A new development in NLP is the construction of hyperbolic word embeddings. As opposed to their Euclidean counterparts, hyperbolic embeddings are represented not by vectors, but by points in hyperbolic space. This makes the most common basic scheme for constructing document representations, namely the averaging of word vectors, meaningless in the hyperbolic setting. We reinterpret the vector mean as the centroid of the points represented by the vectors, and investigate various hyperbolic centroid schemes and their effectiveness at text classification.

由于其几何特性，双曲线空间可以支持树木和图形结构化数据的高保真嵌入。结果，已经开发了各种双曲线网络，这些网络在许多任务上都超过了欧几里得网络：例如双曲线图卷积网络（GCN）在某些图形学习任务上的表现可以胜过香草GCN。但是，大多数现有的双曲线网络都是复杂的，计算昂贵的，并且在数值上不稳定 - 由于这些缺点，它们无法扩展到大图。提出了越来越多的双曲线网络，越来越不清楚什么关键组成部分使模型行为。在本文中，我们提出了HYLA，这是一种简单而最小的方法，用于在网络中使用双曲线空间：Hyla地图一次从双曲空空间从嵌入荷兰的嵌入到欧几里得空间，并通过双曲线空间中的Laplacian操作员的特征函数。我们在图形学习任务上评估HYLA，包括节点分类和文本分类，其中HYLA可以与任何图神经网络一起使用。当与线性模型一起使用时，HYLA对双曲线网络和其他基线显示出显着改善。

跨语言嵌入可以应用于多种语言的几种自然语言处理应用程序。与先前使用基于欧几里得空间嵌入单词嵌入的作品不同，这篇简短的论文提出了一种简单有效的跨语言2VEC模型，该模型适应了PoinCar \'E Ball of双曲空间的球模型，从 - 英语平行语料库。已经表明，双曲线嵌入可以捕获和保留分层关系。我们在高呼气和类比任务上评估了模型。所提出的模型在跨语言类比任务上与香草word2Vec模型实现了可比的性能，超呼气任务表明，跨语义的poincar \'e Word2vec模型可以从跨语言中捕获潜在的层次结构，而这些文本跨越跨语言，这些结构是从跨语言中捕获的基于欧几里得的Word2Vec表示。我们的结果表明，通过保留潜在的分层信息，双曲线空间可以为跨语性嵌入提供更好的表示。

自然语言数据表现出类似的树形层次结构，例如Wordnet中的复义 - 虚幻关系。FastText，作为基于欧几里德空间中的浅神经网络的最先进的文本分类器，可能无法精确地模拟这些层次结构，这些层次结构具有有限的表示容量。考虑到双曲线空间自然适合建模树状分层数据，我们提出了一个名为超文本的新模型，以通过赋予双曲线几何来赋予快速文本的高效文本分类。凭经验，我们显示超文本优于一系列文本分类任务的快速文本，参数大大减少。

The relationship between words in a sentence often tells us more about the underlying semantic content of a document than its actual words, individually. In this work, we propose two novel algorithms, called Flexible Lexical Chain II and Fixed Lexical Chain II. These algorithms combine the semantic relations derived from lexical chains, prior knowledge from lexical databases, and the robustness of the distributional hypothesis in word embeddings as building blocks forming a single system. In short, our approach has three main contributions: (i) a set of techniques that fully integrate word embeddings and lexical chains; (ii) a more robust semantic representation that considers the latent relation between words in a document; and (iii) lightweight word embeddings models that can be extended to any natural language task. We intend to assess the knowledge of pre-trained models to evaluate their robustness in the document classification task. The proposed techniques are tested against seven word embeddings algorithms using five different machine learning classifiers over six scenarios in the document classification task. Our results show the integration between lexical chains and word embeddings representations sustain state-of-the-art results, even against more complex systems.

