We consider the problem of learning knowledge graph (KG) embeddings for entity alignment (EA). Current methods use the embedding models mainly focusing on triple-level learning, which lacks the ability of capturing long-term dependencies existing in KGs. Consequently, the embedding-based EA methods heavily rely on the amount of prior (known) alignment, due to the identity information in the prior alignment cannot be efficiently propagated from one KG to another. In this paper, we propose RSN4EA (recurrent skipping networks for EA), which leverages biased random walk sampling for generating long paths across KGs and models the paths with a novel recurrent skipping network (RSN). RSN integrates the conventional recurrent neural network (RNN) with residual learning and can largely improve the convergence speed and performance with only a few more parameters. We evaluated RSN4EA on a series of datasets constructed from real-world KGs. Our experimental results showed that it outperformed a number of state-of-the-art embedding-based EA methods and also achieved comparable performance for KG completion.
KG representation learning has been widely studied in recent years @cite_13 . One of the most famous translational methods is TransE @cite_2 , which models a triple @math as @math . TransE works well for one-to-one relationships, but fails to model more complex relationships like one-to-many and many-to-many. TransR @cite_21 tries to solve this problem by involving a relation-specific matrix @math to project @math by @math . PTransE @cite_5 leverages path information to learn inferences among relations. For example, if there exist two triples @math , which form a path in KG, and another triple @math holds simultaneously, PTransE models the path information by learning @math , where @math denotes the operator used to merge @math . KG completion is the most prevalent task for KG representation learning, and there also exist some non-translation methods that are particularly tailored for KG completion @cite_17 @cite_1 .
@cite_21 @cite_1 @cite_2 @cite_5 @cite_13 @cite_17
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We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . Knowledge graphs (KGs), i.e. representation of information as a semantic graph, provide a significant test bed for many tasks including question answering, recommendation, and link prediction. Various amount of scholarly metadata have been made vailable as knowledge graphs from the diversity of data providers and agents. However, these high-quantities of data remain far from quality criteria in terms of completeness while growing at a rapid pace. Most of the attempts in completing such KGs are following traditional data digitization, harvesting and collaborative curation approaches. Whereas, advanced AI-related approaches such as embedding models - specifically designed for such tasks - are usually evaluated for standard benchmarks such as Freebase and Wordnet. The tailored nature of such datasets prevents those approaches to shed the lights on more accurate discoveries. Application of such models on domain-specific KGs takes advantage of enriched meta-data and provides accurate results where the underlying domain can enormously benefit. In this work, the TransE embedding model is reconciled for a specific link prediction task on scholarly metadata. The results show a significant shift in the accuracy and performance evaluation of the model on a dataset with scholarly metadata. The newly proposed version of TransE obtains 99.9 for link prediction task while original TransE gets 95 . In terms of accuracy and Hit@10, TransE outperforms other embedding models such as ComplEx, TransH and TransR experimented over scholarly knowledge graphs Embedding knowledge graphs (KGs) into continuous vector spaces is a focus of current research. Combining such an embedding model with logic rules has recently attracted increasing attention. Most previous attempts made a one-time injection of logic rules, ignoring the interactive nature between embedding learning and logical inference. And they focused only on hard rules, which always hold with no exception and usually require extensive manual effort to create or validate. In this paper, we propose Rule-Guided Embedding (RUGE), a novel paradigm of KG embedding with iterative guidance from soft rules. RUGE enables an embedding model to learn simultaneously from 1) labeled triples that have been directly observed in a given KG, 2) unlabeled triples whose labels are going to be predicted iteratively, and 3) soft rules with various confidence levels extracted automatically from the KG. In the learning process, RUGE iteratively queries rules to obtain soft labels for unlabeled triples, and integrates such newly labeled triples to update the embedding model. Through this iterative procedure, knowledge embodied in logic rules may be better transferred into the learned embeddings. We evaluate RUGE in link prediction on Freebase and YAGO. Experimental results show that: 1) with rule knowledge injected iteratively, RUGE achieves significant and consistent improvements over state-of-the-art baselines; and 2) despite their uncertainties, automatically extracted soft rules are highly beneficial to KG embedding, even those with moderate confidence levels. The code and data used for this paper can be obtained from this https URL The representation of a knowledge graph (KG) in a latent space recently has attracted more and more attention. To this end, some proposed models (e.g., TransE) embed entities and relations of a KG into a "point" vector space by optimizing a global loss function which ensures the scores of positive triplets are higher than negative ones. We notice that these models always regard all entities and relations in a same manner and ignore their (un)certainties. In fact, different entities and relations may contain different certainties, which makes identical certainty insufficient for modeling. Therefore, this paper switches to density-based embedding and propose KG2E for explicitly modeling the certainty of entities