drops in accuracy and <inline-formula><tex-math notation=\"LaTeX\">Z_$1.87 \\times$_Z</tex-math></inline-formula> speedup compared with the implementation on CUDA cores. Our TTN algorithm achieves up to <inline-formula><tex-math notation=\"LaTeX\">Z_$11.17\\times$_Z</tex-math></inline-formula> speedup compared with TensorNetwork, indicating the potential of optimized tensor learning primitives for the classical simulation of quantum machine learning algorithms.",
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"content": "Extracting information from large-scale high-dimensional data is a fundamentally important task in high performance computing, where the hierarchical Tucker (HT) tensor learning approach (learning a tensor-tree structure) has been widely used in many applications. However, HT tensor learning algorithms are compute-intensive due to the “<italic>curse of dimensionality</italic>,” i.e., the time complexity grows exponentially with the order of the data tensor. The computation of HT tensor learning algorithms boils down to tensor primitives, which are amenable to computing on GPU tensor cores. Existing work does not support HT tensor learning using GPU tensor cores. There are three main challenges to address: 1) to accelerate tensor learning primitives using GPU tensor cores; 2) to implement the tensor learning algorithms using GPU tensor cores and multiple GPUs; 3) to support large-scale data tensors exceeding the GPU memory capacity. In this paper, we present efficient HT tensor learning primitives using GPU tensor cores and demonstrate three applications. First, we utilize GPU tensor cores to optimize HT tensor learning primitives, including tensor contractions, tensor matricizations and tensor singular value decomposition (SVD). We employ the optimized primitives to optimize HT tensor decomposition algorithms for Big Data analysis. Second, we propose a novel HT tensor layer for deep neural networks, whose training process only involves a forward pass without back propagation. The forward pass consists of tensor operations, thus further exploiting the computing power of GPU tensor cores. Third, we apply the optimized primitives to develop a tensor-tree structured quantum machine learning algorithm <italic>tree-tensor network (TTN)</italic>. Compared with TensorLy and TensorNetwork on NVIDIA A100 GPUs, our third-order HT tensor decomposition algorithm achieves up to <inline-formula><tex-math notation=\"LaTeX\">$8.92 \\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>8</mml:mn><mml:mo>.</mml:mo><mml:mn>92</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"liu-ieq1-3172895.gif\"/></alternatives></inline-formula> and <inline-formula><tex-math notation=\"LaTeX\">$6.42 \\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>6</mml:mn><mml:mo>.</mml:mo><mml:mn>42</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"liu-ieq2-3172895.gif\"/></alternatives></inline-formula> speedups, respectively, and our high-order case achieves up to <inline-formula><tex-math notation=\"LaTeX\">$32.67 \\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>32</mml:mn><mml:mo>.</mml:mo><mml:mn>67</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"liu-ieq3-3172895.gif\"/></alternatives></inline-formula> and <inline-formula><tex-math notation=\"LaTeX\">$23.97 \\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>23</mml:mn><mml:mo>.</mml:mo><mml:mn>97</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"liu-ieq4-3172895.gif\"/></alternatives></inline-formula> speedups, respectively. Our HT tensor layer for a fully connected neural network achieves <inline-formula><tex-math notation=\"LaTeX\">$49.2 \\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>49</mml:mn><mml:mo>.</mml:mo><mml:mn>2</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"liu-ieq5-3172895.gif\"/></alternatives></inline-formula> compression at the cost of 0.5% drops in accuracy and <inline-formula><tex-math notation=\"LaTeX\">$1.42 \\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>1</mml:mn><mml:mo>.</mml:mo><mml:mn>42</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"liu-ieq6-3172895.gif\"/></alternatives></inline-formula> speedup compared with the implementation on CUDA cores; for the AlexNet, our HT tensor layer achieves <inline-formula><tex-math notation=\"LaTeX\">$9.45 \\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>9</mml:mn><mml:mo>.</mml:mo><mml:mn>45</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"liu-ieq7-3172895.gif\"/></alternatives></inline-formula> compression at the cost of 0.8% drops in accuracy and <inline-formula><tex-math notation=\"LaTeX\">$1.87 \\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>1</mml:mn><mml:mo>.</mml:mo><mml:mn>87</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"liu-ieq8-3172895.gif\"/></alternatives></inline-formula> speedup compared with the implementation on CUDA cores. Our TTN algorithm achieves up to <inline-formula><tex-math notation=\"LaTeX\">$11.17\\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>11</mml:mn><mml:mo>.</mml:mo><mml:mn>17</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"liu-ieq9-3172895.gif\"/></alternatives></inline-formula> speedup compared with TensorNetwork, indicating the potential of optimized tensor learning primitives for the classical simulation of quantum machine learning algorithms.",