The choice of geometric space for knowledge graph (KG) embeddings can have significant effects on the performance of KG completion tasks. The hyperbolic geometry has been shown to capture the hierarchical patterns due to its tree-like metrics, which addressed the limitations of the Euclidean embedding models. Recent explorations of the complex hyperbolic geometry further improved the hyperbolic embeddings for capturing a variety of hierarchical structures. However, the performance of the hyperbolic KG embedding models for non-transitive relations is still unpromising, while the complex hyperbolic embeddings do not deal with multi-relations. This paper aims to utilize the representation capacity of the complex hyperbolic geometry in multi-relational KG embeddings. To apply the geometric transformations which account for different relations and the attention mechanism in the complex hyperbolic space, we propose to use the fast Fourier transform (FFT) as the conversion between the real and complex hyperbolic space. Constructing the attention-based transformations in the complex space is very challenging, while the proposed Fourier transform-based complex hyperbolic approaches provide a simple and effective solution. Experimental results show that our methods outperform the baselines, including the Euclidean and the real hyperbolic embedding models.

产品空间的嵌入方法是用于复杂数据结构的低失真和低维表示的强大技术。在这里，我们解决了Euclidean，球形和双曲线产品的产品空间形式的线性分类新问题。首先，我们描述了使用测地仪和黎曼·歧木的线性分类器的新型制剂，其使用大气和黎曼指标在向量空间中推广直线和内部产品。其次，我们证明了$ D $ -dimential空间形式的线性分类器的任何曲率具有相同的表现力，即，它们可以粉碎恰好$ d + 1 $积分。第三，我们在产品空间形式中正式化线性分类器，描述了第一个已知的Perceptron和支持这些空间的传染媒介机分类器，并为感知者建立严格的融合结果。此外，我们证明了vapnik-chervonenkis尺寸在尺寸的产品空间形式的线性分类器的维度为\ {至少} $ d + 1 $。我们支持我们的理论发现，在多个数据集上模拟，包括合成数据，图像数据和单细胞RNA测序（SCRNA-SEQ）数据。结果表明，与相同维度的欧几里德空间中的欧几里德空间中，SCRNA-SEQ数据的低维产品空间形式的分类为SCRNA-SEQ数据提供了$ \ SIM15 \％$的性能改进。

Graph convolutional networks (GCNs) are powerful frameworks for learning embeddings of graph-structured data. GCNs are traditionally studied through the lens of Euclidean geometry. Recent works find that non-Euclidean Riemannian manifolds provide specific inductive biases for embedding hierarchical or spherical data. However, they cannot align well with data of mixed graph topologies. We consider a larger class of pseudo-Riemannian manifolds that generalize hyperboloid and sphere. We develop new geodesic tools that allow for extending neural network operations into geodesically disconnected pseudo-Riemannian manifolds. As a consequence, we derive a pseudo-Riemannian GCN that models data in pseudo-Riemannian manifolds of constant nonzero curvature in the context of graph neural networks. Our method provides a geometric inductive bias that is sufficiently flexible to model mixed heterogeneous topologies like hierarchical graphs with cycles. We demonstrate the representational capabilities of this method by applying it to the tasks of graph reconstruction, node classification and link prediction on a series of standard graphs with mixed topologies. Empirical results demonstrate that our method outperforms Riemannian counterparts when embedding graphs of complex topologies.

双曲线空间可以连续嵌入分层结构。双曲神经网络（HNNS）通过将欧几里德特征提升到用于分类的双曲线空间来利用这种代表性，优于具有已知分层结构的数据集上的欧几里德神经网络（ENNS）。但是，HNNS低于标准基准测试，具有不明确的层次结构，极大地限制了HNNS的实际适用性。我们的主要洞察力是，由于将欧几里德特征连接到双曲线分类器的混合架构引起，HNNS对渐变较差的较差的普通分类性能。我们通过简单地在训练HNN时简单地剪切欧几里德特征幅度来提出有效的解决方案。我们的实验结果表明，剪辑的HNNS成为超级双曲分类器：它们不仅始终如一地优于位于分层数据上的HNN，而且在MNIST，CIFAR10，CIFAR100和ImageNet基准上与ENN一起举行，具有更好的对抗鲁棒性和分销外检测。

3D对象的点云具有固有的组成性质，可以将简单的部分组装成逐渐复杂的形状以形成整个对象。明确捕获这种部分整体层次结构是一个长期的目标，以建立有效的模型，但其树状的性质使这项任务变得难以捉摸。在本文中，我们建议将点云分类器的特征嵌入双曲线空间中，并明确规范空间以说明零件整体结构。双曲线空间是唯一可以成功嵌入层次结构的树状性质的空间。这导致了对点云分类的最先进的监督模型的性能的实质性改善。