and relations, which learn the representations of KGs in the space of multi-dimensional Gaussian distributions. Each entity relation is represented by a Gaussian distribution, where the mean denotes its position and the covariance (currently with diagonal covariance) can properly represent its certainty. In addition, compared with the symmetric measures used in point-based methods, we employ the KL-divergence for scoring triplets, which is a natural asymmetry function for effectively modeling multiple types of relations. We have conducted extensive experiments on link prediction and triplet classification with multiple benchmark datasets (WordNet and Freebase). Our experimental results demonstrate that our method can effectively model the (un)certainties of entities and relations in a KG, and it significantly outperforms state-of-the-art methods (including TransH and TransR). Knowledge graph (KG) embedding is to embed components of a KG including entities and relations into continuous vector spaces, so as to simplify the manipulation while preserving the inherent structure of the KG. It can benefit a variety of downstream tasks such as KG completion and relation extraction, and hence has quickly gained massive attention. In this article, we provide a systematic review of existing techniques, including not only the state-of-the-arts but also those with latest trends. Particularly, we make the review based on the type of information used in the embedding task. Techniques that conduct embedding using only facts observed in the KG are first introduced. We describe the overall framework, specific model design, typical training procedures, as well as pros and cons of such techniques. After that, we discuss techniques that further incorporate additional information besides facts. We focus specifically on the use of entity types, relation paths, textual descriptions, and logical rules. Finally, we briefly introduce how KG embedding can be applied to and benefit a wide variety of downstream tasks such as KG completion, relation extraction, question answering, and so forth. We consider the problem of embedding knowledge graphs (KGs) into continuous vector spaces. Existing methods can only deal with explicit relationships within each triple, i.e., local connectivity patterns, but cannot handle implicit relationships across different triples, i.e., contextual connectivity patterns. This paper proposes context-dependent KG embedding, a twostage scheme that takes into account both types of connectivity patterns and obtains more accurate embeddings. We evaluate our approach on the tasks of link prediction and triple classification, and achieve significant and consistent improvements over state-of-the-art methods. Knowledge Graphs (KGs) have been applied to many tasks including Web search, link prediction, recommendation, natural language processing, and entity linking. However, most KGs are far from complete and are growing at a rapid pace. To address these problems, Knowledge Graph Completion (KGC) has been proposed to improve KGs by filling in its missing connections. Unlike existing methods which hold a closed-world assumption, i.e., where KGs are fixed and new entities cannot be easily added, in the present work we relax this assumption and propose a new open-world KGC task. As a first attempt to solve this task we introduce an open-world KGC model called ConMask. This model learns embeddings of the entity's name and parts of its text-description to connect unseen entities to the KG. To mitigate the presence of noisy text descriptions, ConMask uses a relationship-dependent content masking to extract relevant snippets and then trains a fully convolutional neural network to fuse the extracted snippets with entities in the KG. Experiments on large data sets, both old and new, show that ConMask performs well in the open-world KGC task and even outperforms existing KGC models on the standard closed-world KGC task. We introduce emph Normative Temporal Logic (acro ntl ), a logic for reasoning about normative systems. acro ntl is a generalisation of the well-known branching-time temporal logic acro ctl , in which the path quantifiers @math ( on all pathsldots'') and @math ( on some pathldots'') are replaced by the indexed deontic operators @math and @math , where for example @math means @math is obligatory in the context of normative system @math ''. After defining the logic, we give a sound and complete axiomatisation, and discuss the logic's relationship to standard deontic logics. We present a symbolic representation language for models and normative systems, and identify four different model checking problems, corresponding to whether or not a model is represented symbolically or explicitly, and whether or not we are given an interpretation for the normative systems named in formulae to be checked. We show that the complexity of model checking varies from acro p -complete up to acro exptime -hard for these variations. This paper proposes a novel translation-based knowledge graph embedding that preserves the logical properties of relations such as transitivity and symmetricity. The embedding space generated by existing translation-based embeddings do not represent transitive and symmetric relations precisely, because they ignore the role of entities in triples. Thus, we introduce a role-specific projection which maps an entity to distinct vectors according to its role in a triple. That is, a head entity is projected onto an embedding space by a head projection operator, and a tail entity is projected by a tail projection operator. This idea is applied to TransE, TransR, and TransD to produce lppTransE, lppTransR, and lppTransD, respectively. According to the experimental results on link prediction and triple classification, the proposed logical property preserving embeddings show the state-of-the-art performance at both tasks. These results prove that it is critical to preserve logical properties of relations while embedding knowledge graphs, and the proposed method does it effectively. We develop a parameterized complexity