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"normalizedAbstract": "Extracting information from large-scale high-dimensional data is a fundamentally important task in high performance computing, where the hierarchical Tucker (HT) tensor learning approach (learning a tensor-tree structure) has been widely used in many applications. However, HT tensor learning algorithms are compute-intensive due to the “curse of dimensionality,” i.e., the time complexity grows exponentially with the order of the data tensor. The computation of HT tensor learning algorithms boils down to tensor primitives, which are amenable to computing on GPU tensor cores. Existing work does not support HT tensor learning using GPU tensor cores. There are three main challenges to address: 1) to accelerate tensor learning primitives using GPU tensor cores; 2) to implement the tensor learning algorithms using GPU tensor cores and multiple GPUs; 3) to support large-scale data tensors exceeding the GPU memory capacity. In this paper, we present efficient HT tensor learning primitives using GPU tensor cores and demonstrate three applications. First, we utilize GPU tensor cores to optimize HT tensor learning primitives, including tensor contractions, tensor matricizations and tensor singular value decomposition (SVD). We employ the optimized primitives to optimize HT tensor decomposition algorithms for Big Data analysis. Second, we propose a novel HT tensor layer for deep neural networks, whose training process only involves a forward pass without back propagation. The forward pass consists of tensor operations, thus further exploiting the computing power of GPU tensor cores. Third, we apply the optimized primitives to develop a tensor-tree structured quantum machine learning algorithm tree-tensor network (TTN). Compared with TensorLy and TensorNetwork on NVIDIA A100 GPUs, our third-order HT tensor decomposition algorithm achieves up to - and - speedups, respectively, and our high-order case achieves up to - and - speedups, respectively. Our HT tensor layer for a fully connected neural network achieves - compression at the cost of 0.5% drops in accuracy and - speedup compared with the implementation on CUDA cores; for the AlexNet, our HT tensor layer achieves - compression at the cost of 0.8% drops in accuracy and - speedup compared with the implementation on CUDA cores. Our TTN algorithm achieves up to - speedup compared with TensorNetwork, indicating the potential of optimized tensor learning primitives for the classical simulation of quantum machine learning algorithms.",
"title": "High Performance Hierarchical Tucker Tensor Learning Using GPU Tensor Cores",
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"abstract": "Long short-term memory (LSTM) is a type of powerful deep neural network that has been widely used in many sequence analysis and modeling applications. However, the large model size problem of LSTM networks make their practical deployment still very challenging, especially for the video recognition tasks that require high-dimensional input data. Aiming to overcome this limitation and fully unlock the potentials of LSTM models, in this paper we propose to perform algorithm and hardware co-design towards high-performance energy-efficient LSTM networks. At algorithm level, we propose to develop <italic>fully decomposed hierarchical Tucker (FDHT)</italic> structure-based LSTM, namely FDHT-LSTM, which enjoys ultra-low model complexity while still achieving high accuracy. In order to fully reap such attractive algorithmic benefit, we further develop the corresponding customized hardware architecture to support the efficient execution of the proposed FDHT-LSTM model. With the delicate design of memory access scheme, the complicated matrix transformation can be efficiently supported by the underlying hardware without any access conflict in an on-the-fly way. Our evaluation results show that both the proposed ultra-compact FDHT-LSTM models and the corresponding hardware accelerator achieve very high performance. Compared with the state-of-the-art compressed LSTM models, FDHT-LSTM enjoys both order-of-magnitude reduction (more than <inline-formula><tex-math notation=\"LaTeX\">Z_$1000 \\times$_Z</tex-math></inline-formula>) in model size and significant accuracy improvement (0.6% to 12.7%) across different video recognition datasets. Meanwhile, compared with the state-of-the-art tensor decomposed model-oriented hardware TIE, our proposed FDHT-LSTM architecture achieve <inline-formula><tex-math notation=\"LaTeX\">Z_$2.5\\times$_Z</tex-math></inline-formula>, <inline-formula><tex-math notation=\"LaTeX\">Z_$1.46\\times$_Z</tex-math></inline-formula> and <inline-formula><tex-math notation=\"LaTeX\">Z_$2.41\\times$_Z</tex-math></inline-formula> increase in throughput, area efficiency and energy efficiency, respectively on LSTM-Youtube workload. For LSTM-UCF workload, our proposed design also outperforms TIE with <inline-formula><tex-math notation=\"LaTeX\">Z_$1.9\\times$_Z</tex-math></inline-formula> higher throughput, <inline-formula><tex-math notation=\"LaTeX\">Z_$1.83\\times$_Z</tex-math></inline-formula> higher energy efficiency and comparable area efficiency.",
