Over the past decade, knowledge graphs became popular for capturing structured domain knowledge. Relational learning models enable the prediction of missing links inside knowledge graphs. More specifically, latent distance approaches model the relationships among entities via a distance between latent representations. Translating embedding models (e.g., TransE) are among the most popular latent distance approaches which use one distance function to learn multiple relation patterns. However, they are not capable of capturing symmetric relations. They also force relations with reflexive patterns to become symmetric and transitive. In order to improve distance based embedding, we propose multi-distance embeddings (MDE). Our solution is based on the idea that by learning independent embedding vectors for each entity and relation one can aggregate contrasting distance functions. Benefiting from MDE, we also develop supplementary distances resolving the above-mentioned limitations of TransE. We further propose an extended loss function for distance based embeddings and show that MDE and TransE are fully expressive using this loss function. Furthermore, we obtain a bound on the size of their embeddings for full expressivity. Our empirical results show that MDE significantly improves the translating embeddings and outperforms several state-of-the-art embedding models on benchmark datasets.
train a neural network to learn the interaction of the , and . ER-MLP @cite_18 is a two layer feedforward neural network considering @math , @math and @math vectors in the input.
@cite_18
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The feedforward multilayer perceptron (MLP) with back-propagation of error is described. Since use of this network requires a set of labeled input-output, as such it cannot be used for segmentation of images when only one image is available. (However, if images to be processed are of similar nature, one can use a set of known images for learning and then use the network for processing of other images.) A self-organizing multilayer neural network architecture suitable for image processing is proposed. The proposed architecture is also a feedforward one with back-propagation of errors; but like MLP it does not require any supervised learning. Each neuron is connected to the corresponding neuron in the previous layer and the set of neighbors of that neuron. The output status of neurons in the output layer is described as a fuzzy set. A fuzziness measure of this fuzzy set is used as a measure of error in the system (instability of the network). Learning rates for various measures of fuzziness have been theoretically and experimentally studied. An application of the proposed network in object extraction from noisy scenes is also demonstrated. We are concerned with feed-forward non-linear networks (multi-layer perceptrons, or MLPs) with multiple outputs. We wish to treat the outputs of the network as probabilities of alternatives (e.g. pattern classes), conditioned on the inputs. We look for appropriate output non-linearities and for appropriate criteria for adaptation of the parameters of the network (e.g. weights). We explain two modifications: probability scoring, which is an alternative to squared error minimisation, and a normalised exponential (softmax) multi-input generalisation of the logistic non-linearity. The two modifications together result in quite simple arithmetic, and hardware implementation is not difficult either. The use of radial units (squared distance instead of dot product) immediately before the softmax output stage produces a network which computes posterior distributions over class labels based on an assumption of Gaussian within-class distributions. However the training, which uses cross-class information, can result in better performance at class discrimination than the usual within-class training method, unless the within-class distribution assumptions are actually correct. Deep neural network is difficult to train and this predicament becomes worse as the depth increases. The essence of this problem exists in the magnitude of backpropagated errors that will result in gradient vanishing or exploding phenomenon. We show that a variant of regularizer which utilizes orthonormality among different filter banks can alleviate this problem. Moreover, we design a backward error modulation mechanism based on the quasi-isometry assumption between two consecutive parametric layers. Equipped with these two ingredients, we propose several novel optimization solutions that can be utilized for training a specific-structured (repetitively triple modules of Conv-BNReLU) extremely deep convolutional neural network (CNN) WITHOUT any shortcuts identity mappings from scratch. Experiments show that our proposed solutions can achieve distinct improvements for a 44-layer and a 110-layer plain networks on both the CIFAR-10 and ImageNet datasets. Moreover, we can successfully train plain CNNs to match the performance of the residual counterparts. Besides, we propose new principles for designing network structure from the insights evoked by orthonormality. Combined with residual structure, we achieve comparative performance on the ImageNet dataset. Deep neural network is difficult to train and this predicament becomes worse as the depth increases. The essence of this problem exists in the magnitude of backpropagated errors that will result in gradient vanishing or exploding phenomenon. We show that a variant of regularizer which utilizes orthonormality among different filter banks can alleviate this problem. Moreover, we design a backward error modulation mechanism based on the quasi-isometry assumption between two consecutive parametric layers. Equipped with these two ingredients, we propose several novel optimization solutions that can be utilized for training a specific-structured (repetitively triple modules of Conv-BNReLU) extremely deep convolutional neural network (CNN) WITHOUT any shortcuts identity mappings from scratch. Experiments show that our proposed solutions can achieve distinct improvements for a 44-layer and a 110-layer plain networks on both the CIFAR-10 and ImageNet datasets. Moreover, we can successfully train plain CNNs to match the performance of the residual counterparts. Besides, we propose new principles for designing network structure from the insights evoked by orthonormality. Combined with residual structure, we achieve comparative performance on the ImageNet dataset.