In recent years, along with the overwhelming advances in the field of neural information processing, quantum information processing (QIP) has shown significant progress in solving problems that are intractable on classical computers. Quantum machine learning (QML) explores the ways in which these fields can learn from one another. We propose quantum walk neural networks (QWNN), a new graph neural network architecture based on quantum random walks, the quantum parallel to classical random walks. A QWNN learns a quantum walk on a graph to construct a diffusion operator which can be applied to a signal on a graph. We demonstrate the use of the network for prediction tasks for graph structured signals.
Along with the spectral approaches described above, a number of spatial approaches were proposed that relied on random walks to extract and learn information from the graph. We detail two of them here for comparison. The first approach by Atwood and Towsley @cite_0 , is a spatial convolutional method that performs random walks on the graph and combines information from spatially close neighbors. Their approach, Diffusion Convolution Neural Networks (DCNN) use powers of the transition matrix @math to diffuse information across the graph, where @math is the adjacency matrix, and @math is the diagonal degree matrix such that @math . The @math power of the transition matrix, @math , diffuses information from each node to every node exactly @math hops away from it. The output @math of the DCNN is a weighted combination of the diffused features from across the graph, given by [ Y =h( W P ^* X ), ] where @math is the stacked tensor of powers of transition matrices, the operator @math represents element-wise multiplication, @math are the learned weights of the diffusion-convolutional layer, and @math is an activation function (i.e., reLU).
@cite_0
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We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from graph-structured data and used as an effective basis for node classification. DCNNs have several attractive qualities, including a latent representation for graphical data that is invariant under isomorphism, as well as polynomial-time prediction and learning that can be represented as tensor operations and efficiently implemented on a GPU. Through several experiments with real structured datasets, we demonstrate that DCNNs are able to outperform probabilistic relational models and kernel-on-graph methods at relational node classification tasks. A number of recent studies have shown that a Deep Convolutional Neural Network (DCNN) pretrained on a large dataset can be adopted as a universal image descriptor, and that doing so leads to impressive performance at a range of image classification tasks. Most of these studies, if not all, adopt activations of the fully-connected layer of a DCNN as the image or region representation and it is believed that convolutional layer activations are less discriminative. This paper, however, advocates that if used appropriately, convolutional layer activations constitute a powerful image representation. This is achieved by adopting a new technique proposed in this paper called cross-convolutional-layer pooling. More specifically, it extracts subarrays of feature maps of one convolutional layer as local features, and pools the extracted features with the guidance of the feature maps of the successive convolutional layer. Compared with existing methods that apply DCNNs in the similar local feature setting, the proposed method avoids the input image style mismatching issue which is usually encountered when applying fully connected layer activations to describe local regions. Also, the proposed method is easier to implement since it is codebook free and does not have any tuning parameters. By applying our method to four popular visual classification tasks, it is demonstrated that the proposed method can achieve comparable or in some cases significantly better performance than existing fully-connected layer based image representations. Abstract Visual tracking algorithms based on structured output support vector machine (SOSVM) have demonstrated excellent performance. However, sampling methods and optimization strategies of SOSVM undesirably increase the computational overloads, which hinder real-time application of these algorithms. Moreover, due to the lack of high-dimensional features and dense training samples, SOSVM-based algorithms are unstable to deal with various challenging scenarios, such as occlusions and scale variations. Recently, visual tracking algorithms based on discriminative correlation filters (DCF), especially the combination of DCF and features from deep convolutional neural networks (CNN), have been successfully applied to visual tracking, and attains surprisingly good performance on recent benchmarks. The success is mainly attributed to two aspects: the circular correlation properties of DCF and the powerful representation capabilities of CNN features. Nevertheless, compared with SOSVM, DCF-based algorithms are restricted to simple ridge regression which has a weaker discriminative ability. In this paper, a novel circular and structural operator tracker (CSOT) is proposed for high performance visual tracking, it not only possesses the powerful discriminative capability of SOSVM but also efficiently inherits the superior computational efficiency of DCF. Based on the proposed circular and structural operators, a set of primal confidence score maps can be obtained by circular correlating feature maps with their corresponding structural correlation filters. Furthermore, an implicit interpolation is applied to convert the multi-resolution feature maps to the continuous domain and make all primal confidence score maps have the same spatial resolution. Then, we exploit an efficient ensemble post-processor based on relative entropy, which can coalesce primal confidence score maps and create an optimal confidence score map for more accurate localization. The target is localized on the peak of the optimal confidence score map. Besides, we introduce a collaborative optimization strategy to update circular and structural operators by iteratively training structural correlation filters, which significantly reduces computational complexity and improves robustness. Experimental results demonstrate that our approach achieves state-of-the-art performance in mean AUC scores of 71.5 and 69.4 on the OTB2013 and OTB2015 benchmarks respectively, and obtains a third-best expected average overlap (EAO) score of 29.8 on the VOT2017 benchmark. In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the past few decades. These methods produce excellent results, but can be challenging to deploy in practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyperparameter selection. The starting point of this paper is the observation that unrolled iterative methods have the form of a CNN (filtering followed by pointwise non-linearity) when the normal operator ( @math , where @math is the adjoint of the forward imaging operator, @math ) of the forward model is a convolution. Based on this observation, we propose using direct inversion followed by a CNN to solve normal-convolutional inverse problems. The direct inversion encapsulates the physical model of the system, but leads to artifacts when the problem is ill posed; the CNN combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure. We demonstrate the performance of the proposed network in sparse-view reconstruction (down to 50 views) on parallel beam X-ray computed tomography in synthetic phantoms as well as in real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a @math image on the GPU.