Bin Gao

Yan Yang, Bin Gao, Ya-xiang Yuan

Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure and makes the problem intricate. To this end, we propose a space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints. The "space-decoupling" is reflected in several ways. We show that the tangent cone of coupled constraints is the intersection of tangent cones of each constraint. Moreover, we decouple the intertwined bounded-rank and orthogonally invariant constraints into two spaces, leading to optimization on a smooth manifold. Implementing Riemannian algorithms on this manifold is painless as long as the geometry of additional constraints is known. In addition, we unveil the equivalence between the reformulated problem and the original problem. Numerical experiments on real-world applications -- spherical data fitting, graph similarity measuring, low-rank SDP, model reduction of Markov processes, reinforcement learning, and deep learning -- validate the superiority of the proposed framework.

Yan Yang, Bin Gao, Ya-xiang Yuan

Determinantal varieties -- the sets of bounded-rank matrices or tensors -- have attracted growing interest in low-rank optimization. The tangent cone to low-rank sets is widely studied and underpins a range of geometric methods. The second-order geometry, which encodes curvature information, is more intricate. In this work, we develop a unified framework to derive explicit formulas for both first- and second-order tangent sets to various low-rank sets, including low-rank matrices, tensors, symmetric matrices, and positive semidefinite matrices. The framework also accommodates the intersection of a low-rank set and another set satisfying mild assumptions, thereby yielding a tangent intersection rule. Through the lens of tangent sets, we establish a necessary and sufficient condition under which a nonsmooth problem and its smooth parameterization share equivalent second-order stationary points. Moreover, we exploit tangent sets to characterize optimality conditions for low-rank optimization and prove that verifying second-order optimality is NP-hard. In a separate line of analysis, we investigate variational geometry of the graph of the normal cone to matrix varieties, deriving the explicit Bouligand tangent cone, Fréchet and Mordukhovich normal cones to the graph. These results are further applied to develop optimality conditions for low-rank bilevel programs.

Fei Tian, Bin Gao, Di He et al.

We propose Sentence Level Recurrent Topic Model (SLRTM), a new topic model that assumes the generation of each word within a sentence to depend on both the topic of the sentence and the whole history of its preceding words in the sentence. Different from conventional topic models that largely ignore the sequential order of words or their topic coherence, SLRTM gives full characterization to them by using a Recurrent Neural Networks (RNN) based framework. Experimental results have shown that SLRTM outperforms several strong baselines on various tasks. Furthermore, SLRTM can automatically generate sentences given a topic (i.e., topics to sentences), which is a key technology for real world applications such as personalized short text conversation.

Huazheng Wang, Fei Tian, Bin Gao et al.

Intelligence Quotient (IQ) Test is a set of standardized questions designed to evaluate human intelligence. Verbal comprehension questions appear very frequently in IQ tests, which measure human's verbal ability including the understanding of the words with multiple senses, the synonyms and antonyms, and the analogies among words. In this work, we explore whether such tests can be solved automatically by artificial intelligence technologies, especially the deep learning technologies that are recently developed and successfully applied in a number of fields. However, we found that the task was quite challenging, and simply applying existing technologies (e.g., word embedding) could not achieve a good performance, mainly due to the multiple senses of words and the complex relations among words. To tackle these challenges, we propose a novel framework consisting of three components. First, we build a classifier to recognize the specific type of a verbal question (e.g., analogy, classification, synonym, or antonym). Second, we obtain distributed representations of words and relations by leveraging a novel word embedding method that considers the multi-sense nature of words and the relational knowledge among words (or their senses) contained in dictionaries. Third, for each type of questions, we propose a specific solver based on the obtained distributed word representations and relation representations. Experimental results have shown that the proposed framework can not only outperform existing methods for solving verbal comprehension questions but also exceed the average performance of the Amazon Mechanical Turk workers involved in the study. The results indicate that with appropriate uses of the deep learning technologies we might be a further step closer to the human intelligence.

Fei Tian, Bin Gao, Enhong Chen et al.

Word embedding, which refers to low-dimensional dense vector representations of natural words, has demonstrated its power in many natural language processing tasks. However, it may suffer from the inaccurate and incomplete information contained in the free text corpus as training data. To tackle this challenge, there have been quite a few works that leverage knowledge graphs as an additional information source to improve the quality of word embedding. Although these works have achieved certain success, they have neglected some important facts about knowledge graphs: (i) many relationships in knowledge graphs are \emph{many-to-one}, \emph{one-to-many} or even \emph{many-to-many}, rather than simply \emph{one-to-one}; (ii) most head entities and tail entities in knowledge graphs come from very different semantic spaces. To address these issues, in this paper, we propose a new algorithm named ProjectNet. ProjecNet models the relationships between head and tail entities after transforming them with different low-rank projection matrices. The low-rank projection can allow non \emph{one-to-one} relationships between entities, while different projection matrices for head and tail entities allow them to originate in different semantic spaces. The experimental results demonstrate that ProjectNet yields more accurate word embedding than previous works, thus leads to clear improvements in various natural language processing tasks.

Qing Cui, Bin Gao, Jiang Bian et al.

Neural network techniques are widely applied to obtain high-quality distributed representations of words, i.e., word embeddings, to address text mining, information retrieval, and natural language processing tasks. Recently, efficient methods have been proposed to learn word embeddings from context that captures both semantic and syntactic relationships between words. However, it is challenging to handle unseen words or rare words with insufficient context. In this paper, inspired by the study on word recognition process in cognitive psychology, we propose to take advantage of seemingly less obvious but essentially important morphological knowledge to address these challenges. In particular, we introduce a novel neural network architecture called KNET that leverages both contextual information and morphological word similarity built based on morphological knowledge to learn word embeddings. Meanwhile, the learning architecture is also able to refine the pre-defined morphological knowledge and obtain more accurate word similarity. Experiments on an analogical reasoning task and a word similarity task both demonstrate that the proposed KNET framework can greatly enhance the effectiveness of word embeddings.

Bin Gao, Jiang Bian, Tie-Yan Liu

WordRep is a benchmark collection for the research on learning distributed word representations (or word embeddings), released by Microsoft Research. In this paper, we describe the details of the WordRep collection and show how to use it in different types of machine learning research related to word embedding. Specifically, we describe how the evaluation tasks in WordRep are selected, how the data are sampled, and how the evaluation tool is built. We then compare several state-of-the-art word representations on WordRep, report their evaluation performance, and make discussions on the results. After that, we discuss new potential research topics that can be supported by WordRep, in addition to algorithm comparison. We hope that this paper can help people gain deeper understanding of WordRep, and enable more interesting research on learning distributed word representations and related topics.