arXiv subjects
Publications and source records attributed to Guodong Zhou.
A cohomology theory of weighted Rota-Baxter $3$-Lie algebras is introduced. Formal deformations, abelian extensions, skeletal weighted Rota-Baxter $3$-Lie 2-algebras and crossed modules of weighted Rota-Baxter 3-Lie algebras are interpreted by using lower degree cohomology groups.
It is well known that translations generated by an excellent document-level neural machine translation (NMT) model are consistent and coherent. However, existing sentence-level evaluation metrics like BLEU can hardly reflect the model's performance at the document level. To tackle this issue, we propose a Discourse Cohesion Evaluation Method (DCoEM) in this paper and contribute a new test suite that considers four cohesive manners (reference, conjunction, substitution, and lexical cohesion) to measure the cohesiveness of document translations. The evaluation results on recent document-level NMT systems show that our method is practical and essential in estimating translations at the document level.
This paper is devoted to studying deformation, cohomology theory of Rota-Baxter pre-Lie algebras of arbitrary weights. First we give the notion of a new representation of a Rota-Baxter pre-Lie algebra of arbitrary weight and define the cohomology theory of a Rota-Baxter pre-Lie algebra of arbitrary weight. Then we study formal deformations by lower degree cohomology groups. Finally, we classify abelian extensions of Rota-Baxter pre-Lie algebras of arbitrary weight using the second cohomology group, and classify skeletal Rota-Baxter pre-Lie 2-algebra of arbitrary weight using the third cohomology group as applications.
Causal relation extraction of biomedical entities is one of the most complex tasks in biomedical text mining, which involves two kinds of information: entity relations and entity functions. One feasible approach is to take relation extraction and function detection as two independent sub-tasks. However, this separate learning method ignores the intrinsic correlation between them and leads to unsatisfactory performance. In this paper, we propose a joint learning model, which combines entity relation extraction and entity function detection to exploit their commonality and capture their inter-relationship, so as to improve the performance of biomedical causal relation extraction. Meanwhile, during the model training stage, different function types in the loss function are assigned different weights. Specifically, the penalty coefficient for negative function instances increases to effectively improve the precision of function detection. Experimental results on the BioCreative-V Track 4 corpus show that our joint learning model outperforms the separate models in BEL statement extraction, achieving the F1 scores of 58.4% and 37.3% on the test set in Stage 2 and Stage 1 evaluations, respectively. This demonstrates that our joint learning system reaches the state-of-the-art performance in Stage 2 compared with other systems.
We study a question which can be roughly stated as follows: Given a (unital or nonunital) algebra $A$ together with a Gröbner-Shirshov basis $G$, consider the free operated algebra $B$ over $A$, such that the operator satisfies some polynomial identities $Φ$ which are Gröbner-Shirshov in the sense of Guo et al., when doesthe union $Φ\cup G$ will be an operated Gröbner-Shirshov basis for $B$? We answer this question in the affirmative under a mild condition in our previous work with Wang. When this condition is satisfied, $Φ\cup G$ is an operated Gröbner-Shirshov basis for $ B$ and as a consequence, we also get a linear basis of $B$. However, the condition could not be applied directly to differential type algebras introduced by Guo, Sit and Zhang, including usual differential algebras. This paper solves completely this problem for differential type algebras.Some new monomial orders are introduced which, together with some known ones, permit the application of the previous result to most of differential type algebras, thus providing new operated GS bases and linear bases for these differential type algebras.Versions are presented both for unital and nonunital algebras. However, a class of examples are also presented, for which the natural expectation in the question is wrong and these examples are dealt with by direct inspection.
This paper studies formal deformations and homotopy theory of Rota-Baxter algebras of any weight. We define an $L_\infty$-algebra, which controls simultaneous deformations of associative products and Rota-Baxter operators. As a consequence, we develop a cohomology theory of Rota-Baxter algebras of any weight and justify it by interpreting lower degree cohomology groups as formal deformations and abelian extensions. The notion of homotopy Rota-Baxter algebras is introduced and it is shown that the operad governing homotopy Rota-Baxter algebras is a minimal model of the operad of Rota-Baxter algebras.