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"abstract": "Low-rank tensor recovery (LRTR) is a natural extension of low-rank matrix recovery (LRMR) to high-dimensional arrays, which aims to reconstruct an underlying tensor <inline-formula><tex-math notation=\"LaTeX\">Z_$\\boldsymbol{\\mathcal {X}}$_Z</tex-math></inline-formula> from incomplete linear measurements <inline-formula><tex-math notation=\"LaTeX\">Z_$\\mathfrak {M}(\\boldsymbol{\\mathcal {X}})$_Z</tex-math></inline-formula>. However, LRTR ignores the error caused by quantization, limiting its application when the quantization is low-level. In this work, we take into account the impact of extreme quantization and suppose the quantizer degrades into a comparator that only acquires the signs of <inline-formula><tex-math notation=\"LaTeX\">Z_$\\mathfrak {M}(\\boldsymbol{\\mathcal {X}})$_Z</tex-math></inline-formula>. We still hope to recover <inline-formula><tex-math notation=\"LaTeX\">Z_$\\boldsymbol{\\mathcal {X}}$_Z</tex-math></inline-formula> from these binary measurements. Under the tensor Singular Value Decomposition (t-SVD) framework, two recovery methods are proposed—the first is a tensor hard singular tube thresholding method; the second is a constrained tensor nuclear norm minimization method. These methods can recover a real <inline-formula><tex-math notation=\"LaTeX\">Z_$n_1\\times n_2\\times n_3$_Z</tex-math></inline-formula> tensor <inline-formula><tex-math notation=\"LaTeX\">Z_$\\boldsymbol{\\mathcal {X}}$_Z</tex-math></inline-formula> with tubal rank <inline-formula><tex-math notation=\"LaTeX\">Z_$r$_Z</tex-math></inline-formula> from <inline-formula><tex-math notation=\"LaTeX\">Z_$m$_Z</tex-math></inline-formula> random Gaussian binary measurements with errors decaying at a polynomial speed of the oversampling factor <inline-formula><tex-math notation=\"LaTeX\">Z_$\\lambda :=m/((n_1+n_2)n_3r)$_Z</tex-math></inline-formula>. To improve the convergence rate, we develop a new quantization scheme under which the convergence rate can be accelerated to an exponential function of <inline-formula><tex-math notation=\"LaTeX\">Z_$\\lambda$_Z</tex-math></inline-formula>. Numerical experiments verify our results, and the applications to real-world data demonstrate the promising performance of the proposed methods.",
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"content": "Low-rank tensor recovery (LRTR) is a natural extension of low-rank matrix recovery (LRMR) to high-dimensional arrays, which aims to reconstruct an underlying tensor <inline-formula><tex-math notation=\"LaTeX\">$\\boldsymbol{\\mathcal {X}}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"script\">X</mml:mi></mml:math><inline-graphic xlink:href=\"wang-ieq1-3063527.gif\"/></alternatives></inline-formula> from incomplete linear measurements <inline-formula><tex-math notation=\"LaTeX\">$\\mathfrak {M}(\\boldsymbol{\\mathcal {X}})$</tex-math><alternatives><mml:math><mml:mrow><mml:mi mathvariant=\"fraktur\">M</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant=\"script\">X</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"wang-ieq2-3063527.gif\"/></alternatives></inline-formula>. However, LRTR ignores the error caused by quantization, limiting its application when the quantization is low-level. In this work, we take into account the impact of extreme quantization and suppose the quantizer degrades into a comparator that only acquires the signs of <inline-formula><tex-math notation=\"LaTeX\">$\\mathfrak {M}(\\boldsymbol{\\mathcal {X}})$</tex-math><alternatives><mml:math><mml:mrow><mml:mi mathvariant=\"fraktur\">M</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant=\"script\">X</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"wang-ieq3-3063527.gif\"/></alternatives></inline-formula>. We still hope to recover <inline-formula><tex-math notation=\"LaTeX\">$\\boldsymbol{\\mathcal {X}}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"script\">X</mml:mi></mml:math><inline-graphic xlink:href=\"wang-ieq4-3063527.gif\"/></alternatives></inline-formula> from these binary measurements. Under the tensor Singular Value Decomposition (t-SVD) framework, two recovery methods are proposed—the