我们使用运输公制（Delon和Desolneux 2020）中的单变量高斯混合物中的任意度量空间$ \ MATHCAL {X} $研究数据表示。我们得出了由称为\ emph {Probabilistic Transfersers}的小神经网络实现的特征图的保证。我们的保证是记忆类型：我们证明了深度约为$ n \ log（n）$的概率变压器和大约$ n^2 $ can bi-h \'{o} lder嵌入任何$ n $ - 点数据集从低度量失真的$ \ Mathcal {x} $，从而避免了维数的诅咒。我们进一步得出了概率的bi-lipschitz保证，可以兑换失真量和随机选择的点与该失真的随机选择点的可能性。如果$ \ MATHCAL {X} $的几何形状足够规律，那么我们可以为数据集中的所有点获得更强的Bi-Lipschitz保证。作为应用程序，我们从Riemannian歧管，指标和某些类型的数据集中获得了神经嵌入保证金组合图。

知识图（kg）嵌入在实体的学习表示和链接预测任务的关系方面表现出很大的力量。以前的工作通常将KG嵌入到单个几何空间中，例如欧几里得空间（零弯曲），双曲空间（负弯曲）或超透明空间（积极弯曲），以维持其特定的几何结构（例如，链，层次结构和环形结构）。但是，KGS的拓扑结构似乎很复杂，因为它可能同时包含多种类型的几何结构。因此，将kg嵌入单个空间中，无论欧几里得空间，双曲线空间或透明空间，都无法准确捕获KGS的复杂结构。为了克服这一挑战，我们提出了几何相互作用知识图嵌入（GIE），该图形嵌入了，该图形在欧几里得，双曲线和超级空间之间进行了交互学习的空间结构。从理论上讲，我们提出的GIE可以捕获一组更丰富的关系信息，模型键推理模式，并启用跨实体的表达语义匹配。三个完善的知识图完成基准的实验结果表明，我们的GIE以更少的参数实现了最先进的性能。

测量不同文本的语义相似性在数字人文研究中具有许多重要应用，例如信息检索，文档聚类和文本摘要。不同方法的性能取决于文本，域和语言的长度。本研究侧重于试验一些目前的芬兰方法，这是一种形态学丰富的语言。与此同时，我们提出了一种简单的方法TFW2V，它在处理长文本文档和有限的数据时显示出高效率。此外，我们设计了一种客观评估方法，可以用作基准标记文本相似性方法的框架。

双曲线神经网络由于对几个图形问题的有希望的结果，包括节点分类和链接预测，因此最近引起了极大的关注。取得成功的主要原因是双曲空间在捕获图数据集的固有层次结构方面的有效性。但是，在非层次数据集方面，它们在概括，可伸缩性方面受到限制。在本文中，我们对双曲线网络进行了完全正交的观点。我们使用Poincar \'e磁盘对双曲线几何形状进行建模，并将其视为磁盘本身是原始的切线空间。这使我们能够用欧几里院近似替代非尺度的M \“ Obius Gyrovector操作，因此将整个双曲线模型简化为具有双曲线归一化功能的欧几里得模型。它仍然在Riemannian歧管中起作用，因此我们称其为伪poincar \'e框架。我们将非线性双曲线归一化应用于当前的最新均质和多关系图网络，与欧几里得和双曲线对应物相比，性能的显着改善。这项工作的主要影响在于其在欧几里得空间中捕获层次特征的能力，因此可以替代双曲线网络而不会损失性能指标，同时利用欧几里得网络的功能，例如可解释性和有效执行各种模型组件。