This paper investigates algebraic objects equipped with an operator, such as operated monoids, operated algebras etc. Various free object functors in these operated contexts are explicitly constructed. For operated algebras whose operator satisfies a set $Φ$ of relations (usually called operated polynomial identities (aka. OPIs)), Guo defined free objects, called free $Φ$-algebras, via universal algebra. Free $Φ$-algebras over algebras are studied in details. A mild sufficient condition is found such that $Φ$ together with a Gröbner-Shirshov basis of an algebra $A$ form a Gröbner-Shirshov basis of the free $Φ$-algebra over algebra $A$ in the sense of Guo et al.. Ample examples for which this condition holds are provided, such as all Rota-Baxter type OPIs, a class of differential type OPIs, averaging OPIs and Reynolds OPI.
Various neural-based methods have been proposed so far for joint mention detection and coreference resolution. However, existing works on coreference resolution are mainly dependent on filtered mention representation, while other spans are largely neglected. In this paper, we aim at increasing the utilization rate of data and investigating whether those eliminated spans are totally useless, or to what extent they can improve the performance of coreference resolution. To achieve this, we propose a mention representation refining strategy where spans highly related to mentions are well leveraged using a pointer network for representation enhancing. Notably, we utilize an additional loss term in this work to encourage the diversity between entity clusters. Experimental results on the document-level CoNLL-2012 Shared Task English dataset show that eliminated spans are indeed much effective and our approach can achieve competitive results when compared with previous state-of-the-art in coreference resolution.
Due to its great importance in deep natural language understanding and various down-stream applications, text-level parsing of discourse rhetorical structure (DRS) has been drawing more and more attention in recent years. However, all the previous studies on text-level discourse parsing adopt bottom-up approaches, which much limit the DRS determination on local information and fail to well benefit from global information of the overall discourse. In this paper, we justify from both computational and perceptive points-of-view that the top-down architecture is more suitable for text-level DRS parsing. On the basis, we propose a top-down neural architecture toward text-level DRS parsing. In particular, we cast discourse parsing as a recursive split point ranking task, where a split point is classified to different levels according to its rank and the elementary discourse units (EDUs) associated with it are arranged accordingly. In this way, we can determine the complete DRS as a hierarchical tree structure via an encoder-decoder with an internal stack. Experimentation on both the English RST-DT corpus and the Chinese CDTB corpus shows the great effectiveness of our proposed top-down approach towards text-level DRS parsing.
Continuing a work of Ph.~Monnier, we determine the Gerstenhaber algebra structure over the Poisson cohomology groups for a large class of Poisson structures with isolated singularities over the plane. It reveals that there exists a GAGA type phenomenon. We give an explicit description via generators and relations for the case of simple singularities.
In the literature, the research on abstract meaning representation (AMR) parsing is much restricted by the size of human-curated dataset which is critical to build an AMR parser with good performance. To alleviate such data size restriction, pre-trained models have been drawing more and more attention in AMR parsing. However, previous pre-trained models, like BERT, are implemented for general purpose which may not work as expected for the specific task of AMR parsing. In this paper, we focus on sequence-to-sequence (seq2seq) AMR parsing and propose a seq2seq pre-training approach to build pre-trained models in both single and joint way on three relevant tasks, i.e., machine translation, syntactic parsing, and AMR parsing itself. Moreover, we extend the vanilla fine-tuning method to a multi-task learning fine-tuning method that optimizes for the performance of AMR parsing while endeavors to preserve the response of pre-trained models. Extensive experimental results on two English benchmark datasets show that both the single and joint pre-trained models significantly improve the performance (e.g., from 71.5 to 80.2 on AMR 2.0), which reaches the state of the art. The result is very encouraging since we achieve this with seq2seq models rather than complex models. We make our code and model available at https://github.com/xdqkid/S2S-AMR-Parser.
This paper studies averaging algebras, say, associative algebras endowed with averaging operators. We develop a cohomology theory for averaging algebras and justify it by interpreting lower degree cohomology groups as formal deformations and abelian extensions of averaging algebras. We make explicit the $L_\infty$-algebra structure over the cochain complex defining cohomology groups and introduce the notion of homotopy averaging algebras as Maurer-Cartan elements of this $L_\infty$-algebra.