first is a tensor hard singular tube thresholding method; the second is a constrained tensor nuclear norm minimization method. These methods can recover a real <inline-formula><tex-math notation=\"LaTeX\">$n_1\\times n_2\\times n_3$</tex-math><alternatives><mml:math><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\"wang-ieq5-3063527.gif\"/></alternatives></inline-formula> tensor <inline-formula><tex-math notation=\"LaTeX\">$\\boldsymbol{\\mathcal {X}}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"script\">X</mml:mi></mml:math><inline-graphic xlink:href=\"wang-ieq6-3063527.gif\"/></alternatives></inline-formula> with tubal rank <inline-formula><tex-math notation=\"LaTeX\">$r$</tex-math><alternatives><mml:math><mml:mi>r</mml:mi></mml:math><inline-graphic xlink:href=\"wang-ieq7-3063527.gif\"/></alternatives></inline-formula> from <inline-formula><tex-math notation=\"LaTeX\">$m$</tex-math><alternatives><mml:math><mml:mi>m</mml:mi></mml:math><inline-graphic xlink:href=\"wang-ieq8-3063527.gif\"/></alternatives></inline-formula> random Gaussian binary measurements with errors decaying at a polynomial speed of the oversampling factor <inline-formula><tex-math notation=\"LaTeX\">$\\lambda :=m/((n_1+n_2)n_3r)$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>λ</mml:mi><mml:mo>:</mml:mo><mml:mo>=</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"wang-ieq9-3063527.gif\"/></alternatives></inline-formula>. To improve the convergence rate, we develop a new quantization scheme under which the convergence rate can be accelerated to an exponential function of <inline-formula><tex-math notation=\"LaTeX\">$\\lambda$</tex-math><alternatives><mml:math><mml:mi>λ</mml:mi></mml:math><inline-graphic xlink:href=\"wang-ieq10-3063527.gif\"/></alternatives></inline-formula>. Numerical experiments verify our results, and the applications to real-world data demonstrate the promising performance of the proposed methods.",
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"normalizedAbstract": "Low-rank tensor recovery (LRTR) is a natural extension of low-rank matrix recovery (LRMR) to high-dimensional arrays, which aims to reconstruct an underlying tensor - from incomplete linear measurements -. However, LRTR ignores the error caused by quantization, limiting its application when the quantization is low-level. In this work, we take into account the impact of extreme quantization and suppose the quantizer degrades into a comparator that only acquires the signs of -. We still hope to recover - from these binary measurements. Under the tensor Singular Value Decomposition (t-SVD) framework, two recovery methods are proposed—the first is a tensor hard singular tube thresholding method; the second is a constrained tensor nuclear norm minimization method. These methods can recover a real - tensor - with tubal rank - from - random Gaussian binary measurements with errors decaying at a polynomial speed of the oversampling factor -. To improve the convergence rate, we develop a new quantization scheme under which the convergence rate can be accelerated to an exponential function of -. Numerical experiments verify our results, and the applications to real-world data demonstrate the promising performance of the proposed methods.",
"title": "Robust Low-Tubal-Rank Tensor Recovery From Binary Measurements",
"normalizedTitle": "Robust Low-Tubal-Rank Tensor Recovery From Binary Measurements",
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"keywords": [
"Gaussian Processes",
"Matrix Algebra",
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"authors": [
{
"givenName": "Jingyao",
"surname": "Hou",
"fullName": "Jingyao Hou",
"affiliation": "School of Mathematics and Statistics, Southwest University, Chongqing, China",
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"surname": "Zhang",
"fullName": "Feng Zhang",
"affiliation": "School of Mathematics and Statistics, Southwest University, Chongqing, China",
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{
"givenName": "Haiquan",
"surname": "Qiu",
"fullName": "Haiquan Qiu",
"affiliation": "School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi, China",
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"givenName": "Jianjun",
"surname": "Wang",
"fullName": "Jianjun Wang",
"affiliation": "School of Mathematics and Statistics, Southwest University, Chongqing, China",
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{
"givenName": "Yao",
"surname": "Wang",
"fullName": "Yao Wang",
"affiliation": "Center for Intelligent Decision-Making and Machine Learning, School of Management, Xi'an Jiaotong University, Xi'an, Shaanxi, China",
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"givenName": "Deyu",
"surname": "Meng",
"fullName": "Deyu Meng",
"affiliation": "Faculty of Information Technology, Macau University of Science and Technology, Taipa, Macau, China",
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