theory for counting problems. As the basis of this theory, we introduce a hierarchy of parameterized counting complexity classes #W @math , for @math , that corresponds to Downey and Fellows's W-hierarchy [R. G. Downey and M. R. Fellows, Parameterized Complexity, Springer-Verlag, New York, 1999] and we show that a few central W-completeness results for decision problems translate to #W-completeness results for the corresponding counting problems. Counting complexity gets interesting with problems whose decision version is tractable, but whose counting version is hard. Our main result states that counting cycles and paths of length k in both directed and undirected graphs, parameterized by k, is #W @math f(k) n^c @math f: N N @math 2^ O(k) n^ 2.376 $ algorithm for finding a cycle or path of length k [N. Alon, R. Yuster, and U. Zwick, J. ACM, 42 (1995), pp. 844--856]. Citation relationship between scientific publications has been successfully used for scholarly bibliometrics, information retrieval and data mining tasks, and citation-based recommendation algorithms are well documented. While previous studies investigated citation relations from various viewpoints, most of them share the same assumption that, if paper1 cites paper2 (or author1 cites author2), they are connected, regardless of citation importance, sentiment, reason, topic, or motivation. However, this assumption is oversimplified. In this study, we employ an innovative "context-rich heterogeneous network" approach, which paves a new way for citation recommendation task. In the network, we characterize 1) the importance of citation relationships between citing and cited papers, and 2) the topical citation motivation. Unlike earlier studies, the citation information, in this paper, is characterized by citation textual contexts extracted from the full-text citing paper. We also propose algorithm to cope with the situation when large portion of full-text missing information exists in the bibliographic repository. Evaluation results show that, context-rich heterogeneous network can significantly enhance the citation recommendation performance. Abstract Irregular sampling and “stable sampling” of band-limited functions have been studied by H.J. Landau [H.J. Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967) 37–52]. We prove that quasicrystals are sets of stable sampling. To cite this article: B. Matei, Y. Meyer, C. R. Acad. Sci. Paris, Ser. I 346 (2008). Research has seen considerable achievements concerning translation of natural language patterns into formal queries for Question Answering (QA) based on Knowledge Graphs (KG). One of the main challenges in this research area is about how to identify which property within a Knowledge Graph matches the predicate found in a Natural Language (NL) relation. Current approaches for formal query generation attempt to resolve this problem mainly by first retrieving the named entity from the KG together with a list of its predicates, then filtering out one from all the predicates of the entity. We attempt an approach to directly match an NL predicate to KG properties that can be employed within QA pipelines. In this paper, we specify a systematic approach as well as providing a tool that can be employed to solve this task. Our approach models KB relations with their underlying parts of speech, we then enhance this with extra attributes obtained from Wordnet and Dependency parsing characteristics. From a question, we model a similar representation of query relations. We then define distance measurements between the query relation and the properties representations from the KG to identify which property is referred to by the relation within the query. We report substantive recall values and considerable precision from our evaluation. We present algorithms for reducing the Dueling Bandits problem to the conventional (stochastic) Multi-Armed Bandits problem. The Dueling Bandits problem is an online model of learning with ordinal feedback of the form "A is preferred to B" (as opposed to cardinal feedback like "A has value 2.5"), giving it wide applicability in learning from implicit user feedback and revealed and stated preferences. In contrast to existing algorithms for the Dueling Bandits problem, our reductions -- named @math , @math and @math -- provide a generic schema for translating the extensive body of known results about conventional Multi-Armed Bandit algorithms to the Dueling Bandits setting. For @math and @math we prove regret upper bounds in both finite and infinite settings, and conjecture about the performance of @math which empirically outperforms the other two as well as previous algorithms in our experiments. In addition, we provide the first almost optimal regret bound in terms of second order terms, such as the differences between the values of the arms. In unsupervised domain mapping, the learner is given two unmatched datasets @math and @math . The goal is to learn a mapping @math that translates a sample in @math to the analog sample in @math . Recent approaches have shown that when learning simultaneously both @math and the inverse mapping @math , convincing mappings are obtained. In this work, we present a method of learning @math without learning @math . This is done by learning a mapping that maintains the distance between a pair of samples. Moreover, good mappings are obtained, even by maintaining the distance between different parts of the same sample before and after mapping. We present experimental results that the new method not only allows for one sided mapping learning, but also leads to preferable numerical results over the existing circularity-based constraint. Our entire code is made publicly available at this https URL . We consider the problem @math , and propose algorithms of the form @math , where @math denotes projection on the positive orthant, @math is a stepsize chosen by an Armijo-like rule and @math is a positive definite symmetric matrix which is partly diagonal. We show that @math can be calculated simply on the basis of second derivatives of f so that the