T ensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for T ensor Completion Anonymous Authors Affiliation Address email Abstract In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from laborious model selection problem due to high model sensitivity. Especially for tensor ring (TR) decomposition, the number of model possibility grows exponentially with the tensor order, which makes it rather challenging to find the optimal TR decomposition. In this paper, by exploiting the low-rank structure on TR latent space, we propose a novel tensor completion method, which is robust to model selection. In contrast to imposing low-rank constraint on the data space, we introduce nuclear norm regularization on the latent TR factors, resulting in that the optimization step using singular value decomposition (SVD) can be performed at a much smaller scale. By leveraging the alternating direction method of multipliers (ADMM) scheme, the latent TR factors with optimal rank and the recovered tensor can be obtained simultaneously. Our proposed algorithm effectively alleviates the burden of TR-rank selection, therefore the computational cost is greatly reduced. The extensive experimental results on synthetic data and real-world data demonstrate the superior high performance and efficiency of the proposed approach against the state-of-the-art algorithms. Introduction Tensor decomposition aims to find the latent factors of tensor-valued data (i.e. the generalization of multidimensional arrays), thereby casting large-scale tensors into a multilinear tensor latent space of low-dimensionality (very few degrees of freedom designated by the rank).

Finding biologically plausible alternatives to back-propagation of errors is a fundamentally important challenge in artificial neural network research. In this paper, we propose a simple learning algorithm called error-driven Local Representation Alignment (LRA-E), which has strong connections to predictive coding, a theory that offers a mechanistic way of describing neurocomputational machinery. In addition, we propose an improved variant of Difference Target Propagation, another procedure that comes from the same family of algorithms as Local Representation Alignment. We compare our learning procedures to several other biologically-motivated algorithms, including two feedback alignment algorithms and Equilibrium Propagation. In two benchmark datasets, we find that both of our proposed learning algorithms yield stable performance and strong generalization abilities in comparison to other competing back-propagation alternatives when training deeper, highly nonlinear networks, with LRA-E performing the best overall.

Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on least-squares data fitting and they do not possess a mechanism for tensor rank determination. This leaves them susceptible to outliers and vulnerable to over-fitting. This paper presents a Bayesian robust streaming tensor factorization model to identify sparse outliers, automatically determine the underlying tensor rank and accurately fit low-rank structure. We implement our model in Matlab and compare it with existing algorithms on tensor datasets generated from dynamic MRI and Internet traffic.

We consider a general framework for reducing the number of trainable model parameters in deep learning networks by decomposing linear operators as a product of sums of simpler linear operators. Recently proposed deep learning architectures such as CNN, KFC, Dilated CNN, etc. are all subsumed in this framework and we illustrate other types of neural network architectures within this framework. We show that good accuracy on MNIST and Fashion MNIST can be obtained using a relatively small number of trainable parameters. In addition, since implementation of the convolutional layer is resource-heavy, we consider an approach in the transform domain that obviates the need for convolutional layers. One of the advantages of this general framework over prior approaches is that the number of trainable parameters is not fixed and can be varied arbitrarily. In particular, we illustrate the tradeoff of varying the number of trainable variables and the corresponding error rate. As an example, by using this decomposition on a reference CNN architecture for MNIST with over 3x10^6 trainable parameters, we are able to obtain an accuracy of 98.44% using only 3554 trainable parameters.

Multi-hop reading comprehension focuses on one type of factoid question, where a system needs to properly integrate multiple pieces of evidence to correctly answer a question. Previous work approximates global evidence with local coreference information, encoding coreference chains with DAG-styled GRU layers within a gated-attention reader. However, coreference is limited in providing information for rich inference. We introduce a new method for better connecting global evidence, which forms more complex graphs compared to DAGs. To perform evidence integration on our graphs, we investigate two recent graph neural networks, namely graph convolutional network (GCN) and graph recurrent network (GRN). Experiments on two standard datasets show that richer global information leads to better answers. Our method performs better than all published results on these datasets.

This paper proposes a tutorial on the Data Clustering technique using the Particle Swarm Optimization approach. Following the work proposed by Merwe et al. [1] here we present an in-deep analysis of the algorithm together with a Matlab implementation and a short tutorial that explains how to modify the proposed implementation and the effect of the parameters of the original algorithm. Moreover, we provide a comparison against the results obtained using the well known K-Means approach. All the source code presented in this paper is publicly available under the GPL-v2 license.

Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion. However, it over-penalizes top singular values and lead to biased estimations. In this paper, we propose to use the nonconvex regularizer, which can less penalize large singular values, instead of the convex one for tensor completion. However, as the new regularizer is nonconvex and overlapped with each other, existing algorithms are either too slow or suffer from the huge memory cost. To address these issues, we develop an efficient and scalable algorithm, which is based on the proximal average (PA) algorithm, for real-world problems. Compared with the direct usage of PA algorithm, the proposed algorithm runs orders faster and needs orders less space. We further speed up the proposed algorithm with the acceleration technique, and show the convergence to critical points is still guaranteed. Experimental comparisons of the proposed approach are made with various other tensor completion approaches. Empirical results show that the proposed algorithm is very fast and can produce much better recovery performance.

In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternating Thresholding for Singular Value Decomposition (STAT-SVD) is proposed. The proposed procedure features a novel double projection \& thresholding scheme, which provides a sharp criterion for thresholding in each iteration. Compared with regular tensor SVD model, STAT-SVD permits more robust estimation under weaker assumptions. Both the upper and lower bounds for estimation accuracy are developed. The proposed procedure is shown to be minimax rate-optimal in a general class of situations. Simulation studies show that STAT-SVD performs well under a variety of configurations. We also illustrate the merits of the proposed procedure on a longitudinal tensor dataset on European country mortality rates.

The ability to conduct logical reasoning is a fundamental aspect of intelligent behavior, and thus an important problem along the way to human-level artificial intelligence. Traditionally, symbolic methods from the field of knowledge representation and reasoning have been used to equip agents with capabilities that resemble human logical reasoning qualities. More recently, however, there has been an increasing interest in using machine learning rather than logic-based formalisms to tackle these tasks. In this paper, we employ state-of-the-art methods for training deep neural networks to devise a novel model that is able to learn how to effectively perform basic ontology reasoning. This is an important and at the same time very natural reasoning problem, which is why the presented approach is applicable to a plethora of important real-world problems. We present the outcomes of several experiments, which show that our model learned to perform precise reasoning on diverse and challenging tasks. Furthermore, it turned out that the suggested approach suffers much less from different obstacles that prohibit symbolic reasoning, and, at the same time, is surprisingly plausible from a biological point of view.

We analyze the value-loading problem. This is the problem of encoding moral values into an AI agent interacting with a complex environment. Like many before, we argue that this is both a major concern and an extremely challenging problem. Solving it will likely require years, if not decades, of multidisciplinary work by teams of top scientists and experts. Given how uncertain the timeline of human-level AI research is, we thus argue that a pragmatic partial solution should be designed as soon as possible. To this end, we propose a preliminary research program. This roadmap identifies several key steps. We hope that this will allow scholars, engineers and decision-makers to better grasp the upcoming difficulties, and to foresee how they can best contribute to the global effort.