This paper contributes a novel embedding model which measures the probability of each belief @math in a large-scale knowledge repository via simultaneously learning distributed representations for entities ( @math and @math ), relations ( @math ), and the words in relation mentions ( @math ). It facilitates knowledge completion by means of simple vector operations to discover new beliefs. Given an imperfect belief, we can not only infer the missing entities, predict the unknown relations, but also tell the plausibility of the belief, just leveraging the learnt embeddings of remaining evidences. To demonstrate the scalability and the effectiveness of our model, we conduct experiments on several large-scale repositories which contain millions of beliefs from WordNet, Freebase and NELL, and compare it with other cutting-edge approaches via competing the performances assessed by the tasks of entity inference, relation prediction and triplet classification with respective metrics. Extensive experimental results show that the proposed model outperforms the state-of-the-arts with significant improvements.
Single Layer Model , proposed by @cite_19 thus aims to alleviate the shortcomings of the Distance Model by means of the non-linearity of a single layer neural network @math , in which @math . The linear output layer then gives the scoring function: @math .
@cite_19
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This paper explores the complexity of deep feedforward networks with linear pre-synaptic couplings and rectified linear activations. This is a contribution to the growing body of work contrasting the representational power of deep and shallow network architectures. In particular, we offer a framework for comparing deep and shallow models that belong to the family of piecewise linear functions based on computational geometry. We look at a deep rectifier multi-layer perceptron (MLP) with linear outputs units and compare it with a single layer version of the model. In the asymptotic regime, when the number of inputs stays constant, if the shallow model has @math hidden units and @math inputs, then the number of linear regions is @math . For a @math layer model with @math hidden units on each layer it is @math . The number @math grows faster than @math when @math tends to infinity or when @math tends to infinity and @math . Additionally, even when @math is small, if we restrict @math to be @math , we can show that a deep model has considerably more linear regions that a shallow one. We consider this as a first step towards understanding the complexity of these models and specifically towards providing suitable mathematical tools for future analysis. Deep multi-layer neural networks have many levels of non-linearities allowing them to compactly represent highly non-linear and highly-varying functions. However, until recently it was not clear how to train such deep networks, since gradient-based optimization starting from random initialization often appears to get stuck in poor solutions. recently proposed a greedy layer-wise unsupervised learning procedure relying on the training algorithm of restricted Boltzmann machines (RBM) to initialize the parameters of a deep belief network (DBN), a generative model with many layers of hidden causal variables. This was followed by the proposal of another greedy layer-wise procedure, relying on the usage of autoassociator networks. In the context of the above optimization problem, we study these algorithms empirically to better understand their success. Our experiments confirm the hypothesis that the greedy layer-wise unsupervised training strategy helps the optimization by initializing weights in a region near a good local minimum, but also implicitly acts as a sort of regularization that brings better generalization and encourages internal distributed representations that are high-level abstractions of the input. We also present a series of experiments aimed at evaluating the link between the performance of deep neural networks and practical aspects of their topology, for example, demonstrating cases where the addition of more depth helps. Finally, we empirically explore simple variants of these training algorithms, such as the use of different RBM input unit distributions, a simple way of combining gradient estimators to improve performance, as well as on-line versions of those algorithms. In this paper, we analyze the spatial information of deep features, and propose two complementary regressions for robust visual tracking. First, we propose a kernelized ridge regression model wherein the kernel value is defined as the weighted sum of similarity scores of all pairs of patches between two samples. We show that this model can be formulated as a neural network and thus can be efficiently solved. Second, we propose a fully convolutional neural network with spatially regularized kernels, through which the filter kernel corresponding to each output channel is forced to focus on a specific region of the target. Distance transform pooling is further exploited to determine the effectiveness of each output channel of the convolution layer. The outputs from the kernelized ridge regression model and the fully convolutional neural network are combined to obtain the ultimate response. Experimental results on two benchmark datasets validate the effectiveness of the proposed method. This paper aims to accelerate the test-time computation of convolutional neural networks (CNNs), especially very deep CNNs [1] that have substantially impacted the computer vision community. Unlike previous methods that are designed for approximating linear filters or linear responses, our method takes the nonlinear units into account. We develop an effective solution to the resulting nonlinear optimization problem without the need of stochastic gradient descent (SGD). More importantly, while previous methods mainly focus on optimizing one or two layers, our nonlinear method enables an asymmetric reconstruction that reduces the rapidly accumulated error when multiple (e.g., @math 10) layers are approximated. For the widely used very deep VGG-16 model [1] , our method achieves a whole-model speedup of 4 @math with merely a 0.3 percent increase of top-5 error in ImageNet classification. Our 4 @math accelerated VGG-16 model also shows a graceful accuracy degradation for object detection when plugged into the Fast R-CNN detector [2] .