As an algebraic study of differential equations, differential algebras have been studied for a century and and become an important area of mathematics. In recent years the area has been expended to the noncommutative associative and Lie algebra contexts and to the case when the operator identity has a weight in order to include difference operators and difference algebras. This paper provides a cohomology theory for differential algebras of any weights. This gives a uniform approach to both the zero weight case which is similar to the earlier study of differential Lie algebras, and the non-zero weight case which poses new challenges. As applications, abelian extensions of a differential algebra are classified by the second cohomology group. Furthermore, formal deformations of differential algebras are obtained and the rigidity of a differential algebra is characterized by the vanishing of the second cohomology group.
Neural conversation models such as encoder-decoder models are easy to generate bland and generic responses. Some researchers propose to use the conditional variational autoencoder(CVAE) which maximizes the lower bound on the conditional log-likelihood on a continuous latent variable. With different sampled la-tent variables, the model is expected to generate diverse responses. Although the CVAE-based models have shown tremendous potential, their improvement of generating high-quality responses is still unsatisfactory. In this paper, we introduce a discrete latent variable with an explicit semantic meaning to improve the CVAE on short-text conversation. A major advantage of our model is that we can exploit the semantic distance between the latent variables to maintain good diversity between the sampled latent variables. Accordingly, we pro-pose a two-stage sampling approach to enable efficient diverse variable selection from a large latent space assumed in the short-text conversation task. Experimental results indicate that our model outperforms various kinds of generation models under both automatic and human evaluations and generates more diverse and in-formative responses.
Recently, neural networks have shown promising results on Document-level Aspect Sentiment Classification (DASC). However, these approaches often offer little transparency w.r.t. their inner working mechanisms and lack interpretability. In this paper, to simulating the steps of analyzing aspect sentiment in a document by human beings, we propose a new Hierarchical Reinforcement Learning (HRL) approach to DASC. This approach incorporates clause selection and word selection strategies to tackle the data noise problem in the task of DASC. First, a high-level policy is proposed to select aspect-relevant clauses and discard noisy clauses. Then, a low-level policy is proposed to select sentiment-relevant words and discard noisy words inside the selected clauses. Finally, a sentiment rating predictor is designed to provide reward signals to guide both clause and word selection. Experimental results demonstrate the impressive effectiveness of the proposed approach to DASC over the state-of-the-art baselines.
Recent studies on AMR-to-text generation often formalize the task as a sequence-to-sequence (seq2seq) learning problem by converting an Abstract Meaning Representation (AMR) graph into a word sequence. Graph structures are further modeled into the seq2seq framework in order to utilize the structural information in the AMR graphs. However, previous approaches only consider the relations between directly connected concepts while ignoring the rich structure in AMR graphs. In this paper we eliminate such a strong limitation and propose a novel structure-aware self-attention approach to better modeling the relations between indirectly connected concepts in the state-of-the-art seq2seq model, i.e., the Transformer. In particular, a few different methods are explored to learn structural representations between two concepts. Experimental results on English AMR benchmark datasets show that our approach significantly outperforms the state of the art with 29.66 and 31.82 BLEU scores on LDC2015E86 and LDC2017T10, respectively. To the best of our knowledge, these are the best results achieved so far by supervised models on the benchmarks.
There have been a recent line of works to automatically predict the emotions of posts in social media. Existing approaches consider the posts individually and predict their emotions independently. Different from previous researches, we explore the dependence among relevant posts via the authors' backgrounds, since the authors with similar backgrounds, e.g., gender, location, tend to express similar emotions. However, such personal attributes are not easy to obtain in most social media websites, and it is hard to capture attributes-aware words to connect similar people. Accordingly, we propose a Neural Personal Discrimination (NPD) approach to address above challenges by determining personal attributes from posts, and connecting relevant posts with similar attributes to jointly learn their emotions. In particular, we employ adversarial discriminators to determine the personal attributes, with attention mechanisms to aggregate attributes-aware words. In this way, social correlationship among different posts can be better addressed. Experimental results show the usefulness of personal attributes, and the effectiveness of our proposed NPD approach in capturing such personal attributes with significant gains over the state-of-the-art models.
We determine the Batalin-Vilkovisky structure on the Tate-Hochschild cohomology of the group algebra $kG$ of a finite group $G$ in terms of the additive decomposition. In particular, we show that the Tate cohomology of $G$ is a Batalin-Vilkovisky subalgebra of the Tate-Hochschild cohomology of the group algebra $kG$, and that the Tate cochain complex of $G$ is a cyclic $A_{\infty}$-subalgebra of the Tate-Hochschild cochain complex of $kG$.