Hyperbolic space is emerging as a promising learning space for representation learning, owning to its exponential growth volume. Compared with the flat Euclidean space, the curved hyperbolic space is far more ambient and embeddable, particularly for datasets with implicit tree-like architectures, such as hierarchies and power-law distributions. On the other hand, the structure of a real-world network is usually intricate, with some regions being tree-like, some being flat, and others being circular. Directly embedding heterogeneous structural networks into a homogeneous embedding space unavoidably brings inductive biases and distortions. Inspiringly, the discrete curvature can well describe the local structure of a node and its surroundings, which motivates us to investigate the information conveyed by the network topology explicitly in improving geometric learning. To this end, we explore the properties of the local discrete curvature of graph topology and the continuous global curvature of embedding space. Besides, a Hyperbolic Curvature-aware Graph Neural Network, HCGNN, is further proposed. In particular, HCGNN utilizes the discrete curvature to lead message passing of the surroundings and adaptively adjust the continuous curvature simultaneously. Extensive experiments on node classification and link prediction tasks show that the proposed method outperforms various competitive models by a large margin in both high and low hyperbolic graph data. Case studies further illustrate the efficacy of discrete curvature in finding local clusters and alleviating the distortion caused by hyperbolic geometry.

This paper aims to provide an unsupervised modelling approach that allows for a more flexible representation of text embeddings. It jointly encodes the words and the paragraphs as individual matrices of arbitrary column dimension with unit Frobenius norm. The representation is also linguistically motivated with the introduction of a novel similarity metric. The proposed modelling and the novel similarity metric exploits the matrix structure of embeddings. We then go on to show that the same matrices can be reshaped into vectors of unit norm and transform our problem into an optimization problem over the spherical manifold. We exploit manifold optimization to efficiently train the matrix embeddings. We also quantitatively verify the quality of our text embeddings by showing that they demonstrate improved results in document classification, document clustering, and semantic textual similarity benchmark tests.

双曲线空间已成为从树状结构和文本到图表的各种数据类型的歧管的流行选择。建立在欧几里德和超球空间的型原型的深度学习成功，最近的一些作品已经提出了用于分类的双曲线原型。这种方法能够在低维输出空间中实现有效的学习，并且可以利用类之间的分层关系，但需要有关类标签的特权信息来定位双曲型原型。在这项工作中，我们提出了双曲线的Busemann学习。我们的方法背后的主要思想是将原型定位在Poincar \ E球的理想边界上，这不需要先前的标签知识。为了能够计算邻近的理想原型，我们介绍了受到惩罚的Busemann损失。我们提供了支持使用理想原型和建议损失的理论，通过证明其在一维案件中的物流回归。凭经验，我们表明我们的方法提供了对分类信心的自然解释，而最近的最近的超球和双曲线原型方法。

Knowledge graph embedding (KGE) is a increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.

Natural Language Understanding has seen an increasing number of publications in the last few years, especially after robust word embeddings models became prominent, when they proved themselves able to capture and represent semantic relationships from massive amounts of data. Nevertheless, traditional models often fall short in intrinsic issues of linguistics, such as polysemy and homonymy. Any expert system that makes use of natural language in its core, can be affected by a weak semantic representation of text, resulting in inaccurate outcomes based on poor decisions. To mitigate such issues, we propose a novel approach called Most Suitable Sense Annotation (MSSA), that disambiguates and annotates each word by its specific sense, considering the semantic effects of its context. Our approach brings three main contributions to the semantic representation scenario: (i) an unsupervised technique that disambiguates and annotates words by their senses, (ii) a multi-sense embeddings model that can be extended to any traditional word embeddings algorithm, and (iii) a recurrent methodology that allows our models to be re-used and their representations refined. We test our approach on six different benchmarks for the word similarity task, showing that our approach can produce state-of-the-art results and outperforms several more complex state-of-the-art systems.

命名实体识别是一项信息提取任务，可作为其他自然语言处理任务的预处理步骤，例如机器翻译，信息检索和问题答案。命名实体识别能够识别专有名称以及开放域文本中的时间和数字表达式。对于诸如阿拉伯语，阿姆哈拉语和希伯来语之类的闪族语言，由于这些语言的结构严重变化，指定的实体识别任务更具挑战性。在本文中，我们提出了一个基于双向长期记忆的Amharic命名实体识别系统，并带有条件随机字段层。我们注释了一种新的Amharic命名实体识别数据集（8,070个句子，具有182,691个令牌），并将合成少数群体过度采样技术应用于我们的数据集，以减轻不平衡的分类问题。我们命名的实体识别系统的F_1得分为93％，这是Amharic命名实体识别的新最新结果。