resulting Newton-like algorithm has a typically superlinear rate of convergence. With other choices of @math convergence at a typically linear rate is obtained. The algorithms are almost as simple as their unconstrained counterparts. They are well suited for problems of large dimension such as those arising in optimal control while being competitive with existing methods for low-dimensional problems. The effectiveness of the Newton-like algorithm is demonstrated via computational examples involving as many as 10,000 variables. Extensions to general linearly constrained pr... In the distributed all-pairs shortest paths problem (APSP), every node in the weighted undirected distributed network (the CONGEST model) needs to know the distance from every other node using least number of communication rounds (typically called time complexity ). The problem admits @math -approximation @math -time algorithm and a nearly-tight @math lower bound [Nanongkai, STOC'14; Lenzen and Patt-Shamir PODC'15] @math , @math and @math hide polylogarithmic factors. Note that the lower bounds also hold even in the unweighted case and in the weighted case with polynomial approximation ratios LenzenP_podc13,HolzerW12,PelegRT12,Nanongkai-STOC14 . . For the exact case, Elkin [STOC'17] presented an @math time bound, which was later improved to @math [Huang, Nanongkai, Saranurak FOCS'17]. It was shown that any super-linear lower bound (in @math ) requires a new technique [Censor-Hillel, Khoury, Paz, DISC'17], but otherwise it remained widely open whether there exists a @math -time algorithm for the exact case, which would match the best possible approximation algorithm. This paper resolves this question positively: we present a randomized (Las Vegas) @math -time algorithm, matching the lower bound up to polylogarithmic factors. Like the previous @math bound, our result works for directed graphs with zero (and even negative) edge weights. In addition to the improved running time, our algorithm works in a more general setting than that required by the previous @math bound; in our setting (i) the communication is only along edge directions (as opposed to bidirectional), and (ii) edge weights are arbitrary (as opposed to integers in 1, 2, ... poly(n) ). ... Knowledge graph completion aims to perform link prediction between entities. In this paper, we consider the approach of knowledge graph embeddings. Recently, models such as TransE and TransH build entity and relation embeddings by regarding a relation as translation from head entity to tail entity. We note that these models simply put both entities and relations within the same semantic space. In fact, an entity may have multiple aspects and various relations may focus on different aspects of entities, which makes a common space insufficient for modeling. In this paper, we propose TransR to build entity and relation embeddings in separate entity space and relation spaces. Afterwards, we learn embeddings by first projecting entities from entity space to corresponding relation space and then building translations between projected entities. In experiments, we evaluate our models on three tasks including link prediction, triple classification and relational fact extraction. Experimental results show significant and consistent improvements compared to state-of-the-art baselines including TransE and TransH. The source code of this paper can be obtained from https: github.com mrlyk423 relation_extraction. Let @math be the maximal value such that the product of an @math matrix by an @math matrix can be computed with @math arithmetic operations. In this paper we show that @math , which improves the previous record @math by Coppersmith (Journal of Complexity, 1997). More generally, we construct a new algorithm for multiplying an @math matrix by an @math matrix, for any value @math . The complexity of this algorithm is better than all known algorithms for rectangular matrix multiplication. In the case of square matrix multiplication (i.e., for @math ), we recover exactly the complexity of the algorithm by Coppersmith and Wino grad (Journal of Symbolic Computation, 1990). These new upper bounds can be used to improve the time complexity of several known algorithms that rely on rectangular matrix multiplication. For example, we directly obtain a @math -time algorithm for the all-pairs shortest paths problem over directed graphs with small integer weights, where @math denotes the number of vertices, and also improve the time complexity of sparse square matrix multiplication. We propose Scene Graph Auto-Encoder (SGAE) that incorporates the language inductive bias into the encoder-decoder image captioning framework for more human-like captions. Intuitively, we humans use the inductive bias to compose collocations and contextual inference in discourse. For example, when we see the relation person on bike', it is natural to replace on' with ride' and infer person riding bike on a road' even the road' is not evident. Therefore, exploiting such bias as a language prior is expected to help the conventional encoder-decoder models less likely overfit to the dataset bias and focus on reasoning. Specifically, we use the scene graph --- a directed graph ( @math ) where an object node is connected by adjective nodes and relationship nodes --- to represent the complex structural layout of both image ( @math ) and sentence ( @math ). In the textual domain, we use SGAE to learn a dictionary ( @math ) that helps to reconstruct sentences in the @math pipeline, where @math encodes the desired language prior; in the vision-language domain, we use the shared @math to guide the encoder-decoder in the @math pipeline. Thanks to the scene graph representation and shared dictionary, the inductive bias is transferred across domains in principle. We validate the effectiveness of SGAE on the challenging MS-COCO image captioning benchmark, e.g., our SGAE-based single-model achieves a new state-of-the-art @math CIDEr-D on the Karpathy split, and a competitive @math CIDEr-D (c40) on the official server even compared to other ensemble models.